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Vulcanus

2025-06-12T17:12:52Z

MadKingAyres: /* Biomes */ Added detail regarding trees, as may be useful information for players wondering why bots are being damaged.

{{Languages}}
{{Stub}}
{{About/Space age}}
[[File:volcanus_preview.png|210px|right]]
'''Vulcanus''' is a hot volcanic [[planet]] with mountainous volcanoes, rivers of lava, plains of ash, and sulfuric acid geysers.

It is home to [[Demolisher|demolishers]]{{SA}}, a large boss‐like [[Enemies|enemy]] that defends its territory. There's no [[pollution]] on Vulcanus.

[[Planet discovery Vulcanus (research)]] is required to travel to the planet.

== Achievements ==
{{Achievement|visit-vulcanus}}

== Exclusive recipes ==
The following recipes can only be crafted on Vulcanus:
* {{imagelink|Metallurgic science pack|space-age=yes}}
* {{imagelink|Foundry|space-age=yes}}
* {{imagelink|Big mining drill|space-age=yes}}
* {{imagelink|Turbo transport belt|space-age=yes}}
* {{imagelink|Turbo underground belt|space-age=yes}}
* {{imagelink|Turbo splitter|space-age=yes}}
* {{imagelink|Acid neutralisation|space-age=yes}}

The following items and recipes are unlocked on Vulcanus but can be crafted elsewhere:

* {{imagelink|Artillery turret}}/{{imagelink|Artillery wagon}} and {{imagelink|Artillery shell}}s
* {{imagelink|Simple coal liquefaction|space-age=yes}} and {{imagelink|Coal liquefaction}}
* {{imagelink|Cliff explosives}}
* {{imagelink|Speed module 3}}
* {{imagelink|Asteroid reprocessing (research)|space-age=yes}}

== Surface ==

=== Properties ===
{| class="wikitable"
|+ Vulcanus Surface Properties
|-
! Property !! Value
|-
| Pollutant Type || None
|-
| Day Night Cycle || 1.5 Minutes
|-
| Magnetic Field|| 25
|-
| Solar Power || 400%
|-
| Pressure || 4000
|-
| Gravity || 40
|}

== Biomes ==
Vulcanus has three distinct biomes.
* '''Ashlands''' are plateaus speckled with sparse vegetation and deposits of [[coal]]. They are home to leafless alien trees, some of which may be on fire and will spawn flames temporarily if felled. They are relatively free of cliffs and lava, making them ideal for building.
* '''Lava basins''' are filled with winding lava rivers. Within them are deposits of [[tungsten ore]]{{SA}}, which can only be mined using the big mining drill.
* '''Mountains''' are large volcanoes, covered in cliffs and with a large lava pool at their center. They are home to [[sulfuric acid]] geysers and [[calcite]]{{SA}}. 

== Demolisher territories ==
[[File:Demolisher entity.png|thumb|250px|right|Demolisher patrolling.]]
Native to Vulcanus are the giant centipede-like enemies known as "[[Enemies#Demolishers|demolishers]]".

Demolishers have well-defined territories. On the map, these territories are outlined by an opaque, bright red line and the inside is marked by diagonal, translucent, red lines. Only one demolisher will spawn per territory, and the territories themselves do not overlap. However, they are tightly packed, as they follow a Voronoi-like pattern. At the start of the game, only Vulcanus' starting area is not inside a demolisher's territory.

When left alone, a demolisher will patrol the border of its territory. However, if players build inside of a demolisher's territory, it will soon make a beeline towards these buildings with the intent of destroying them. Building inside of a demolisher's territory is therefore extremely risky and dangerous.

The death of a demolisher is permanent, as they only spawn during world generation. Likewise, upon the death of a demolisher, its territory permanently becomes free for the player to use, as other demolishers will not try to expand their territories.

== Access to basic resources ==

* [[Water]] can be obtained via [[acid neutralisation]] and [[steam condensation]]
* [[Stone]] is a byproduct of processing [[lava]] into molten iron/copper.
* [[Iron ore]] is only available in limited quantities from mining volcanic [[rock]], but [[iron plate]] and [[concrete]] may be obtained from [[molten iron]]
* [[Copper ore]] is only available in limited quantities from mining volcanic [[rock]], but [[copper plate]] may be obtained from [[molten copper]].
* [[Coal]] can be mined from patches on the surface as normal.
* [[Crude oil]] is not available, but [[heavy oil]] can be obtained via [[simple coal liquefaction]]. Heavy oil can then be cracked into light oil and petroleum. Once metallurgic science is produced and a stockpile of heavy oil built up, this can be switched to regular [[coal liquefaction]].
* [[Wood]] cannot be obtained, but [[medium electric pole]]s can be constructed using the small amount of ores available. Note that this can soft-lock players that did not unlock the research.

=== Power production ===

[[Solar panel]]s on Vulcanus give 4× the power they would on Nauvis. [[Acid neutralization]] generates 500°C steam, which can be fed through [[steam turbine]]s to generate electricity. The calcite processing technology does not actually give the player access to steam turbines, so [[steam engine]]s can be used instead (which generate less power for the same steam).

== Space routes ==
[[Vulcanus]] is connected to 2 other planets: [[Nauvis]] and [[Gleba]]{{SA}}.

{| class="wikitable"
|+ Planet Distance
|-
! Planet !! Distance (km)
|-
| [[Nauvis]]|| 15,000
|-
| [[Gleba]]{{SA}}|| 15,000
|-
|}

Asteroid rate graphs:

{| class="wikitable" style="text-align:center;"
|-
| [[File:Asteroid_chart_Nauvis_Vulcanus.png]] <br> Space route from [[Nauvis]] to [[Vulcanus]]
| [[File:Asteroid_chart_Vulcanus_Gleba.png]] <br> Space route from [[Vulcanus]] to [[Gleba]]
|}

Graph legend:
<table class="wikitable">
<tr>
<th>Asteroid Type</th>
<th>Chunk</th>
<th>Medium</th>
</tr>
<tr>
<td>[[File:Metallic asteroid chunk.png|32px]] [[Asteroids|Metallic]] {{SA}}</td>
<td><span style="color: blue;">●</span> Blue</td>
<td><span style="color: red;">●</span> Red</td>
</tr>
<tr>
<td>[[File:Carbonic asteroid chunk.png|32px]] [[Asteroids|Carbonic]] {{SA}}</td>
<td><span style="color: orange;">●</span> Orange</td>
<td><span style="color: yellow;">●</span> Yellow</td>
</tr>
<tr>
<td>[[File:Oxide asteroid chunk.png|32px]] [[Asteroids|Oxide]] {{SA}}</td>
<td><span style="color: green;">●</span> Green</td>
<td><span style="color: magenta;">●</span> Magenta</td>
</tr>
</table>

== Orbit ==

=== Properties ===
{| class="wikitable"
|-
! Property !! Value
|-
| Solar Power || 600%
|-
|}

{| class="wikitable"
|+ Asteroid Spawning Types
|-
! [[Asteroids| Asteroid]] Type !! Spawn Ratio
|-
| [[Metallic asteroid chunk]] || 5
|-
| [[Carbonic asteroid chunk]] || 2
|-
| [[Oxide asteroid chunk]] || 1
|-
| [[Promethium asteroid chunk]] || 0
|}

{| class="wikitable"
|+ Asteroid Spawning Sizes
|-
! [[Asteroids| Asteroid]] Size !! Spawn %
|-
| Chunk|| .20
|-
| Medium|| .25
|-
| Big || 0
|-
| Huge || 0
|}

'''Note:'''
*Chunks spawn at Nauvis at 1.25%
*Huge Asteroids only spawn past [[Aquilo]]{{SA}}

== Gallery ==
<gallery widths="300px" heights="200px">
vulcanus landscape.png|Example of Vulcanus' landscape.
vulcanus map.png|Example mapview of Vulcanus, Demolisher territories are outlined by bright red lines.
vulcanus landscape titlescreen.png|Vulcanus seen on the expansion's title screen.
</gallery>

== Trivia ==
* In mythology, Vulcanus (also spelt Vulcan), is the Roman god of fire, metalworking, and the forge.
* The planet's design, with lava, volcanoes, and sulfur, is based on [https://en.wikipedia.org/wiki/Lava_planet lava planets].

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

== See also ==
* [[Aquilo]] {{SA}}
* [[Fulgora]] {{SA}}
* [[Gleba]] {{SA}}
* [[Nauvis]]
* [[Space platform]] {{SA}}

{{C|Planets}}
{{SpaceNav}}

Quality

2024-12-12T12:45:52Z

MadKingAyres:

{{Languages}}
{{Boilerplate
|icon=No-building-material-icon.png
|line-1=This article is a lacking sources for details of upcoming changes.
|line-2=You can help this wiki by [{{fullurl:{{FULLPAGENAME}}|action=edit}} adding them].}}
{{About/Space age}}

'''Quality''' is a feature of the [[Space Age]] expansion. It introduces four higher quality levels for all items, structures and equipment with improved attributes. The goal of quality is to allow vertical factory upgrading as alternative to expansion in size. Items of higher quality are created by chance when using quality modules in the producing structure. The two highest quality tiers require technology not available on Nauvis. Different buildings and items can have different attributes that can be upgraded. When hovering over something, the attributes that will be upgraded with quality will be marked with a blue diamond in the tooltip.

While players are required to own Space Age to access this feature, quality is a separate mod, and can be activated independent of most Space Age content.

== Quality tiers ==
There are 5 quality tiers in vanilla gameplay, with tier strength in brackets:
* [[File:quality_normal.png|15px]] Normal (0)
* [[File:quality_uncommon.png|15px]] Uncommon (1)
* [[File:quality_rare.png|15px]] Rare (2)
* [[File:quality_epic.png|15px]] Epic (3)
* [[File:quality_legendary.png|15px]] Legendary ('''5''')

Note that legendary quality represents a 2-tier improvement over epic.

== Technologies ==
Certain tiers of quality cannot be created until they have been researched.
{|class="wikitable"
|-
! Research !! Base Game !! {{SA}} Space Age !! Unlocks
|-
| {{icontech|Quality module (research)|}} [[Quality module (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}} x 300
| {{icon|Time|30}}{{icon|Automation science pack}}{{icon|Logistic science pack}} x 500
| [[File:quality_uncommon.png|32px]] [[File:quality_rare.png|32px]]
|-
| {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Agricultural science pack}} x 5000
| [[File:quality_epic.png|32px]]
|-
| {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Metallurgic science pack}}{{icon|Electromagnetic science pack}}{{icon|Agricultural science pack}}{{icon|Cryogenic science pack}} x 5000
| [[File:quality_legendary.png|32px]]
|-
|}

== Quality effects ==
The currently known effects of each level of quality are as follows:
* +30% health
* +30% crafting speed
* +30% robot limit (rounded down)
* +30% robot recharge rate (both number and speed, rounded down)
* +30% positive module effects (rounded down for at least quality modules)
* +10% turret range
* +10% weapon range
* +1 tile reach and +2 wire reach on power poles
* +1 equipment grid size (both dimensions)
* +30% chest inventory size (rounded down)
* +30% increased ammo damage
* +30% inserter rotation speed
* -16.67% (1/6) resource drain on miners.
** This is multiplicative with productivity
* +100% (+5 MJ) capacity on accumulators
* +30% output rate on [[boiler]]s, [[steam engine]]s, [[steam turbine]]s, [[accumulator]]s (also affects input rate), and [[nuclear reactor]]s
** Note that consumption and pollution are also increased at the same rate
* −16% power consumption on beacons
* +1 to both continuous coverage distance and exploration coverage distance in [[radar]]s
* +100% durability on consumable items ([[repair pack]]s, [[science pack]]s)
* +5% fork chance on the [[tesla turret]] and tesla ammo for the tesla gun

These effects are per quality strength and additive: a Legendary (5 tier-levels) [[Productivity module 3]] (base +10% productivity) would grant 25% productivity.

Some buildings only get increased health, with no special effect. Examples are:
*Buildings related to [[Circuit network]]s and [[Rail signal]]s
*[[Transport belt]]s
*[[Pipe]]s
*[[Wall]]s
*[[Locomotive|Trains]]
*[[Cargo wagon]]s

{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-

| [[File:assembling_machine_1.png|15px]] [[Assembling machine 1]] ||
* Health - 300
* Crafting speed - 0.5

||
* Health - 390
* Crafting speed - 0.65

||
* Health - 480
* Crafting speed - 0.8

||
* Health - 570
* Crafting speed - 0.95

||
* Health - 750
* Crafting speed - 1.25
|-

| [[File:assembling_machine_2.png|15px]] [[Assembling machine 2]] ||
* Health - 350
* Crafting speed - 0.75

||
* Health - 455
* Crafting speed - 0.975

||
* Health - 560
* Crafting speed - 1.2

||
* Health - 665
* Crafting speed - 1.425

||
* Health - 875
* Crafting speed - 1.875

|-

| [[File:assembling_machine_3.png|15px]] [[Assembling machine 3]] ||
* Health - 400
* Crafting speed - 1.25

||
* Health - 520
* Crafting speed - 1.625

||
* Health - 640
* Crafting speed - 2

||
* Health - 760
* Crafting speed - 2.375

||
* Health - 1000
* Crafting speed - 3.125

|-

| [[File:construction_robot.png|15px]] [[Construction robot]]||
* Health - 100
* Max flying reach - 571m
* Energy capacity - 3MJ

||
* Health - 130
* Max flying reach - 1152m
* Energy capacity - 6MJ

||
* Health - 160
* Max flying reach - 1728m
* Energy capacity - 9MJ

||
* Health - 190
* Max flying reach - 2305m
* Energy capacity - 12MJ

||
* Health - 250
* Max flying reach - 3457m
* Energy capacity - 18MJ
|-

| [[File:inserter.png|15px]] [[Inserter]] ||
* Health - 150
* Energy consumption - 15.1kW
* Rotation speed - 302°/s

||
* Health - 195
* Energy consumption - 19.51kW
* Rotation speed - 393°/s

||
* Health - 240
* Energy consumption - 23.92kW
* Rotation speed - 484°/s

||
* Health - 285
* Energy consumption - 28.33kW
* Rotation speed - 575°/s

||
* Health - 375
* Energy consumption - 37.15kW
* Rotation speed - 756°/s

|-

| [[File:fast_inserter.png|15px]] [[Fast inserter]] ||
* Health - 150
* Energy consumption - 59.3kW
* Rotation speed - 864°/s
||
* Health - 195
* Energy consumption - 76.94kW
* Rotation speed - 1123°/s

||
* Health - 240
* Energy consumption - 94.58kW
* Rotation speed - 1382°/s

||
* Health - 285
* Energy consumption - 112kW
* Rotation speed - 1642°/s

||
* Health - 375
* Energy consumption - 148kW
* Rotation speed - 2160°/s
|-

| [[File:iron_chest.png|15px]] [[Iron chest]] ||
* Health - 200
* Storage size - 32

||
* Health - 260
* Storage size - 41

||
* Health - 320
* Storage size - 51

||
* Health - 380
* Storage size - 60

||
* Health - 500
* Storage size - 80

|-

| [[File:laser_turret.png|15px]] [[Laser turret]] ||
* Health - 1000
* Range - 24 tiles

||
* Health - 1300
* Range - 26.4 tiles

||
* Health - 1600
* Range - 28.8 tiles

||
* Health - 1900
* Range - 31.2 tiles

||
* Health - 2500
* Range - 36 tiles

|-

| [[File:pipe.png|15px]] [[Pipe]] ||
* Health - 100

||
* Health - 130

||
* Health - 160

||
* Health - 190

||
* Health - 250
|-

| [[File:roboport.png|15px]] [[Roboport]] ||
* Health - 500
* Energy consumption - 2.1MW
* Robot recharge rate - 4 x 500kW

||
* Health - 650
* Energy consumption - 2.7MW
* Robot recharge rate - 4 x 650kW

||
* Health - 800
* Energy consumption - 3.3MW
* Robot recharge rate - 4 x 800kW

||
* Health - 950
* Energy consumption - 3.9MW
* Robot recharge rate - 4 x 950kW

||
* Health - 1250
* Energy consumption - 5.1MW
* Robot recharge rate - 4 x 1.25MW

|-

| [[File:small_electric_pole.png|15px]] [[Small electric pole]] ||
* Health - 100
* 5x5 supply area
* Wire reach - 7.5 tiles

||
* Health - 130
* 7x7 supply area
* Wire reach - 9.5 tiles

||
* Health - 160
* 9x9 supply area
* Wire reach - 11.5 tiles

||
* Health - 190
* 11x11 supply area
* Wire reach - 13.5 tiles

||
* Health - 250
* 15x15 supply area
* Wire reach - 17.5 tiles

|-

| [[File:steel_chest.png|15px]] [[Steel chest]] ||
* Health - 350
* Storage size - 48

||
* Health - 455
* Storage size - 62

||
* Health - 560
* Storage size - 76

||
* Health - 665
* Storage size - 91

||
* Health - 875
* Storage size - 120

|-

| [[File:wooden_chest.png|15px]] [[Wooden chest]] ||
* Health - 100
* Storage size - 16

||
* Health - 130
* Storage size - 20

||
* Health - 160
* Storage size - 25

||
* Health - 190
* Storage size - 30

||
* Health - 250
* Storage size - 40

|}

== Creating high-quality items ==

There are two ways to create an item with above normal quality: The player must either use ingredient items of the same quality, or use quality modules for a random chance of a higher-quality item.

=== Quality ingredients ===
Recipes that create items have variations for each quality that the item might take. When setting such a recipe in a production unit, an ingredient quality must be selected. For these variations, the set of ingredients required is the same, except that all item ingredients must have the specified quality.

Item ingredient quality requirements are exact, not minimum. For example, one can not combine uncommon [[iron plate]]s with rare [[battery|batteries]] to make an [[accumulator]] of any quality. One must therefore ensure that high-quality items do not clog up belts and starve production units of lower-quality items.

As fluids do not possess any quality, they are exempt from ingredient quality requirements; the same [[lubricant]] can be used to create [[electric engine unit]]s of any quality.

=== Quality modules ===
{{Main|Quality module}}
[[File:quality_module_animated.png|64px|right]]'''Quality modules''' allow crafting machines to produce items of a higher quality than their ingredients. Each module adds a quality chance to a machine, depending on its tier and quality. See the following table for all quality chances:

{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Module|Quality}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! {{Icon|quality_module}}
| +1% || +1.3% || +1.6% || +1.9% || +2.5%
|-
! {{Icon|quality_module_2}}
| +2% || +2.6% || +3.2% || +3.8% || +5%
|-
! {{Icon|quality_module_3}}
| +2.5% || +3.2% || +4% || +4.7% || +6.2%
|}

When working out the odds of improving quality, a machine starts with the sum of the quality chance of all its modules. When the machine produces an item, it performs a random roll with that chance to succeed. If it succeeds, the product is upgraded 1 level from its ingredients. If the product was upgraded, the machine repeats this process, now with a constant 10% chance of passing, rolling and upgrading until a roll fails.

When using quality ingredients as an input, the base quality is the quality of the recipe. You can only use items with the same quality as input.

Quality modules are only required to ''improve'' quality, crafting will always give the base quality of the used items. Additionally, the odds of improving from a given base quality is the same as improving the same number of tiers from Normal quality.

Where Q is quality chance, the following tables present expected outputs for each level of research.
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Quality module (research)|}} [[Quality module (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 1/100
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 9/1000 || Q * 1/1000
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 9/100 || Q * 1/100
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1 - Q || Q
|-
! [[File:quality_legendary.png|Legendary|16px]]
| - || - || - || - || 1
|}
</div>

==== Examples ====
<div style="display:inline-block; margin-right:20px; vertical-align:top;">
{|class="wikitable" style="text-align: center;"
|+ 2× {{Icon|quality_module_2|[[File:quality_normal.png|Normal|16px]]}} → Q = 4%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 96% || 3.6% || 0.4%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 96% || 4%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
|+ 4× {{Icon|quality_module_3|[[File:quality_normal.png|Normal|16px]]}} → Q = 10%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 90% || 9% || 0.9% || 0.09% || 0.01%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 90% || 9% || 0.9% || 0.1%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 90% || 9% || 1%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 90% || 10%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|+ 4× {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}} → Q = 24.8%
|-
! [[File:quality_normal.png|Normal|32px]]
| 75.2% || 22.32% || 2.232% || 0.2232% || 0.0248%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 75.2% || 22.32% || 2.232% || 0.248%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 75.2% || 22.32% || 2.48%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 75.2% || 24.8%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div>

==== Optimal module usage ====

It is optimal to improve quality on the lead-up to the target output item due to the recycler only giving back 25% of the input items, except for cases where the chosen item has a productivity research available, in which case looping through a recycler is optimal and has no added material cost (ignoring fluids).

The following tables summarize the number of normal crafts (rounded up) needed to produce 1 legendary output using ideal ratios of quality module 3s to productivity module 3s, with 4 matching quality module 3 in the recycler.

It is important to emphasize that these ratios maximize return per input material. If input capacity isn't a concern and the goal is speed rather than material efficiency, then switch out productivity modules for quality modules as needed. Beware, however, that in many cases material inefficiency nearly keeps pace with the legendary output rate.

<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_rare.png|Rare|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_rare.png|Rare|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 891
|-
| 3 || 0% || 0 || 3 || 533
|-
| 4 || 0% || 1 || 3 || 342
|-
| 4 || 50% || 0 || 4 || 97
|-
| 5 || 50% || 1 || 4 || 67
|-
| 8 || 0% || 4 || 4 || 70
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_epic.png|Epic|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_epic.png|Epic|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 608
|-
| 3 || 0% || 1 || 2 || 356
|-
| 4 || 0% || 1 || 3 || 212
|-
| 4 || 50% || 1 || 3 || 62
|-
| 5 || 50% || 2 || 3 || 40
|-
| 8 || 0% || 5 || 3 || 34
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 309
|-
| 3 || 0% || 1 || 2 || 153
|-
| 4 || 0% || 2 || 2 || 80
|-
| 4 || 50% || 3 || 1 || 25
|-
| 5 || 50% || 4 || 1 || 14
|-
| 8 || 0% || 8 || 0 || 7
|}
</div><div style="white-space: nowrap;">For example, suppose the goal is to produce{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}and legendary T3 modules are available. If each electromagnetic plant producing epic quality or below has 1{{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}and 4{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, and the electromagnetic plant with the legendary recipe has 5{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, then on average an input of 280{{Icon|Electronic_circuit|[[File:quality_normal.png|Normal|16px]]}}and 28{{Icon|Advanced_circuit|[[File:quality_normal.png|Normal|16px]]}}is expected to produce 1{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}.</div>

;Derivation

Derivation of the tables above was as follows:
Starting with 1 set of common ingredients, with an assembly quality chance of Q and total productivity bonus of P, the statistical expected number of product is as follows:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + P) * (1 - Q) || (1 + P) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + P) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + P) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + P) * (Q * 10<sup>-3</sup>)
|-
| (1 + P) * (1 - Q) || (1 + P) * Q * 9/10|| (1 + P) * Q * 9/100 || (1 + P) * Q * 9/1000 || (1 + P) * Q * 1/1000
|}

In a similar vein, the same calculations can be done for recycling products, except that there is, in effect, -75% productivity bonus, where only a quarter of the items are returned.

{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + -0.75) * (1-Q) || (1 + -0.75) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + -0.75) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + -0.75) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + -0.75) * (Q * 10<sup>-3</sup>)
|-
| 0.25 * (1-Q) || 0.25 * Q * 9/10|| 0.25 * Q * 9/100 || 0.25 * Q * 9/1000 || 0.25 * Q * 1/1000
|}

For example, recycling an uncommon ingredient with a Q of 25%:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
|style="background:#424242"| [[File:quality_uncommon.png|Uncommon|16px]] || - || 0.1875 || 0.05625 || 0.005625 || 0.000625
|}

Combining these results allows a 'Transition Matrix' to be developed (see Stochastic Matrix on wikipedia) which after iteration can generate the expected number of legendary products from 1 set of common ingredients via matrix multiplication. An example matrix for P of 50% and Q of 25% for both recycling and assembly is copied below. Note that since legendary products are the goal, they are not recycled.

{| class="wikitable" style="border:2px solid; text-align:center;"
! !!style="border-left:2px solid"| I<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! I<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! I<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
!style="border-left:2px solid"| P<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! P<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! P<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|- style="border-top:2px solid"
! I<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 1.125 || 0.3375 || 0.03375 || 0.003375 || 0.000375
|-
! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 1.125 || 0.3375 || 0.03375 || 0.00375
|-
! I<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 1.125 || 0.3375 || 0.0375
|-
! I<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 1.125 || 0.375
|-
! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1.5
|- style="border-top:2px solid"
! P<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0.1875 || 0.5625 || 0.005625 || 0.0005625 || 0.0000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0.1875 || 0.05625 || 0.005625 || 0.000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0.1875 || 0.05625 || 0.00625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0.1875 || 0.0625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1
|}

To iterate this matrix (M) apply the matrix to itself. For example, M<sup>6</sup> would indicate 6 iterations, corresponding to 3 crafting steps and 3 recycling steps. To see how much 1 ingredient set produces after a given iteration, x, multiply an input vector by M<sup>x</sup>. The vector format follows that of the matrix labels, so with the table arranged as above, left multiply a row vector of ingredient(s) by the matrix. In order to see the expected product of 1 set of normal ingredients, the vector will have '1' in the first column and '0's everywhere else. Likewise, a set of uncommon ingredients will correspond to '1' in the second column of the vector.

It is important to note that since the recycling step has a material loss of 75% most recycling loops will be well behaved and converge quickly.<br>
Extreme productivity from research breaks this pattern and will prevent convergence, but this simply means that there is a positive material cycle, so 1 set of ingredients will produce infinite legendary crafts, on average. The closer the total productivity is to 400%, the slower the convergence of the matrix iteration and the higher you need to calculate x in M<sup>x</sup>.


== Usage tips ==
=== Using quality to increase production ===
There are four ways in which quality can increase the output of a single production machine:
* Increasing the quality of the machine itself will improve its base crafting speed.
* Increasing the quality of [[speed module]]s will increase the effect of their speed improvements.
* Increasing the quality of [[productivity module]]s will increase their productivity bonus without reducing crafting speed. Since extra items obtained from the productivity bonus do not take extra time to produce, this will also increase the number of items produced over time.
* Increasing the quality of [[beacon]]s will increase their transmission efficiency. If they contain speed modules, then the effect of these modules is increased.

These four options share a powerful synergy, as they react multiplicatively with one another. This makes it possible to achieve very high production rates with very few machines when compared to only using normal quality items. For example, imagine a setup where [[electronic circuit]]s are made using one [[electromagnetic plant]] with five [[productivity module 3]]s, which is surrounded by 12 [[beacon]]s with two [[speed module 3]]s, each. With normal quality, this will achieve an output rate of almost 45 items per second (almost enough to saturate one non-layered [[express transport belt]]). However, if the electromagnetic plant and all beacons and modules have legendary quality, the output rate becomes slightly more than 600 items per second (enough to saturate two and a half [[turbo transport belt]]s with four layers of items). This is more than 13 times as many items as without quality.

It should be noted that quality beacons are the only one of these factors that may increase energy consumption over time, as the transmission effect is also applied to the energy cost of speed modules. However, this is offset or even negated by the reduced energy consumption of the beacons themselves (which is also affected by quality), especially with high beacon counts wherein the transmission effect is subject to diminishing returns. For speed modules, productivity modules, and the machine itself, only the speed increase, productivity bonus, and base crafting speed are affected, respectively.

The increased transmission effect of high-quality beacons is also notable because unlike when increasing the number of beacons, there are no diminishing returns for increasing their quality (aside from the exponentially increasing cost of producing those higher-quality beacons in the first place). This means that, despite a legendary beacon only being 1.66 times as powerful as a normal-quality beacon, one would need 0.36 times as many legendary beacons as normal ones to achieve the same effect. Aside from making more powerful beacon setups, this can also be used to save space by achieving the same effect with fewer beacons, thereby leaving more room for machines and belts.

Higher-quality machines are also particularly useful for producing quality items as, unlike speed modules, machine quality does not reduce the chance of increasing a product's quality.

=== Using quality to save space ===
Another use for quality is decreasing the amount of buildings needed to perform the same production. This is particularly useful in a [[space platform]], where small, compact designs are rewarded with increased speed, as well as needing fewer rockets to build the platform.

== Relevant Factorio Friday Facts ==
* [https://www.factorio.com/blog/post/fff-375 FFF 375 - Quality]
* [https://www.factorio.com/blog/post/fff-376 FFF 376 - Research and Technology]

== Trivia ==
* Quality is not technically exclusive to player-made entities; Though this does not occur naturally, quality is also allowed on enemies, asteroids, and even the [[player]] character.
** Some enemies with qualities above normal can even be created in regular sandbox gameplay: Big biters, behemoth biters, and big premature wriggler pentapods born from spoiled [[biter egg]]s, [[captive biter spawner]]s, and [[pentapod egg]]s inherit the quality of the spoiled items, with the latter two being possible to craft with quality modules. Furthermore, a starved captured biter spawner will retain its quality upon converting into a hostile biter spawner, with said quality even being inherited by the biters that it will spawn. Should these biters chose to expand, they may also create quality spitters and worms.

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

{{C|Main}}

Quality

2024-12-12T10:12:53Z

MadKingAyres: /* Quality effects */ Adding additional items to Quality Effects table

{{Languages}}
{{Boilerplate
|icon=No-building-material-icon.png
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{{About/Space age}}

'''Quality''' is a feature of the [[Space Age]] expansion. It introduces four higher quality levels for all items, structures and equipment with improved attributes. The goal of quality is to allow vertical factory upgrading as alternative to expansion in size. Items of higher quality are created by chance when using quality modules in the producing structure. The two highest quality tiers require technology not available on Nauvis. Different buildings and items can have different attributes that can be upgraded. When hovering over something, the attributes that will be upgraded with quality will be marked with a blue diamond in the tooltip.

While players are required to own Space Age to access this feature, quality is a separate mod, and can be activated independent of most Space Age content.

== Quality tiers ==
There are 5 quality tiers in vanilla gameplay, with tier strength in brackets:
* [[File:quality_normal.png|15px]] Normal (0)
* [[File:quality_uncommon.png|15px]] Uncommon (1)
* [[File:quality_rare.png|15px]] Rare (2)
* [[File:quality_epic.png|15px]] Epic (3)
* [[File:quality_legendary.png|15px]] Legendary ('''5''')

Note that legendary quality represents a 2-tier improvement over epic.

== Technologies ==
Certain tiers of quality cannot be created until they have been researched.
{|class="wikitable"
|-
! Research !! Base Game !! {{SA}} Space Age !! Unlocks
|-
| {{icontech|Quality module (research)|}} [[Quality module (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}} x 300
| {{icon|Time|30}}{{icon|Automation science pack}}{{icon|Logistic science pack}} x 500
| [[File:quality_uncommon.png|32px]] [[File:quality_rare.png|32px]]
|-
| {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Agricultural science pack}} x 5000
| [[File:quality_epic.png|32px]]
|-
| {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Metallurgic science pack}}{{icon|Electromagnetic science pack}}{{icon|Agricultural science pack}}{{icon|Cryogenic science pack}} x 5000
| [[File:quality_legendary.png|32px]]
|-
|}

== Quality effects ==
The currently known effects of each level of quality are as follows:
* +30% health
* +30% crafting speed
* +30% robot limit (rounded down)
* +30% robot recharge rate (both number and speed, rounded down)
* +30% positive module effects (rounded down for at least quality modules)
* +10% turret range
* +10% weapon range
* +1 tile reach and +2 wire reach on power poles
* +1 equipment grid size (both dimensions)
* +30% chest inventory size (rounded down)
* +30% increased ammo damage
* +30% inserter rotation speed
* -16.67% (1/6) resource drain on miners.
** This is multiplicative with productivity
* +100% (+5 MJ) capacity on accumulators
* +30% output rate on [[boiler]]s, [[steam engine]]s, [[steam turbine]]s, [[accumulator]]s (also affects input rate), and [[nuclear reactor]]s
** Note that consumption and pollution are also increased at the same rate
* −16% power consumption on beacons
* +1 to both continuous coverage distance and exploration coverage distance in [[radar]]s
* +100% durability on consumable items ([[repair pack]]s, [[science pack]]s)
* +5% fork chance on the [[tesla turret]] and tesla ammo for the tesla gun

These effects are per quality strength and additive: a Legendary (5 tier-levels) [[Productivity module 3]] (base +10% productivity) would grant 25% productivity.

Some buildings only get increased health, with no special effect. Examples are:
*Buildings related to [[Circuit network]]s and [[Rail signal]]s
*[[Transport belt]]s
*[[Pipe]]s
*[[Wall]]s
*[[Locomotive|Trains]]
*[[Cargo wagon]]s

{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-

| [[File:assembling_machine_1.png|15px]] [[Assembling machine 1]] ||
* Health - 300
* Crafting speed - 0.5

||
* Health - 390
* Crafting speed - 0.65

||
* Health - 480
* Crafting speed - 0.8

||
* Health - 570
* Crafting speed - 0.95

||
* Health - 750
* Crafting speed - 1.25
|-

| [[File:assembling_machine_2.png|15px]] [[Assembling machine 2]] ||
* Health - 350
* Crafting speed - 0.75

||
* Health - 455
* Crafting speed - 0.975

||
* Health - 560
* Crafting speed - 1.2

||
* Health - 665
* Crafting speed - 1.425

||
* Health - 875
* Crafting speed - 1.875

|-

| [[File:assembling_machine_3.png|15px]] [[Assembling machine 3]] ||
* Health - 400
* Crafting speed - 1.25

||
* Health - 520
* Crafting speed - 1.625

||
* Health - 640
* Crafting speed - 2

||
* Health - 760
* Crafting speed - 2.375

||
* Health - 1000
* Crafting speed - 3.125

|-

| [[File:construction_robot.png|15px]] [[Construction robot]]||
* Health - 100
* Max flying reach - 571m
* Energy capacity - 3MJ

||
* Health - 130
* Max flying reach - 1152m
* Energy capacity - 6MJ

||
* Health - 160
* Max flying reach - 1728m
* Energy capacity - 9MJ

||
* Health - 190
* Max flying reach - 2305m
* Energy capacity - 12MJ

||
* Health - 250
* Max flying reach - 3457m
* Energy capacity - 18MJ
|-

| [[File:inserter.png|15px]] [[Inserter]] ||
* Health - 150
* Energy consumption - 15.1kW
* Rotation speed - 302°/s

||
* Health - 195
* Energy consumption - 19.51kW
* Rotation speed - 393°/s

||
* Health - 240
* Energy consumption - 23.92kW
* Rotation speed - 484°/s

||
* Health - 285
* Energy consumption - 28.33kW
* Rotation speed - 575°/s

||
* Health - 375
* Energy consumption - 37.15kW
* Rotation speed - 756°/s

|-

| [[File:fast_inserter.png|15px]] [[Fast inserter]] ||
* Health - 150
* Energy consumption - 59.3kW
* Rotation speed - 864°/s
||
* Health - 195
* Energy consumption - 76.94kW
* Rotation speed - 1123°/s

||
* Health - 240
* Energy consumption - 94.58kW
* Rotation speed - 1382°/s

||
* Health - 285
* Energy consumption - 112kW
* Rotation speed - 1642°/s

||
* Health - 375
* Energy consumption - 148kW
* Rotation speed - 2160°/s
|-

| [[File:iron_chest.png|15px]] [[Iron chest]] ||
* Health - 200
* Storage size - 32

||
* Health - 260
* Storage size - 41

||
* Health - 320
* Storage size - 51

||
* Health - 380
* Storage size - 60

||
* Health - 500
* Storage size - 80

|-

| [[File:laser_turret.png|15px]] [[Laser turret]] ||
* Health - 1000
* Range - 24 tiles

||
* Health - 1300
* Range - 26.4 tiles

||
* Health - 1600
* Range - 28.8 tiles

||
* Health - 1900
* Range - 31.2 tiles

||
* Health - 2500
* Range - 36 tiles

|-

| [[File:pipe.png|15px]] [[Pipe]] ||
* Health - 100

||
* Health - 130

||
* Health - 160

||
* Health - 190

||
* Health - 250
|-

| [[File:roboport.png|15px]] [[Roboport]] ||
* Health - 500
* Energy consumption - 2.1MW
* Robot recharge rate - 4 x 500kW

||
* Health - 650
* Energy consumption - 2.7MW
* Robot recharge rate - 4 x 650kW

||
* Health - 800
* Energy consumption - 3.3MW
* Robot recharge rate - 4 x 800kW

||
* Health - 950
* Energy consumption - 3.9MW
* Robot recharge rate - 4 x 950kW

||
* Health - 1250
* Energy consumption - 5.1MW
* Robot recharge rate - 4 x 1.25MW

|-

| [[File:small_electric_pole.png|15px]] [[Small electric pole]] ||
* Health - 100
* 5x5 supply area
* Wire reach - 7.5 tiles

||
* Health - 130
* 7x7 supply area
* Wire reach - 9.5 tiles

||
* Health - 160
* 9x9 supply area
* Wire reach - 11.5 tiles

||
* Health - 190
* 11x11 supply area
* Wire reach - 13.5 tiles

||
* Health - 250
* 15x15 supply area
* Wire reach - 17.5 tiles

|-

| [[File:steel_chest.png|15px]] [[Steel chest]] ||
* Health - 350
* Storage size - 48

||
* Health - 455
* Storage size - 62

||
* Health - 560
* Storage size - 76

||
* Health - 665
* Storage size - 91

||
* Health - 875
* Storage size - 120

|-

| [[File:wooden_chest.png|15px]] [[Wooden chest]] ||
* Health - 100
* Storage size - 16

||
* Health - 130
* Storage size - 20

||
* Health - 160
* Storage size - 25

||
* Health - 190
* Storage size - 30

||
* Health - 250
* Storage size - 40

|-

}

== Creating high-quality items ==

There are two ways to create an item with above normal quality: The player must either use ingredient items of the same quality, or use quality modules for a random chance of a higher-quality item.

=== Quality ingredients ===
Recipes that create items have variations for each quality that the item might take. When setting such a recipe in a production unit, an ingredient quality must be selected. For these variations, the set of ingredients required is the same, except that all item ingredients must have the specified quality.

Item ingredient quality requirements are exact, not minimum. For example, one can not combine uncommon [[iron plate]]s with rare [[battery|batteries]] to make an [[accumulator]] of any quality. One must therefore ensure that high-quality items do not clog up belts and starve production units of lower-quality items.

As fluids do not possess any quality, they are exempt from ingredient quality requirements; the same [[lubricant]] can be used to create [[electric engine unit]]s of any quality.

=== Quality modules ===
{{Main|Quality module}}
[[File:quality_module_animated.png|64px|right]]'''Quality modules''' allow crafting machines to produce items of a higher quality than their ingredients. Each module adds a quality chance to a machine, depending on its tier and quality. See the following table for all quality chances:

{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Module|Quality}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! {{Icon|quality_module}}
| +1% || +1.3% || +1.6% || +1.9% || +2.5%
|-
! {{Icon|quality_module_2}}
| +2% || +2.6% || +3.2% || +3.8% || +5%
|-
! {{Icon|quality_module_3}}
| +2.5% || +3.2% || +4% || +4.7% || +6.2%
|}

When working out the odds of improving quality, a machine starts with the sum of the quality chance of all its modules. When the machine produces an item, it performs a random roll with that chance to succeed. If it succeeds, the product is upgraded 1 level from its ingredients. If the product was upgraded, the machine repeats this process, now with a constant 10% chance of passing, rolling and upgrading until a roll fails.

When using quality ingredients as an input, the base quality is the quality of the recipe. You can only use items with the same quality as input.

Quality modules are only required to ''improve'' quality, crafting will always give the base quality of the used items. Additionally, the odds of improving from a given base quality is the same as improving the same number of tiers from Normal quality.

Where Q is quality chance, the following tables present expected outputs for each level of research.
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Quality module (research)|}} [[Quality module (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 1/100
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 9/1000 || Q * 1/1000
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 9/100 || Q * 1/100
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1 - Q || Q
|-
! [[File:quality_legendary.png|Legendary|16px]]
| - || - || - || - || 1
|}
</div>

==== Examples ====
<div style="display:inline-block; margin-right:20px; vertical-align:top;">
{|class="wikitable" style="text-align: center;"
|+ 2× {{Icon|quality_module_2|[[File:quality_normal.png|Normal|16px]]}} → Q = 4%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 96% || 3.6% || 0.4%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 96% || 4%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
|+ 4× {{Icon|quality_module_3|[[File:quality_normal.png|Normal|16px]]}} → Q = 10%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 90% || 9% || 0.9% || 0.09% || 0.01%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 90% || 9% || 0.9% || 0.1%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 90% || 9% || 1%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 90% || 10%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|+ 4× {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}} → Q = 24.8%
|-
! [[File:quality_normal.png|Normal|32px]]
| 75.2% || 22.32% || 2.232% || 0.2232% || 0.0248%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 75.2% || 22.32% || 2.232% || 0.248%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 75.2% || 22.32% || 2.48%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 75.2% || 24.8%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div>

==== Optimal module usage ====

It is optimal to improve quality on the lead-up to the target output item due to the recycler only giving back 25% of the input items, except for cases where the chosen item has a productivity research available, in which case looping through a recycler is optimal and has no added material cost (ignoring fluids).

The following tables summarize the number of normal crafts (rounded up) needed to produce 1 legendary output using ideal ratios of quality module 3s to productivity module 3s, with 4 matching quality module 3 in the recycler.

It is important to emphasize that these ratios maximize return per input material. If input capacity isn't a concern and the goal is speed rather than material efficiency, then switch out productivity modules for quality modules as needed. Beware, however, that in many cases material inefficiency nearly keeps pace with the legendary output rate.

<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_rare.png|Rare|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_rare.png|Rare|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 891
|-
| 3 || 0% || 0 || 3 || 533
|-
| 4 || 0% || 1 || 3 || 342
|-
| 4 || 50% || 0 || 4 || 97
|-
| 5 || 50% || 1 || 4 || 67
|-
| 8 || 0% || 4 || 4 || 70
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_epic.png|Epic|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_epic.png|Epic|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 608
|-
| 3 || 0% || 1 || 2 || 356
|-
| 4 || 0% || 1 || 3 || 212
|-
| 4 || 50% || 1 || 3 || 62
|-
| 5 || 50% || 2 || 3 || 40
|-
| 8 || 0% || 5 || 3 || 34
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 309
|-
| 3 || 0% || 1 || 2 || 153
|-
| 4 || 0% || 2 || 2 || 80
|-
| 4 || 50% || 3 || 1 || 25
|-
| 5 || 50% || 4 || 1 || 14
|-
| 8 || 0% || 8 || 0 || 7
|}
</div><div style="white-space: nowrap;">For example, suppose the goal is to produce{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}and legendary T3 modules are available. If each electromagnetic plant producing epic quality or below has 1{{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}and 4{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, and the electromagnetic plant with the legendary recipe has 5{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, then on average an input of 280{{Icon|Electronic_circuit|[[File:quality_normal.png|Normal|16px]]}}and 28{{Icon|Advanced_circuit|[[File:quality_normal.png|Normal|16px]]}}is expected to produce 1{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}.</div>

;Derivation

Derivation of the tables above was as follows:
Starting with 1 set of common ingredients, with an assembly quality chance of Q and total productivity bonus of P, the statistical expected number of product is as follows:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + P) * (1 - Q) || (1 + P) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + P) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + P) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + P) * (Q * 10<sup>-3</sup>)
|-
| (1 + P) * (1 - Q) || (1 + P) * Q * 9/10|| (1 + P) * Q * 9/100 || (1 + P) * Q * 9/1000 || (1 + P) * Q * 1/1000
|}

In a similar vein, the same calculations can be done for recycling products, except that there is, in effect, -75% productivity bonus, where only a quarter of the items are returned.

{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + -0.75) * (1-Q) || (1 + -0.75) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + -0.75) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + -0.75) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + -0.75) * (Q * 10<sup>-3</sup>)
|-
| 0.25 * (1-Q) || 0.25 * Q * 9/10|| 0.25 * Q * 9/100 || 0.25 * Q * 9/1000 || 0.25 * Q * 1/1000
|}

For example, recycling an uncommon ingredient with a Q of 25%:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
|style="background:#424242"| [[File:quality_uncommon.png|Uncommon|16px]] || - || 0.1875 || 0.05625 || 0.005625 || 0.000625
|}

Combining these results allows a 'Transition Matrix' to be developed (see Stochastic Matrix on wikipedia) which after iteration can generate the expected number of legendary products from 1 set of common ingredients via matrix multiplication. An example matrix for P of 50% and Q of 25% for both recycling and assembly is copied below. Note that since legendary products are the goal, they are not recycled.

{| class="wikitable" style="border:2px solid; text-align:center;"
! !!style="border-left:2px solid"| I<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! I<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! I<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
!style="border-left:2px solid"| P<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! P<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! P<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|- style="border-top:2px solid"
! I<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 1.125 || 0.3375 || 0.03375 || 0.003375 || 0.000375
|-
! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 1.125 || 0.3375 || 0.03375 || 0.00375
|-
! I<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 1.125 || 0.3375 || 0.0375
|-
! I<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 1.125 || 0.375
|-
! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1.5
|- style="border-top:2px solid"
! P<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0.1875 || 0.5625 || 0.005625 || 0.0005625 || 0.0000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0.1875 || 0.05625 || 0.005625 || 0.000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0.1875 || 0.05625 || 0.00625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0.1875 || 0.0625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1
|}

To iterate this matrix (M) apply the matrix to itself. For example, M<sup>6</sup> would indicate 6 iterations, corresponding to 3 crafting steps and 3 recycling steps. To see how much 1 ingredient set produces after a given iteration, x, multiply an input vector by M<sup>x</sup>. The vector format follows that of the matrix labels, so with the table arranged as above, left multiply a row vector of ingredient(s) by the matrix. In order to see the expected product of 1 set of normal ingredients, the vector will have '1' in the first column and '0's everywhere else. Likewise, a set of uncommon ingredients will correspond to '1' in the second column of the vector.

It is important to note that since the recycling step has a material loss of 75% most recycling loops will be well behaved and converge quickly.<br>
Extreme productivity from research breaks this pattern and will prevent convergence, but this simply means that there is a positive material cycle, so 1 set of ingredients will produce infinite legendary crafts, on average. The closer the total productivity is to 400%, the slower the convergence of the matrix iteration and the higher you need to calculate x in M<sup>x</sup>.


== Usage tips ==
=== Using quality to increase production ===
There are four ways in which quality can increase the output of a single production machine:
* Increasing the quality of the machine itself will improve its base crafting speed.
* Increasing the quality of [[speed module]]s will increase the effect of their speed improvements.
* Increasing the quality of [[productivity module]]s will increase their productivity bonus without reducing crafting speed. Since extra items obtained from the productivity bonus do not take extra time to produce, this will also increase the number of items produced over time.
* Increasing the quality of [[beacon]]s will increase their transmission efficiency. If they contain speed modules, then the effect of these modules is increased.

These four options share a powerful synergy, as they react multiplicatively with one another. This makes it possible to achieve very high production rates with very few machines when compared to only using normal quality items. For example, imagine a setup where [[electronic circuit]]s are made using one [[electromagnetic plant]] with five [[productivity module 3]]s, which is surrounded by 12 [[beacon]]s with two [[speed module 3]]s, each. With normal quality, this will achieve an output rate of almost 45 items per second (almost enough to saturate one non-layered [[express transport belt]]). However, if the electromagnetic plant and all beacons and modules have legendary quality, the output rate becomes slightly more than 600 items per second (enough to saturate two and a half [[turbo transport belt]]s with four layers of items). This is more than 13 times as many items as without quality.

It should be noted that quality beacons are the only one of these factors that may increase energy consumption over time, as the transmission effect is also applied to the energy cost of speed modules. However, this is offset or even negated by the reduced energy consumption of the beacons themselves (which is also affected by quality), especially with high beacon counts wherein the transmission effect is subject to diminishing returns. For speed modules, productivity modules, and the machine itself, only the speed increase, productivity bonus, and base crafting speed are affected, respectively.

The increased transmission effect of high-quality beacons is also notable because unlike when increasing the number of beacons, there are no diminishing returns for increasing their quality (aside from the exponentially increasing cost of producing those higher-quality beacons in the first place). This means that, despite a legendary beacon only being 1.66 times as powerful as a normal-quality beacon, one would need 0.36 times as many legendary beacons as normal ones to achieve the same effect. Aside from making more powerful beacon setups, this can also be used to save space by achieving the same effect with fewer beacons, thereby leaving more room for machines and belts.

Higher-quality machines are also particularly useful for producing quality items as, unlike speed modules, machine quality does not reduce the chance of increasing a product's quality.

=== Using quality to save space ===
Another use for quality is decreasing the amount of buildings needed to perform the same production. This is particularly useful in a [[space platform]], where small, compact designs are rewarded with increased speed, as well as needing fewer rockets to build the platform.

== Relevant Factorio Friday Facts ==
* [https://www.factorio.com/blog/post/fff-375 FFF 375 - Quality]
* [https://www.factorio.com/blog/post/fff-376 FFF 376 - Research and Technology]

== Trivia ==
* Quality is not technically exclusive to player-made entities; Though this does not occur naturally, quality is also allowed on enemies, asteroids, and even the [[player]] character.
** Some enemies with qualities above normal can even be created in regular sandbox gameplay: Big biters, behemoth biters, and big premature wriggler pentapods born from spoiled [[biter egg]]s, [[captive biter spawner]]s, and [[pentapod egg]]s inherit the quality of the spoiled items, with the latter two being possible to craft with quality modules. Furthermore, a starved captured biter spawner will retain its quality upon converting into a hostile biter spawner, with said quality even being inherited by the biters that it will spawn. Should these biters chose to expand, they may also create quality spitters and worms.

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

{{C|Main}}

Quality

2024-12-11T17:16:32Z

MadKingAyres: /* Quality effects */

{{Languages}}
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{{About/Space age}}

'''Quality''' is a feature of the [[Space Age]] expansion. It introduces four higher quality levels for all items, structures and equipment with improved attributes. The goal of quality is to allow vertical factory upgrading as alternative to expansion in size. Items of higher quality are created by chance when using quality modules in the producing structure. The two highest quality tiers require technology not available on Nauvis. Different buildings and items can have different attributes that can be upgraded. When hovering over something, the attributes that will be upgraded with quality will be marked with a blue diamond in the tooltip.

While players are required to own Space Age to access this feature, quality is a separate mod, and can be activated independent of most Space Age content.

== Quality tiers ==
There are 5 quality tiers in vanilla gameplay, with tier strength in brackets:
* [[File:quality_normal.png|15px]] Normal (0)
* [[File:quality_uncommon.png|15px]] Uncommon (1)
* [[File:quality_rare.png|15px]] Rare (2)
* [[File:quality_epic.png|15px]] Epic (3)
* [[File:quality_legendary.png|15px]] Legendary ('''5''')

Note that legendary quality represents a 2-tier improvement over epic.

== Technologies ==
Certain tiers of quality cannot be created until they have been researched.
{|class="wikitable"
|-
! Research !! Base Game !! {{SA}} Space Age !! Unlocks
|-
| {{icontech|Quality module (research)|}} [[Quality module (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}} x 300
| {{icon|Time|30}}{{icon|Automation science pack}}{{icon|Logistic science pack}} x 500
| [[File:quality_uncommon.png|32px]] [[File:quality_rare.png|32px]]
|-
| {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Agricultural science pack}} x 5000
| [[File:quality_epic.png|32px]]
|-
| {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Metallurgic science pack}}{{icon|Electromagnetic science pack}}{{icon|Agricultural science pack}}{{icon|Cryogenic science pack}} x 5000
| [[File:quality_legendary.png|32px]]
|-
|}

== Quality effects ==
The currently known effects of each level of quality are as follows:
* +30% health
* +30% crafting speed
* +30% robot limit (rounded down)
* +30% robot recharge rate (both number and speed, rounded down)
* +30% positive module effects (rounded down for at least quality modules)
* +10% turret range
* +10% weapon range
* +1 tile reach and +2 wire reach on power poles
* +1 equipment grid size (both dimensions)
* +30% chest inventory size (rounded down)
* +30% increased ammo damage
* +30% inserter rotation speed
* -16.67% (1/6) resource drain on miners.
** This is multiplicative with productivity
* +100% (+5 MJ) capacity on accumulators
* +30% output rate on [[boiler]]s, [[steam engine]]s, [[steam turbine]]s, [[accumulator]]s (also affects input rate), and [[nuclear reactor]]s
** Note that consumption and pollution are also increased at the same rate
* −16% power consumption on beacons
* +1 to both continuous coverage distance and exploration coverage distance in [[radar]]s
* +100% durability on consumable items ([[repair pack]]s, [[science pack]]s)
* +5% fork chance on the [[tesla turret]] and tesla ammo for the tesla gun

These effects are per quality strength and additive: a Legendary (5 tier-levels) [[Productivity module 3]] (base +10% productivity) would grant 25% productivity.

A few buildings only get increased health, with no special effect, such as:
*Buildings related to [[Circuit network]]s and [[Rail signal]]s
*[[Transport belt]]s
*[[Pipe]]s
*[[Wall]]s
*[[Locomotive|Trains]]
*[[Cargo wagon]]s

{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-

| [[File:assembling_machine_1.png|15px]] [[Assembling machine 1]] ||
* Health - 300
* Crafting speed - 0.5

||
* Health - 390
* Crafting speed - 0.65

||
* Health - 480
* Crafting speed - 0.8

||
* Health - 570
* Crafting speed - 0.95

||
* Health - 750
* Crafting speed - 1.25
|-

| [[File:assembling_machine_2.png|15px]] [[Assembling machine 2]] ||
* Health - 350
* Crafting speed - 0.75

||
* Health - 455
* Crafting speed - 0.975

||
* Health - 560
* Crafting speed - 1.2

||
* Health - 665
* Crafting speed - 1.425

||
* Health - 875
* Crafting speed - 1.875

|-

| [[File:assembling_machine_3.png|15px]] [[Assembling machine 3]] ||
* Health - 400
* Crafting speed - 1.25

||
* Health - 520
* Crafting speed - 1.625

||
* Health - 640
* Crafting speed - 2

||
* Health - 760
* Crafting speed - 2.375

||
* Health - 1000
* Crafting speed - 3.125

|-

| [[File:construction_robot.png|15px]] [[Construction robot]]||
* Health - 100
* Max flying reach - 571m
* Energy capacity - 3MJ

||
* Health - 130
* Max flying reach - 1152m
* Energy capacity - 6MJ

||
* Health - 160
* Max flying reach - 1728m
* Energy capacity - 9MJ

||
* Health - 190
* Max flying reach - 2305m
* Energy capacity - 12MJ

||
* Health - 250
* Max flying reach - 3457m
* Energy capacity - 18MJ
|-

| [[File:inserter.png|15px]] [[Inserter]] ||
* Health - 150
* Energy consumption - 15.1kW
* Rotation speed - 302°/s

||
* Health - 195
* Energy consumption - 19.51kW
* Rotation speed - 393°/s

||
* Health - 240
* Energy consumption - 23.92kW
* Rotation speed - 484°/s

||
* Health - 285
* Energy consumption - 28.33kW
* Rotation speed - 575°/s

||
* Health - 375
* Energy consumption - 37.15kW
* Rotation speed - 756°/s

|-

| [[File:fast_inserter.png|15px]] [[Fast inserter]] ||
* Health - 150
* Energy consumption - 59.3kW
* Rotation speed - 864°/s
||
* Health - 195
* Energy consumption - 76.94kW
* Rotation speed - 1123°/s

||
* Health - 240
* Energy consumption - 94.58kW
* Rotation speed - 1382°/s

||
* Health - 285
* Energy consumption - 112kW
* Rotation speed - 1642°/s

||
* Health - 375
* Energy consumption - 148kW
* Rotation speed - 2160°/s
|-

| [[File:laser_turret.png|15px]] [[Laser turret]] ||
* Health - 1000
* Range - 24 tiles

||
* Health - 1300
* Range - 26.4 tiles

||
* Health - 1600
* Range - 28.8 tiles

||
* Health - 1900
* Range - 31.2 tiles

||
* Health - 2500
* Range - 36 tiles

|-

| [[File:pipe.png|15px]] [[Pipe]] ||
* Health - 100

||
* Health - 130

||
* Health - 160

||
* Health - 190

||
* Health - 250
|-

| [[File:small_electric_pole.png|15px]] [[Small electric pole]] ||
* Health - 100
* 5x5 supply area
* Wire reach - 7.5 tiles

||
* Health - 130
* 7x7 supply area
* Wire reach - 9.5 tiles

||
* Health - 160
* 9x9 supply area
* Wire reach - 11.5 tiles

||
* Health - 190
* 11x11 supply area
* Wire reach - 13.5 tiles

||
* Health - 250
* 15x15 supply area
* Wire reach - 17.5 tiles

|}

== Creating high-quality items ==

There are two ways to create an item with above normal quality: The player must either use ingredient items of the same quality, or use quality modules for a random chance of a higher-quality item.

=== Quality ingredients ===
Recipes that create items have variations for each quality that the item might take. When setting such a recipe in a production unit, an ingredient quality must be selected. For these variations, the set of ingredients required is the same, except that all item ingredients must have the specified quality.

Item ingredient quality requirements are exact, not minimum. For example, one can not combine uncommon [[iron plate]]s with rare [[battery|batteries]] to make an [[accumulator]] of any quality. One must therefore ensure that high-quality items do not clog up belts and starve production units of lower-quality items.

As fluids do not possess any quality, they are exempt from ingredient quality requirements; the same [[lubricant]] can be used to create [[electric engine unit]]s of any quality.

=== Quality modules ===
{{Main|Quality module}}
[[File:quality_module_animated.png|64px|right]]'''Quality modules''' allow crafting machines to produce items of a higher quality than their ingredients. Each module adds a quality chance to a machine, depending on its tier and quality. See the following table for all quality chances:

{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Module|Quality}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! {{Icon|quality_module}}
| +1% || +1.3% || +1.6% || +1.9% || +2.5%
|-
! {{Icon|quality_module_2}}
| +2% || +2.6% || +3.2% || +3.8% || +5%
|-
! {{Icon|quality_module_3}}
| +2.5% || +3.2% || +4% || +4.7% || +6.2%
|}

When working out the odds of improving quality, a machine starts with the sum of the quality chance of all its modules. When the machine produces an item, it performs a random roll with that chance to succeed. If it succeeds, the product is upgraded 1 level from its ingredients. If the product was upgraded, the machine repeats this process, now with a constant 10% chance of passing, rolling and upgrading until a roll fails.

When using quality ingredients as an input, the base quality is the quality of the recipe. You can only use items with the same quality as input.

Quality modules are only required to ''improve'' quality, crafting will always give the base quality of the used items. Additionally, the odds of improving from a given base quality is the same as improving the same number of tiers from Normal quality.

Where Q is quality chance, the following tables present expected outputs for each level of research.
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Quality module (research)|}} [[Quality module (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 1/100
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 9/1000 || Q * 1/1000
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 9/100 || Q * 1/100
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1 - Q || Q
|-
! [[File:quality_legendary.png|Legendary|16px]]
| - || - || - || - || 1
|}
</div>

==== Examples ====
<div style="display:inline-block; margin-right:20px; vertical-align:top;">
{|class="wikitable" style="text-align: center;"
|+ 2× {{Icon|quality_module_2|[[File:quality_normal.png|Normal|16px]]}} → Q = 4%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 96% || 3.6% || 0.4%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 96% || 4%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
|+ 4× {{Icon|quality_module_3|[[File:quality_normal.png|Normal|16px]]}} → Q = 10%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 90% || 9% || 0.9% || 0.09% || 0.01%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 90% || 9% || 0.9% || 0.1%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 90% || 9% || 1%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 90% || 10%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|+ 4× {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}} → Q = 24.8%
|-
! [[File:quality_normal.png|Normal|32px]]
| 75.2% || 22.32% || 2.232% || 0.2232% || 0.0248%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 75.2% || 22.32% || 2.232% || 0.248%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 75.2% || 22.32% || 2.48%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 75.2% || 24.8%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div>

==== Optimal module usage ====

It is optimal to improve quality on the lead-up to the target output item due to the recycler only giving back 25% of the input items, except for cases where the chosen item has a productivity research available, in which case looping through a recycler is optimal and has no added material cost (ignoring fluids).

The following tables summarize the number of normal crafts (rounded up) needed to produce 1 legendary output using ideal ratios of quality module 3s to productivity module 3s, with 4 matching quality module 3 in the recycler.

It is important to emphasize that these ratios maximize return per input material. If input capacity isn't a concern and the goal is speed rather than material efficiency, then switch out productivity modules for quality modules as needed. Beware, however, that in many cases material inefficiency nearly keeps pace with the legendary output rate.

<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_rare.png|Rare|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_rare.png|Rare|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 891
|-
| 3 || 0% || 0 || 3 || 533
|-
| 4 || 0% || 1 || 3 || 342
|-
| 4 || 50% || 0 || 4 || 97
|-
| 5 || 50% || 1 || 4 || 67
|-
| 8 || 0% || 4 || 4 || 70
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_epic.png|Epic|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_epic.png|Epic|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 608
|-
| 3 || 0% || 1 || 2 || 356
|-
| 4 || 0% || 1 || 3 || 212
|-
| 4 || 50% || 1 || 3 || 62
|-
| 5 || 50% || 2 || 3 || 40
|-
| 8 || 0% || 5 || 3 || 34
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 309
|-
| 3 || 0% || 1 || 2 || 153
|-
| 4 || 0% || 2 || 2 || 80
|-
| 4 || 50% || 3 || 1 || 25
|-
| 5 || 50% || 4 || 1 || 14
|-
| 8 || 0% || 8 || 0 || 7
|}
</div><div style="white-space: nowrap;">For example, suppose the goal is to produce{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}and legendary T3 modules are available. If each electromagnetic plant producing epic quality or below has 1{{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}and 4{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, and the electromagnetic plant with the legendary recipe has 5{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, then on average an input of 280{{Icon|Electronic_circuit|[[File:quality_normal.png|Normal|16px]]}}and 28{{Icon|Advanced_circuit|[[File:quality_normal.png|Normal|16px]]}}is expected to produce 1{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}.</div>

;Derivation

Derivation of the tables above was as follows:
Starting with 1 set of common ingredients, with an assembly quality chance of Q and total productivity bonus of P, the statistical expected number of product is as follows:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + P) * (1 - Q) || (1 + P) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + P) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + P) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + P) * (Q * 10<sup>-3</sup>)
|-
| (1 + P) * (1 - Q) || (1 + P) * Q * 9/10|| (1 + P) * Q * 9/100 || (1 + P) * Q * 9/1000 || (1 + P) * Q * 1/1000
|}

In a similar vein, the same calculations can be done for recycling products, except that there is, in effect, -75% productivity bonus, where only a quarter of the items are returned.

{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + -0.75) * (1-Q) || (1 + -0.75) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + -0.75) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + -0.75) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + -0.75) * (Q * 10<sup>-3</sup>)
|-
| 0.25 * (1-Q) || 0.25 * Q * 9/10|| 0.25 * Q * 9/100 || 0.25 * Q * 9/1000 || 0.25 * Q * 1/1000
|}

For example, recycling an uncommon ingredient with a Q of 25%:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
|style="background:#424242"| [[File:quality_uncommon.png|Uncommon|16px]] || - || 0.1875 || 0.05625 || 0.005625 || 0.000625
|}

Combining these results allows a 'Transition Matrix' to be developed (see Stochastic Matrix on wikipedia) which after iteration can generate the expected number of legendary products from 1 set of common ingredients via matrix multiplication. An example matrix for P of 50% and Q of 25% for both recycling and assembly is copied below. Note that since legendary products are the goal, they are not recycled.

{| class="wikitable" style="border:2px solid; text-align:center;"
! !!style="border-left:2px solid"| I<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! I<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! I<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
!style="border-left:2px solid"| P<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! P<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! P<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|- style="border-top:2px solid"
! I<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 1.125 || 0.3375 || 0.03375 || 0.003375 || 0.000375
|-
! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 1.125 || 0.3375 || 0.03375 || 0.00375
|-
! I<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 1.125 || 0.3375 || 0.0375
|-
! I<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 1.125 || 0.375
|-
! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1.5
|- style="border-top:2px solid"
! P<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0.1875 || 0.5625 || 0.005625 || 0.0005625 || 0.0000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0.1875 || 0.05625 || 0.005625 || 0.000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0.1875 || 0.05625 || 0.00625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0.1875 || 0.0625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1
|}

To iterate this matrix (M) apply the matrix to itself. For example, M<sup>6</sup> would indicate 6 iterations, corresponding to 3 crafting steps and 3 recycling steps. To see how much 1 ingredient set produces after a given iteration, x, multiply an input vector by M<sup>x</sup>. The vector format follows that of the matrix labels, so with the table arranged as above, left multiply a row vector of ingredient(s) by the matrix. In order to see the expected product of 1 set of normal ingredients, the vector will have '1' in the first column and '0's everywhere else. Likewise, a set of uncommon ingredients will correspond to '1' in the second column of the vector.

It is important to note that since the recycling step has a material loss of 75% most recycling loops will be well behaved and converge quickly.<br>
Extreme productivity from research breaks this pattern and will prevent convergence, but this simply means that there is a positive material cycle, so 1 set of ingredients will produce infinite legendary crafts, on average. The closer the total productivity is to 400%, the slower the convergence of the matrix iteration and the higher you need to calculate x in M<sup>x</sup>.


== Usage tips ==
=== Using quality to increase production ===
There are four ways in which quality can increase the output of a single production machine:
* Increasing the quality of the machine itself will improve its base crafting speed.
* Increasing the quality of [[speed module]]s will increase the effect of their speed improvements.
* Increasing the quality of [[productivity module]]s will increase their productivity bonus without reducing crafting speed. Since extra items obtained from the productivity bonus do not take extra time to produce, this will also increase the number of items produced over time.
* Increasing the quality of [[beacon]]s will increase their transmission efficiency. If they contain speed modules, then the effect of these modules is increased.

These four options share a powerful synergy, as they react multiplicatively with one another. This makes it possible to achieve very high production rates with very few machines when compared to only using normal quality items. For example, imagine a setup where [[electronic circuit]]s are made using one [[electromagnetic plant]] with five [[productivity module 3]]s, which is surrounded by 12 [[beacon]]s with two [[speed module 3]]s, each. With normal quality, this will achieve an output rate of almost 45 items per second (almost enough to saturate one non-layered [[express transport belt]]). However, if the electromagnetic plant and all beacons and modules have legendary quality, the output rate becomes slightly more than 600 items per second (enough to saturate two and a half [[turbo transport belt]]s with four layers of items). This is more than 13 times as many items as without quality.

It should be noted that quality beacons are the only one of these factors that may increase energy consumption over time, as the transmission effect is also applied to the energy cost of speed modules. However, this is offset or even negated by the reduced energy consumption of the beacons themselves (which is also affected by quality), especially with high beacon counts wherein the transmission effect is subject to diminishing returns. For speed modules, productivity modules, and the machine itself, only the speed increase, productivity bonus, and base crafting speed are affected, respectively.

The increased transmission effect of high-quality beacons is also notable because unlike when increasing the number of beacons, there are no diminishing returns for increasing their quality (aside from the exponentially increasing cost of producing those higher-quality beacons in the first place). This means that, despite a legendary beacon only being 1.66 times as powerful as a normal-quality beacon, one would need 0.36 times as many legendary beacons as normal ones to achieve the same effect. Aside from making more powerful beacon setups, this can also be used to save space by achieving the same effect with fewer beacons, thereby leaving more room for machines and belts.

Higher-quality machines are also particularly useful for producing quality items as, unlike speed modules, machine quality does not reduce the chance of increasing a product's quality.

=== Using quality to save space ===
Another use for quality is decreasing the amount of buildings needed to perform the same production. This is particularly useful in a [[space platform]], where small, compact designs are rewarded with increased speed, as well as needing fewer rockets to build the platform.

== Relevant Factorio Friday Facts ==
* [https://www.factorio.com/blog/post/fff-375 FFF 375 - Quality]
* [https://www.factorio.com/blog/post/fff-376 FFF 376 - Research and Technology]

== Trivia ==
* Quality is not technically exclusive to player-made entities; Though this does not occur naturally, quality is also allowed on enemies, asteroids, and even the [[player]] character.
** Some enemies with qualities above normal can even be created in regular sandbox gameplay: Big biters, behemoth biters, and big premature wriggler pentapods born from spoiled [[biter egg]]s, [[captive biter spawner]]s, and [[pentapod egg]]s inherit the quality of the spoiled items, with the latter two being possible to craft with quality modules. Furthermore, a starved captured biter spawner will retain its quality upon converting into a hostile biter spawner, with said quality even being inherited by the biters that it will spawn. Should these biters chose to expand, they may also create quality spitters and worms.

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

{{C|Main}}

Talk:Quality

2024-12-11T15:07:24Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine.<br>
-- [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it.
:-- [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

::I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

::[[File:Screenshot 2024-11-21 094640.png|thumb]]
::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

:::Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.

:::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

::::Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
::::Not sure whether i should delete my post and move it to this discussion.

::::Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

::::At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

::::The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
::::[[File:Screenshot 2024-11-23 002509.png|thumb]]
::::-- [[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

:::::I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

:::::https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
:::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

::::::With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

::::::<math>\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}</math>

::::::where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

::::::<math>\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}</math>

::::::As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

::::::I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

::::::I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

::::::-- [[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

:::::::I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
:::::::1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
:::::::2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
:::::::3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
:::::::3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

:::::::I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

:::::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

::::::::I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.
::::::::I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

::::::::Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.
::::::::Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

::::::::Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.
::::::::I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

:::::::::Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

:::::::::I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

:::::::::But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.
:::::::::Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

:::::::::Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

:::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

::::::::::I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

::::::::::For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The table presents rates per minute, averaged over an hour of in-game time.

::::::::::{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
::::::::::The figures are rather close. Not sure why it was off though.

::::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?

-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

:Could you perhaps post a more fleshed out example?

:My gut reaction is that this will make for a cumbersome table given how many effects there are. Plus, there are items with multiple quality effects, how would the table handle this?
:-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 16:23, 10 December 2024 (UTC)

::I think it would be a lot less cumbersome than any other format it could be put in. As for items with multiple effects per quality level, the extra effects would simply be listed in the relevant cell on a new line.

::Here is an example of what I would put on the page, if all are happy with it. Items would be arranged in alphabetical order for easy perusal.

::What do you think?

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-
| [[File:small_electric_pole.png|15px]] Small electric pole ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-
| [[File:laser_turret.png|15px]] Laser turret ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:assembling_machine_2.png|15px]] Assembling machine 2 ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-
| [[File:construction_robot.png|15px]] Construction robot||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

|}
::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

::: Looks good to me. Having a reference with actual items and their numbers would be nice.
::: Imo, we shouldn't ''replace'' the current list though. Having the quality effect rules stated explicitly is useful. Best to simply have both the list and the table.

::: Unrelated to the topic, to sign your talk page comments use <code><nowiki>~~~~</nowiki></code>. This generates the user name tag with a timestamp automatically. The user stamp along with indentation helps keep the message chain clear.

:::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 12:54, 11 December 2024 (UTC)

:::: Cool, so am I ok to start adding this in at the bottom of the Quality Effects section (i.e. below the current bulletpoint list)? Or should it go in its own section below Quality Effects?

:::: Also, thanks for the bit about signing the talk page comments; I wasn't sure if it was something that got added in automatically or not when I last replied.

::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 13:30, 11 December 2024 (UTC)

:::::I think the Quality Effects section is good, yeah, but put it wherever you feel best. We can always adjust it as needed.

:::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:14, 11 December 2024 (UTC)

::::::Great, I have added the table to the page (now alphabetised and I have also linked each item's name to its respective page). Will continue to add to the table as and when I have time.

::::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 14:28, 11 December 2024 (UTC)

:::::::For some reason it's displaying the table in the "Creating high-quality items" section despite my placing it in the Quality Effects section. Anyone able to tell me what I'm doing wrong there?

:::::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 14:43, 11 December 2024 (UTC)

::::::::I believe you missed the closing <code>|}</code> table tag, so it's placing the table nearest the next wikitable closing tag.
::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:46, 11 December 2024 (UTC)

:::::::::That was it, thanks. Fixed now.
:::::::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 15:07, 11 December 2024 (UTC)

Quality

2024-12-11T15:06:58Z

MadKingAyres:

{{Languages}}
{{Boilerplate
|icon=No-building-material-icon.png
|line-1=This article is a lacking sources for details of upcoming changes.
|line-2=You can help this wiki by [{{fullurl:{{FULLPAGENAME}}|action=edit}} adding them].}}
{{About/Space age}}

'''Quality''' is a feature of the [[Space Age]] expansion. It introduces four higher quality levels for all items, structures and equipment with improved attributes. The goal of quality is to allow vertical factory upgrading as alternative to expansion in size. Items of higher quality are created by chance when using quality modules in the producing structure. The two highest quality tiers require technology not available on Nauvis. Different buildings and items can have different attributes that can be upgraded. When hovering over something, the attributes that will be upgraded with quality will be marked with a blue diamond in the tooltip.

While players are required to own Space Age to access this feature, quality is a separate mod, and can be activated independent of most Space Age content.

== Quality tiers ==
There are 5 quality tiers in vanilla gameplay, with tier strength in brackets:
* [[File:quality_normal.png|15px]] Normal (0)
* [[File:quality_uncommon.png|15px]] Uncommon (1)
* [[File:quality_rare.png|15px]] Rare (2)
* [[File:quality_epic.png|15px]] Epic (3)
* [[File:quality_legendary.png|15px]] Legendary ('''5''')

Note that legendary quality represents a 2-tier improvement over epic.

== Technologies ==
Certain tiers of quality cannot be created until they have been researched.
{|class="wikitable"
|-
! Research !! Base Game !! {{SA}} Space Age !! Unlocks
|-
| {{icontech|Quality module (research)|}} [[Quality module (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}} x 300
| {{icon|Time|30}}{{icon|Automation science pack}}{{icon|Logistic science pack}} x 500
| [[File:quality_uncommon.png|32px]] [[File:quality_rare.png|32px]]
|-
| {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Agricultural science pack}} x 5000
| [[File:quality_epic.png|32px]]
|-
| {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Metallurgic science pack}}{{icon|Electromagnetic science pack}}{{icon|Agricultural science pack}}{{icon|Cryogenic science pack}} x 5000
| [[File:quality_legendary.png|32px]]
|-
|}

== Quality effects ==
The currently known effects of each level of quality are as follows:
* +30% health
* +30% crafting speed
* +30% robot limit (rounded down)
* +30% robot recharge rate (both number and speed, rounded down)
* +30% positive module effects (rounded down for at least quality modules)
* +10% turret range
* +10% weapon range
* +1 tile reach and +2 wire reach on power poles
* +1 equipment grid size (both dimensions)
* +30% chest inventory size (rounded down)
* +30% increased ammo damage
* +30% inserter rotation speed
* -16.67% (1/6) resource drain on miners.
** This is multiplicative with productivity
* +100% (+5 MJ) capacity on accumulators
* +30% output rate on [[boiler]]s, [[steam engine]]s, [[steam turbine]]s, [[accumulator]]s (also affects input rate), and [[nuclear reactor]]s
** Note that consumption and pollution are also increased at the same rate
* −16% power consumption on beacons
* +1 to both continuous coverage distance and exploration coverage distance in [[radar]]s
* +100% durability on consumable items ([[repair pack]]s, [[science pack]]s)
* +5% fork chance on the [[tesla turret]] and tesla ammo for the tesla gun

These effects are per quality strength and additive: a Legendary (5 tier-levels) [[Productivity module 3]] (base +10% productivity) would grant 25% productivity.

Some buildings, such as [[Transport belt]]s and [[Wall]]s, only gain increased health.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-

| [[File:assembling_machine_1.png|15px]] [[Assembling machine 1]] ||
* Crafting speed - 0.5
* Health - 300

||
* Crafting speed - 0.65
* Health - 390

||
* Crafting speed - 0.8
* Health - 480

||
* Crafting speed - 0.95
* Health - 570

||
* Crafting speed - 1.25
* Health - 750
|-

| [[File:assembling_machine_2.png|15px]] [[Assembling machine 2]] ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-

| [[File:assembling_machine_3.png|15px]] [[Assembling machine 3]] ||
* Crafting speed - 1.25
* Health - 400

||
* Crafting speed - 1.625
* Health - 520

||
* Crafting speed - 2
* Health - 640

||
* Crafting speed - 2.375
* Health - 760

||
* Crafting speed - 3.125
* Health - 1000
|-

| [[File:construction_robot.png|15px]] [[Construction robot]]||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

| [[File:laser_turret.png|15px]] [[Laser turret]] ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:small_electric_pole.png|15px]] [[Small electric pole]] ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|}

== Creating high-quality items ==

There are two ways to create an item with above normal quality: The player must either use ingredient items of the same quality, or use quality modules for a random chance of a higher-quality item.

=== Quality ingredients ===
Recipes that create items have variations for each quality that the item might take. When setting such a recipe in a production unit, an ingredient quality must be selected. For these variations, the set of ingredients required is the same, except that all item ingredients must have the specified quality.

Item ingredient quality requirements are exact, not minimum. For example, one can not combine uncommon [[iron plate]]s with rare [[battery|batteries]] to make an [[accumulator]] of any quality. One must therefore ensure that high-quality items do not clog up belts and starve production units of lower-quality items.

As fluids do not possess any quality, they are exempt from ingredient quality requirements; the same [[lubricant]] can be used to create [[electric engine unit]]s of any quality.

=== Quality modules ===
{{Main|Quality module}}
[[File:quality_module_animated.png|64px|right]]'''Quality modules''' allow crafting machines to produce items of a higher quality than their ingredients. Each module adds a quality chance to a machine, depending on its tier and quality. See the following table for all quality chances:

{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Module|Quality}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! {{Icon|quality_module}}
| +1% || +1.3% || +1.6% || +1.9% || +2.5%
|-
! {{Icon|quality_module_2}}
| +2% || +2.6% || +3.2% || +3.8% || +5%
|-
! {{Icon|quality_module_3}}
| +2.5% || +3.2% || +4% || +4.7% || +6.2%
|}

When working out the odds of improving quality, a machine starts with the sum of the quality chance of all its modules. When the machine produces an item, it performs a random roll with that chance to succeed. If it succeeds, the product is upgraded 1 level from its ingredients. If the product was upgraded, the machine repeats this process, now with a constant 10% chance of passing, rolling and upgrading until a roll fails.

When using quality ingredients as an input, the base quality is the quality of the recipe. You can only use items with the same quality as input.

Quality modules are only required to ''improve'' quality, crafting will always give the base quality of the used items. Additionally, the odds of improving from a given base quality is the same as improving the same number of tiers from Normal quality.

Where Q is quality chance, the following tables present expected outputs for each level of research.
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Quality module (research)|}} [[Quality module (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 1/100
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 9/1000 || Q * 1/1000
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 9/100 || Q * 1/100
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1 - Q || Q
|-
! [[File:quality_legendary.png|Legendary|16px]]
| - || - || - || - || 1
|}
</div>

==== Examples ====
<div style="display:inline-block; margin-right:20px; vertical-align:top;">
{|class="wikitable" style="text-align: center;"
|+ 2× {{Icon|quality_module_2|[[File:quality_normal.png|Normal|16px]]}} → Q = 4%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 96% || 3.6% || 0.4%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 96% || 4%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
|+ 4× {{Icon|quality_module_3|[[File:quality_normal.png|Normal|16px]]}} → Q = 10%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 90% || 9% || 0.9% || 0.09% || 0.01%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 90% || 9% || 0.9% || 0.1%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 90% || 9% || 1%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 90% || 10%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|+ 4× {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}} → Q = 24.8%
|-
! [[File:quality_normal.png|Normal|32px]]
| 75.2% || 22.32% || 2.232% || 0.2232% || 0.0248%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 75.2% || 22.32% || 2.232% || 0.248%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 75.2% || 22.32% || 2.48%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 75.2% || 24.8%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div>

==== Optimal module usage ====

It is optimal to improve quality on the lead-up to the target output item due to the recycler only giving back 25% of the input items, except for cases where the chosen item has a productivity research available, in which case looping through a recycler is optimal and has no added material cost (ignoring fluids).

The following tables summarize the number of normal crafts (rounded up) needed to produce 1 legendary output using ideal ratios of quality module 3s to productivity module 3s, with 4 matching quality module 3 in the recycler.

It is important to emphasize that these ratios maximize return per input material. If input capacity isn't a concern and the goal is speed rather than material efficiency, then switch out productivity modules for quality modules as needed. Beware, however, that in many cases material inefficiency nearly keeps pace with the legendary output rate.

<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_rare.png|Rare|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_rare.png|Rare|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 891
|-
| 3 || 0% || 0 || 3 || 533
|-
| 4 || 0% || 1 || 3 || 342
|-
| 4 || 50% || 0 || 4 || 97
|-
| 5 || 50% || 1 || 4 || 67
|-
| 8 || 0% || 4 || 4 || 70
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_epic.png|Epic|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_epic.png|Epic|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 608
|-
| 3 || 0% || 1 || 2 || 356
|-
| 4 || 0% || 1 || 3 || 212
|-
| 4 || 50% || 1 || 3 || 62
|-
| 5 || 50% || 2 || 3 || 40
|-
| 8 || 0% || 5 || 3 || 34
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 309
|-
| 3 || 0% || 1 || 2 || 153
|-
| 4 || 0% || 2 || 2 || 80
|-
| 4 || 50% || 3 || 1 || 25
|-
| 5 || 50% || 4 || 1 || 14
|-
| 8 || 0% || 8 || 0 || 7
|}
</div><div style="white-space: nowrap;">For example, suppose the goal is to produce{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}and legendary T3 modules are available. If each electromagnetic plant producing epic quality or below has 1{{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}and 4{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, and the electromagnetic plant with the legendary recipe has 5{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, then on average an input of 280{{Icon|Electronic_circuit|[[File:quality_normal.png|Normal|16px]]}}and 28{{Icon|Advanced_circuit|[[File:quality_normal.png|Normal|16px]]}}is expected to produce 1{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}.</div>

;Derivation

Derivation of the tables above was as follows:
Starting with 1 set of common ingredients, with an assembly quality chance of Q and total productivity bonus of P, the statistical expected number of product is as follows:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + P) * (1 - Q) || (1 + P) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + P) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + P) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + P) * (Q * 10<sup>-3</sup>)
|-
| (1 + P) * (1 - Q) || (1 + P) * Q * 9/10|| (1 + P) * Q * 9/100 || (1 + P) * Q * 9/1000 || (1 + P) * Q * 1/1000
|}

In a similar vein, the same calculations can be done for recycling products, except that there is, in effect, -75% productivity bonus, where only a quarter of the items are returned.

{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + -0.75) * (1-Q) || (1 + -0.75) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + -0.75) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + -0.75) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + -0.75) * (Q * 10<sup>-3</sup>)
|-
| 0.25 * (1-Q) || 0.25 * Q * 9/10|| 0.25 * Q * 9/100 || 0.25 * Q * 9/1000 || 0.25 * Q * 1/1000
|}

For example, recycling an uncommon ingredient with a Q of 25%:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
|style="background:#424242"| [[File:quality_uncommon.png|Uncommon|16px]] || - || 0.1875 || 0.05625 || 0.005625 || 0.000625
|}

Combining these results allows a 'Transition Matrix' to be developed (see Stochastic Matrix on wikipedia) which after iteration can generate the expected number of legendary products from 1 set of common ingredients via matrix multiplication. An example matrix for P of 50% and Q of 25% for both recycling and assembly is copied below. Note that since legendary products are the goal, they are not recycled.

{| class="wikitable" style="border:2px solid; text-align:center;"
! !!style="border-left:2px solid"| I<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! I<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! I<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
!style="border-left:2px solid"| P<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! P<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! P<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|- style="border-top:2px solid"
! I<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 1.125 || 0.3375 || 0.03375 || 0.003375 || 0.000375
|-
! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 1.125 || 0.3375 || 0.03375 || 0.00375
|-
! I<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 1.125 || 0.3375 || 0.0375
|-
! I<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 1.125 || 0.375
|-
! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1.5
|- style="border-top:2px solid"
! P<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0.1875 || 0.5625 || 0.005625 || 0.0005625 || 0.0000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0.1875 || 0.05625 || 0.005625 || 0.000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0.1875 || 0.05625 || 0.00625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0.1875 || 0.0625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1
|}

To iterate this matrix (M) apply the matrix to itself. For example, M<sup>6</sup> would indicate 6 iterations, corresponding to 3 crafting steps and 3 recycling steps. To see how much 1 ingredient set produces after a given iteration, x, multiply an input vector by M<sup>x</sup>. The vector format follows that of the matrix labels, so with the table arranged as above, left multiply a row vector of ingredient(s) by the matrix. In order to see the expected product of 1 set of normal ingredients, the vector will have '1' in the first column and '0's everywhere else. Likewise, a set of uncommon ingredients will correspond to '1' in the second column of the vector.

It is important to note that since the recycling step has a material loss of 75% most recycling loops will be well behaved and converge quickly.<br>
Extreme productivity from research breaks this pattern and will prevent convergence, but this simply means that there is a positive material cycle, so 1 set of ingredients will produce infinite legendary crafts, on average. The closer the total productivity is to 400%, the slower the convergence of the matrix iteration and the higher you need to calculate x in M<sup>x</sup>.


== Usage tips ==
=== Using quality to increase production ===
There are four ways in which quality can increase the output of a single production machine:
* Increasing the quality of the machine itself will improve its base crafting speed.
* Increasing the quality of [[speed module]]s will increase the effect of their speed improvements.
* Increasing the quality of [[productivity module]]s will increase their productivity bonus without reducing crafting speed. Since extra items obtained from the productivity bonus do not take extra time to produce, this will also increase the number of items produced over time.
* Increasing the quality of [[beacon]]s will increase their transmission efficiency. If they contain speed modules, then the effect of these modules is increased.

These four options share a powerful synergy, as they react multiplicatively with one another. This makes it possible to achieve very high production rates with very few machines when compared to only using normal quality items. For example, imagine a setup where [[electronic circuit]]s are made using one [[electromagnetic plant]] with five [[productivity module 3]]s, which is surrounded by 12 [[beacon]]s with two [[speed module 3]]s, each. With normal quality, this will achieve an output rate of almost 45 items per second (almost enough to saturate one non-layered [[express transport belt]]). However, if the electromagnetic plant and all beacons and modules have legendary quality, the output rate becomes slightly more than 600 items per second (enough to saturate two and a half [[turbo transport belt]]s with four layers of items). This is more than 13 times as many items as without quality.

It should be noted that quality beacons are the only one of these factors that may increase energy consumption over time, as the transmission effect is also applied to the energy cost of speed modules. However, this is offset or even negated by the reduced energy consumption of the beacons themselves (which is also affected by quality), especially with high beacon counts wherein the transmission effect is subject to diminishing returns. For speed modules, productivity modules, and the machine itself, only the speed increase, productivity bonus, and base crafting speed are affected, respectively.

The increased transmission effect of high-quality beacons is also notable because unlike when increasing the number of beacons, there are no diminishing returns for increasing their quality (aside from the exponentially increasing cost of producing those higher-quality beacons in the first place). This means that, despite a legendary beacon only being 1.66 times as powerful as a normal-quality beacon, one would need 0.36 times as many legendary beacons as normal ones to achieve the same effect. Aside from making more powerful beacon setups, this can also be used to save space by achieving the same effect with fewer beacons, thereby leaving more room for machines and belts.

Higher-quality machines are also particularly useful for producing quality items as, unlike speed modules, machine quality does not reduce the chance of increasing a product's quality.

=== Using quality to save space ===
Another use for quality is decreasing the amount of buildings needed to perform the same production. This is particularly useful in a [[space platform]], where small, compact designs are rewarded with increased speed, as well as needing fewer rockets to build the platform.

== Relevant Factorio Friday Facts ==
* [https://www.factorio.com/blog/post/fff-375 FFF 375 - Quality]
* [https://www.factorio.com/blog/post/fff-376 FFF 376 - Research and Technology]

== Trivia ==
* Quality is not technically exclusive to player-made entities; Though this does not occur naturally, quality is also allowed on enemies, asteroids, and even the [[player]] character.
** Some enemies with qualities above normal can even be created in regular sandbox gameplay: Big biters, behemoth biters, and big premature wriggler pentapods born from spoiled [[biter egg]]s, [[captive biter spawner]]s, and [[pentapod egg]]s inherit the quality of the spoiled items, with the latter two being possible to craft with quality modules. Furthermore, a starved captured biter spawner will retain its quality upon converting into a hostile biter spawner, with said quality even being inherited by the biters that it will spawn. Should these biters chose to expand, they may also create quality spitters and worms.

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

{{C|Main}}

Talk:Quality

2024-12-11T14:43:50Z

MadKingAyres:

Quality

2024-12-11T14:41:51Z

MadKingAyres:

{{Languages}}
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{{About/Space age}}

'''Quality''' is a feature of the [[Space Age]] expansion. It introduces four higher quality levels for all items, structures and equipment with improved attributes. The goal of quality is to allow vertical factory upgrading as alternative to expansion in size. Items of higher quality are created by chance when using quality modules in the producing structure. The two highest quality tiers require technology not available on Nauvis. Different buildings and items can have different attributes that can be upgraded. When hovering over something, the attributes that will be upgraded with quality will be marked with a blue diamond in the tooltip.

While players are required to own Space Age to access this feature, quality is a separate mod, and can be activated independent of most Space Age content.

== Quality tiers ==
There are 5 quality tiers in vanilla gameplay, with tier strength in brackets:
* [[File:quality_normal.png|15px]] Normal (0)
* [[File:quality_uncommon.png|15px]] Uncommon (1)
* [[File:quality_rare.png|15px]] Rare (2)
* [[File:quality_epic.png|15px]] Epic (3)
* [[File:quality_legendary.png|15px]] Legendary ('''5''')

Note that legendary quality represents a 2-tier improvement over epic.

== Technologies ==
Certain tiers of quality cannot be created until they have been researched.
{|class="wikitable"
|-
! Research !! Base Game !! {{SA}} Space Age !! Unlocks
|-
| {{icontech|Quality module (research)|}} [[Quality module (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}} x 300
| {{icon|Time|30}}{{icon|Automation science pack}}{{icon|Logistic science pack}} x 500
| [[File:quality_uncommon.png|32px]] [[File:quality_rare.png|32px]]
|-
| {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Agricultural science pack}} x 5000
| [[File:quality_epic.png|32px]]
|-
| {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Metallurgic science pack}}{{icon|Electromagnetic science pack}}{{icon|Agricultural science pack}}{{icon|Cryogenic science pack}} x 5000
| [[File:quality_legendary.png|32px]]
|-
|}

== Quality effects ==
The currently known effects of each level of quality are as follows:
* +30% health
* +30% crafting speed
* +30% robot limit (rounded down)
* +30% robot recharge rate (both number and speed, rounded down)
* +30% positive module effects (rounded down for at least quality modules)
* +10% turret range
* +10% weapon range
* +1 tile reach and +2 wire reach on power poles
* +1 equipment grid size (both dimensions)
* +30% chest inventory size (rounded down)
* +30% increased ammo damage
* +30% inserter rotation speed
* -16.67% (1/6) resource drain on miners.
** This is multiplicative with productivity
* +100% (+5 MJ) capacity on accumulators
* +30% output rate on [[boiler]]s, [[steam engine]]s, [[steam turbine]]s, [[accumulator]]s (also affects input rate), and [[nuclear reactor]]s
** Note that consumption and pollution are also increased at the same rate
* −16% power consumption on beacons
* +1 to both continuous coverage distance and exploration coverage distance in [[radar]]s
* +100% durability on consumable items ([[repair pack]]s, [[science pack]]s)
* +5% fork chance on the [[tesla turret]] and tesla ammo for the tesla gun

These effects are per quality strength and additive: a Legendary (5 tier-levels) [[Productivity module 3]] (base +10% productivity) would grant 25% productivity.

Some buildings, such as [[Transport belt]]s and [[Wall]]s, only gain increased health.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-

| [[File:assembling_machine_1.png|15px]] [[Assembling machine 1]] ||
* Crafting speed - 0.5
* Health - 300

||
* Crafting speed - 0.65
* Health - 390

||
* Crafting speed - 0.8
* Health - 480

||
* Crafting speed - 0.95
* Health - 570

||
* Crafting speed - 1.25
* Health - 750
|-

| [[File:assembling_machine_2.png|15px]] [[Assembling machine 2]] ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-

| [[File:assembling_machine_3.png|15px]] [[Assembling machine 3]] ||
* Crafting speed - 1.25
* Health - 400

||
* Crafting speed - 1.625
* Health - 520

||
* Crafting speed - 2
* Health - 640

||
* Crafting speed - 2.375
* Health - 760

||
* Crafting speed - 3.125
* Health - 1000
|-

| [[File:construction_robot.png|15px]] [[Construction robot]]||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

| [[File:laser_turret.png|15px]] [[Laser turret]] ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:small_electric_pole.png|15px]] [[Small electric pole]] ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

== Creating high-quality items ==

There are two ways to create an item with above normal quality: The player must either use ingredient items of the same quality, or use quality modules for a random chance of a higher-quality item.

=== Quality ingredients ===
Recipes that create items have variations for each quality that the item might take. When setting such a recipe in a production unit, an ingredient quality must be selected. For these variations, the set of ingredients required is the same, except that all item ingredients must have the specified quality.

Item ingredient quality requirements are exact, not minimum. For example, one can not combine uncommon [[iron plate]]s with rare [[battery|batteries]] to make an [[accumulator]] of any quality. One must therefore ensure that high-quality items do not clog up belts and starve production units of lower-quality items.

As fluids do not possess any quality, they are exempt from ingredient quality requirements; the same [[lubricant]] can be used to create [[electric engine unit]]s of any quality.

=== Quality modules ===
{{Main|Quality module}}
[[File:quality_module_animated.png|64px|right]]'''Quality modules''' allow crafting machines to produce items of a higher quality than their ingredients. Each module adds a quality chance to a machine, depending on its tier and quality. See the following table for all quality chances:

{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Module|Quality}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! {{Icon|quality_module}}
| +1% || +1.3% || +1.6% || +1.9% || +2.5%
|-
! {{Icon|quality_module_2}}
| +2% || +2.6% || +3.2% || +3.8% || +5%
|-
! {{Icon|quality_module_3}}
| +2.5% || +3.2% || +4% || +4.7% || +6.2%
|}

When working out the odds of improving quality, a machine starts with the sum of the quality chance of all its modules. When the machine produces an item, it performs a random roll with that chance to succeed. If it succeeds, the product is upgraded 1 level from its ingredients. If the product was upgraded, the machine repeats this process, now with a constant 10% chance of passing, rolling and upgrading until a roll fails.

When using quality ingredients as an input, the base quality is the quality of the recipe. You can only use items with the same quality as input.

Quality modules are only required to ''improve'' quality, crafting will always give the base quality of the used items. Additionally, the odds of improving from a given base quality is the same as improving the same number of tiers from Normal quality.

Where Q is quality chance, the following tables present expected outputs for each level of research.
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Quality module (research)|}} [[Quality module (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 1/100
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 9/1000 || Q * 1/1000
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 9/100 || Q * 1/100
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1 - Q || Q
|-
! [[File:quality_legendary.png|Legendary|16px]]
| - || - || - || - || 1
|}
</div>

==== Examples ====
<div style="display:inline-block; margin-right:20px; vertical-align:top;">
{|class="wikitable" style="text-align: center;"
|+ 2× {{Icon|quality_module_2|[[File:quality_normal.png|Normal|16px]]}} → Q = 4%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 96% || 3.6% || 0.4%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 96% || 4%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
|+ 4× {{Icon|quality_module_3|[[File:quality_normal.png|Normal|16px]]}} → Q = 10%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 90% || 9% || 0.9% || 0.09% || 0.01%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 90% || 9% || 0.9% || 0.1%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 90% || 9% || 1%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 90% || 10%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|+ 4× {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}} → Q = 24.8%
|-
! [[File:quality_normal.png|Normal|32px]]
| 75.2% || 22.32% || 2.232% || 0.2232% || 0.0248%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 75.2% || 22.32% || 2.232% || 0.248%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 75.2% || 22.32% || 2.48%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 75.2% || 24.8%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div>

==== Optimal module usage ====

It is optimal to improve quality on the lead-up to the target output item due to the recycler only giving back 25% of the input items, except for cases where the chosen item has a productivity research available, in which case looping through a recycler is optimal and has no added material cost (ignoring fluids).

The following tables summarize the number of normal crafts (rounded up) needed to produce 1 legendary output using ideal ratios of quality module 3s to productivity module 3s, with 4 matching quality module 3 in the recycler.

It is important to emphasize that these ratios maximize return per input material. If input capacity isn't a concern and the goal is speed rather than material efficiency, then switch out productivity modules for quality modules as needed. Beware, however, that in many cases material inefficiency nearly keeps pace with the legendary output rate.

<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_rare.png|Rare|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_rare.png|Rare|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 891
|-
| 3 || 0% || 0 || 3 || 533
|-
| 4 || 0% || 1 || 3 || 342
|-
| 4 || 50% || 0 || 4 || 97
|-
| 5 || 50% || 1 || 4 || 67
|-
| 8 || 0% || 4 || 4 || 70
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_epic.png|Epic|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_epic.png|Epic|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 608
|-
| 3 || 0% || 1 || 2 || 356
|-
| 4 || 0% || 1 || 3 || 212
|-
| 4 || 50% || 1 || 3 || 62
|-
| 5 || 50% || 2 || 3 || 40
|-
| 8 || 0% || 5 || 3 || 34
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 309
|-
| 3 || 0% || 1 || 2 || 153
|-
| 4 || 0% || 2 || 2 || 80
|-
| 4 || 50% || 3 || 1 || 25
|-
| 5 || 50% || 4 || 1 || 14
|-
| 8 || 0% || 8 || 0 || 7
|}
</div><div style="white-space: nowrap;">For example, suppose the goal is to produce{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}and legendary T3 modules are available. If each electromagnetic plant producing epic quality or below has 1{{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}and 4{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, and the electromagnetic plant with the legendary recipe has 5{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, then on average an input of 280{{Icon|Electronic_circuit|[[File:quality_normal.png|Normal|16px]]}}and 28{{Icon|Advanced_circuit|[[File:quality_normal.png|Normal|16px]]}}is expected to produce 1{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}.</div>

;Derivation

Derivation of the tables above was as follows:
Starting with 1 set of common ingredients, with an assembly quality chance of Q and total productivity bonus of P, the statistical expected number of product is as follows:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + P) * (1 - Q) || (1 + P) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + P) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + P) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + P) * (Q * 10<sup>-3</sup>)
|-
| (1 + P) * (1 - Q) || (1 + P) * Q * 9/10|| (1 + P) * Q * 9/100 || (1 + P) * Q * 9/1000 || (1 + P) * Q * 1/1000
|}

In a similar vein, the same calculations can be done for recycling products, except that there is, in effect, -75% productivity bonus, where only a quarter of the items are returned.

{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + -0.75) * (1-Q) || (1 + -0.75) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + -0.75) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + -0.75) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + -0.75) * (Q * 10<sup>-3</sup>)
|-
| 0.25 * (1-Q) || 0.25 * Q * 9/10|| 0.25 * Q * 9/100 || 0.25 * Q * 9/1000 || 0.25 * Q * 1/1000
|}

For example, recycling an uncommon ingredient with a Q of 25%:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
|style="background:#424242"| [[File:quality_uncommon.png|Uncommon|16px]] || - || 0.1875 || 0.05625 || 0.005625 || 0.000625
|}

Combining these results allows a 'Transition Matrix' to be developed (see Stochastic Matrix on wikipedia) which after iteration can generate the expected number of legendary products from 1 set of common ingredients via matrix multiplication. An example matrix for P of 50% and Q of 25% for both recycling and assembly is copied below. Note that since legendary products are the goal, they are not recycled.

{| class="wikitable" style="border:2px solid; text-align:center;"
! !!style="border-left:2px solid"| I<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! I<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! I<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
!style="border-left:2px solid"| P<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! P<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! P<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|- style="border-top:2px solid"
! I<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 1.125 || 0.3375 || 0.03375 || 0.003375 || 0.000375
|-
! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 1.125 || 0.3375 || 0.03375 || 0.00375
|-
! I<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 1.125 || 0.3375 || 0.0375
|-
! I<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 1.125 || 0.375
|-
! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1.5
|- style="border-top:2px solid"
! P<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0.1875 || 0.5625 || 0.005625 || 0.0005625 || 0.0000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0.1875 || 0.05625 || 0.005625 || 0.000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0.1875 || 0.05625 || 0.00625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0.1875 || 0.0625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1
|}

To iterate this matrix (M) apply the matrix to itself. For example, M<sup>6</sup> would indicate 6 iterations, corresponding to 3 crafting steps and 3 recycling steps. To see how much 1 ingredient set produces after a given iteration, x, multiply an input vector by M<sup>x</sup>. The vector format follows that of the matrix labels, so with the table arranged as above, left multiply a row vector of ingredient(s) by the matrix. In order to see the expected product of 1 set of normal ingredients, the vector will have '1' in the first column and '0's everywhere else. Likewise, a set of uncommon ingredients will correspond to '1' in the second column of the vector.

It is important to note that since the recycling step has a material loss of 75% most recycling loops will be well behaved and converge quickly.<br>
Extreme productivity from research breaks this pattern and will prevent convergence, but this simply means that there is a positive material cycle, so 1 set of ingredients will produce infinite legendary crafts, on average. The closer the total productivity is to 400%, the slower the convergence of the matrix iteration and the higher you need to calculate x in M<sup>x</sup>.


== Usage tips ==
=== Using quality to increase production ===
There are four ways in which quality can increase the output of a single production machine:
* Increasing the quality of the machine itself will improve its base crafting speed.
* Increasing the quality of [[speed module]]s will increase the effect of their speed improvements.
* Increasing the quality of [[productivity module]]s will increase their productivity bonus without reducing crafting speed. Since extra items obtained from the productivity bonus do not take extra time to produce, this will also increase the number of items produced over time.
* Increasing the quality of [[beacon]]s will increase their transmission efficiency. If they contain speed modules, then the effect of these modules is increased.

These four options share a powerful synergy, as they react multiplicatively with one another. This makes it possible to achieve very high production rates with very few machines when compared to only using normal quality items. For example, imagine a setup where [[electronic circuit]]s are made using one [[electromagnetic plant]] with five [[productivity module 3]]s, which is surrounded by 12 [[beacon]]s with two [[speed module 3]]s, each. With normal quality, this will achieve an output rate of almost 45 items per second (almost enough to saturate one non-layered [[express transport belt]]). However, if the electromagnetic plant and all beacons and modules have legendary quality, the output rate becomes slightly more than 600 items per second (enough to saturate two and a half [[turbo transport belt]]s with four layers of items). This is more than 13 times as many items as without quality.

It should be noted that quality beacons are the only one of these factors that may increase energy consumption over time, as the transmission effect is also applied to the energy cost of speed modules. However, this is offset or even negated by the reduced energy consumption of the beacons themselves (which is also affected by quality), especially with high beacon counts wherein the transmission effect is subject to diminishing returns. For speed modules, productivity modules, and the machine itself, only the speed increase, productivity bonus, and base crafting speed are affected, respectively.

The increased transmission effect of high-quality beacons is also notable because unlike when increasing the number of beacons, there are no diminishing returns for increasing their quality (aside from the exponentially increasing cost of producing those higher-quality beacons in the first place). This means that, despite a legendary beacon only being 1.66 times as powerful as a normal-quality beacon, one would need 0.36 times as many legendary beacons as normal ones to achieve the same effect. Aside from making more powerful beacon setups, this can also be used to save space by achieving the same effect with fewer beacons, thereby leaving more room for machines and belts.

Higher-quality machines are also particularly useful for producing quality items as, unlike speed modules, machine quality does not reduce the chance of increasing a product's quality.

=== Using quality to save space ===
Another use for quality is decreasing the amount of buildings needed to perform the same production. This is particularly useful in a [[space platform]], where small, compact designs are rewarded with increased speed, as well as needing fewer rockets to build the platform.

== Relevant Factorio Friday Facts ==
* [https://www.factorio.com/blog/post/fff-375 FFF 375 - Quality]
* [https://www.factorio.com/blog/post/fff-376 FFF 376 - Research and Technology]

== Trivia ==
* Quality is not technically exclusive to player-made entities; Though this does not occur naturally, quality is also allowed on enemies, asteroids, and even the [[player]] character.
** Some enemies with qualities above normal can even be created in regular sandbox gameplay: Big biters, behemoth biters, and big premature wriggler pentapods born from spoiled [[biter egg]]s, [[captive biter spawner]]s, and [[pentapod egg]]s inherit the quality of the spoiled items, with the latter two being possible to craft with quality modules. Furthermore, a starved captured biter spawner will retain its quality upon converting into a hostile biter spawner, with said quality even being inherited by the biters that it will spawn. Should these biters chose to expand, they may also create quality spitters and worms.

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

{{C|Main}}

Talk:Quality

2024-12-11T14:28:51Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

Talk:Quality

2024-12-11T14:28:37Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine.<br>
-- [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it.
:-- [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

::I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

::[[File:Screenshot 2024-11-21 094640.png|thumb]]
::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

:::Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.

:::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

::::Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
::::Not sure whether i should delete my post and move it to this discussion.

::::Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

::::At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

::::The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
::::[[File:Screenshot 2024-11-23 002509.png|thumb]]
::::-- [[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

:::::I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

:::::https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
:::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

::::::With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

::::::<math>\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}</math>

::::::where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

::::::<math>\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}</math>

::::::As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

::::::I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

::::::I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

::::::-- [[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

:::::::I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
:::::::1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
:::::::2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
:::::::3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
:::::::3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

:::::::I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

:::::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

::::::::I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.
::::::::I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

::::::::Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.
::::::::Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

::::::::Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.
::::::::I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

:::::::::Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

:::::::::I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

:::::::::But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.
:::::::::Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

:::::::::Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

:::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

::::::::::I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

::::::::::For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The table presents rates per minute, averaged over an hour of in-game time.

::::::::::{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
::::::::::The figures are rather close. Not sure why it was off though.

::::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?

-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

:Could you perhaps post a more fleshed out example?

:My gut reaction is that this will make for a cumbersome table given how many effects there are. Plus, there are items with multiple quality effects, how would the table handle this?
:-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 16:23, 10 December 2024 (UTC)

::I think it would be a lot less cumbersome than any other format it could be put in. As for items with multiple effects per quality level, the extra effects would simply be listed in the relevant cell on a new line.

::Here is an example of what I would put on the page, if all are happy with it. Items would be arranged in alphabetical order for easy perusal.

::What do you think?

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-
| [[File:small_electric_pole.png|15px]] Small electric pole ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-
| [[File:laser_turret.png|15px]] Laser turret ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:assembling_machine_2.png|15px]] Assembling machine 2 ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-
| [[File:construction_robot.png|15px]] Construction robot||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

|}
::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

::: Looks good to me. Having a reference with actual items and their numbers would be nice.
::: Imo, we shouldn't ''replace'' the current list though. Having the quality effect rules stated explicitly is useful. Best to simply have both the list and the table.

::: Unrelated to the topic, to sign your talk page comments use <code><nowiki>~~~~</nowiki></code>. This generates the user name tag with a timestamp automatically. The user stamp along with indentation helps keep the message chain clear.

:::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 12:54, 11 December 2024 (UTC)

:::: Cool, so am I ok to start adding this in at the bottom of the Quality Effects section (i.e. below the current bulletpoint list)? Or should it go in its own section below Quality Effects?

:::: Also, thanks for the bit about signing the talk page comments; I wasn't sure if it was something that got added in automatically or not when I last replied.

::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 13:30, 11 December 2024 (UTC)

:::::I think the Quality Effects section is good, yeah, but put it wherever you feel best. We can always adjust it as needed.

:::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:14, 11 December 2024 (UTC)

::::::Great, I have added the table to the page (now alphabetised and I have also linked each item's name to its respective page. Will continue to add to the table as and when I have time.

::::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 14:28, 11 December 2024 (UTC)

Talk:Quality

2024-12-11T14:28:23Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine.<br>
-- [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it.
:-- [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

::I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

::[[File:Screenshot 2024-11-21 094640.png|thumb]]
::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

:::Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.

:::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

::::Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
::::Not sure whether i should delete my post and move it to this discussion.

::::Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

::::At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

::::The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
::::[[File:Screenshot 2024-11-23 002509.png|thumb]]
::::-- [[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

:::::I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

:::::https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
:::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

::::::With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

::::::<math>\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}</math>

::::::where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

::::::<math>\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}</math>

::::::As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

::::::I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

::::::I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

::::::-- [[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

:::::::I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
:::::::1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
:::::::2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
:::::::3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
:::::::3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

:::::::I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

:::::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

::::::::I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.
::::::::I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

::::::::Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.
::::::::Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

::::::::Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.
::::::::I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

:::::::::Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

:::::::::I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

:::::::::But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.
:::::::::Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

:::::::::Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

:::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

::::::::::I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

::::::::::For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The table presents rates per minute, averaged over an hour of in-game time.

::::::::::{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
::::::::::The figures are rather close. Not sure why it was off though.

::::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?

-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

:Could you perhaps post a more fleshed out example?

:My gut reaction is that this will make for a cumbersome table given how many effects there are. Plus, there are items with multiple quality effects, how would the table handle this?
:-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 16:23, 10 December 2024 (UTC)

::I think it would be a lot less cumbersome than any other format it could be put in. As for items with multiple effects per quality level, the extra effects would simply be listed in the relevant cell on a new line.

::Here is an example of what I would put on the page, if all are happy with it. Items would be arranged in alphabetical order for easy perusal.

::What do you think?

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-
| [[File:small_electric_pole.png|15px]] Small electric pole ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-
| [[File:laser_turret.png|15px]] Laser turret ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:assembling_machine_2.png|15px]] Assembling machine 2 ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-
| [[File:construction_robot.png|15px]] Construction robot||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

|}
::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

::: Looks good to me. Having a reference with actual items and their numbers would be nice.
::: Imo, we shouldn't ''replace'' the current list though. Having the quality effect rules stated explicitly is useful. Best to simply have both the list and the table.

::: Unrelated to the topic, to sign your talk page comments use <code><nowiki>~~~~</nowiki></code>. This generates the user name tag with a timestamp automatically. The user stamp along with indentation helps keep the message chain clear.

:::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 12:54, 11 December 2024 (UTC)

:::: Cool, so am I ok to start adding this in at the bottom of the Quality Effects section (i.e. below the current bulletpoint list)? Or should it go in its own section below Quality Effects?

:::: Also, thanks for the bit about signing the talk page comments; I wasn't sure if it was something that got added in automatically or not when I last replied.

::::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 13:30, 11 December 2024 (UTC)

:::::I think the Quality Effects section is good, yeah, but put it wherever you feel best. We can always adjust it as needed.

:::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:14, 11 December 2024 (UTC)

::::::Great, I have added the table to the page (now alphabetised and I have also linked each item's name to its respective page. Will continue to add to the table as and when I have time.

::::::[[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 14:28, 11 December 2024 (UTC)

Quality

2024-12-11T14:26:59Z

MadKingAyres: /* Quality effects */

{{Languages}}
{{Boilerplate
|icon=No-building-material-icon.png
|line-1=This article is a lacking sources for details of upcoming changes.
|line-2=You can help this wiki by [{{fullurl:{{FULLPAGENAME}}|action=edit}} adding them].}}
{{About/Space age}}

'''Quality''' is a feature of the [[Space Age]] expansion. It introduces four higher quality levels for all items, structures and equipment with improved attributes. The goal of quality is to allow vertical factory upgrading as alternative to expansion in size. Items of higher quality are created by chance when using quality modules in the producing structure. The two highest quality tiers require technology not available on Nauvis. Different buildings and items can have different attributes that can be upgraded. When hovering over something, the attributes that will be upgraded with quality will be marked with a blue diamond in the tooltip.

While players are required to own Space Age to access this feature, quality is a separate mod, and can be activated independent of most Space Age content.

== Quality tiers ==
There are 5 quality tiers in vanilla gameplay, with tier strength in brackets:
* [[File:quality_normal.png|15px]] Normal (0)
* [[File:quality_uncommon.png|15px]] Uncommon (1)
* [[File:quality_rare.png|15px]] Rare (2)
* [[File:quality_epic.png|15px]] Epic (3)
* [[File:quality_legendary.png|15px]] Legendary ('''5''')

Note that legendary quality represents a 2-tier improvement over epic.

== Technologies ==
Certain tiers of quality cannot be created until they have been researched.
{|class="wikitable"
|-
! Research !! Base Game !! {{SA}} Space Age !! Unlocks
|-
| {{icontech|Quality module (research)|}} [[Quality module (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}} x 300
| {{icon|Time|30}}{{icon|Automation science pack}}{{icon|Logistic science pack}} x 500
| [[File:quality_uncommon.png|32px]] [[File:quality_rare.png|32px]]
|-
| {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Agricultural science pack}} x 5000
| [[File:quality_epic.png|32px]]
|-
| {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}} x 5000
| {{icon|Time|60}}{{icon|Automation science pack}}{{icon|Logistic science pack}}{{icon|Chemical science pack}}{{icon|Production science pack}}{{icon|Utility science pack}}{{icon|Space science pack}}{{icon|Metallurgic science pack}}{{icon|Electromagnetic science pack}}{{icon|Agricultural science pack}}{{icon|Cryogenic science pack}} x 5000
| [[File:quality_legendary.png|32px]]
|-
|}

== Quality effects ==
The currently known effects of each level of quality are as follows:
* +30% health
* +30% crafting speed
* +30% robot limit (rounded down)
* +30% robot recharge rate (both number and speed, rounded down)
* +30% positive module effects (rounded down for at least quality modules)
* +10% turret range
* +10% weapon range
* +1 tile reach and +2 wire reach on power poles
* +1 equipment grid size (both dimensions)
* +30% chest inventory size (rounded down)
* +30% increased ammo damage
* +30% inserter rotation speed
* -16.67% (1/6) resource drain on miners.
** This is multiplicative with productivity
* +100% (+5 MJ) capacity on accumulators
* +30% output rate on [[boiler]]s, [[steam engine]]s, [[steam turbine]]s, [[accumulator]]s (also affects input rate), and [[nuclear reactor]]s
** Note that consumption and pollution are also increased at the same rate
* −16% power consumption on beacons
* +1 to both continuous coverage distance and exploration coverage distance in [[radar]]s
* +100% durability on consumable items ([[repair pack]]s, [[science pack]]s)
* +5% fork chance on the [[tesla turret]] and tesla ammo for the tesla gun

These effects are per quality strength and additive: a Legendary (5 tier-levels) [[Productivity module 3]] (base +10% productivity) would grant 25% productivity.

Some buildings, such as [[Transport belt]]s and [[Wall]]s, only gain increased health.

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-

| [[File:assembling_machine_1.png|15px]] [[Assembling machine 1]] ||
* Crafting speed - 0.5
* Health - 300

||
* Crafting speed - 0.65
* Health - 390

||
* Crafting speed - 0.8
* Health - 480

||
* Crafting speed - 0.95
* Health - 570

||
* Crafting speed - 1.25
* Health - 750
|-

| [[File:assembling_machine_2.png|15px]] [[Assembling machine 2]] ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-

| [[File:assembling_machine_3.png|15px]] [[Assembling machine 3]] ||
* Crafting speed - 1.25
* Health - 400

||
* Crafting speed - 1.625
* Health - 520

||
* Crafting speed - 2
* Health - 640

||
* Crafting speed - 2.375
* Health - 760

||
* Crafting speed - 3.125
* Health - 1000
|-

| [[File:construction_robot.png|15px]] [[Construction robot]]||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

| [[File:laser_turret.png|15px]] [[Laser turret]] ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:small_electric_pole.png|15px]] [[Small electric pole]] ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-

== Creating high-quality items ==

There are two ways to create an item with above normal quality: The player must either use ingredient items of the same quality, or use quality modules for a random chance of a higher-quality item.

=== Quality ingredients ===
Recipes that create items have variations for each quality that the item might take. When setting such a recipe in a production unit, an ingredient quality must be selected. For these variations, the set of ingredients required is the same, except that all item ingredients must have the specified quality.

Item ingredient quality requirements are exact, not minimum. For example, one can not combine uncommon [[iron plate]]s with rare [[battery|batteries]] to make an [[accumulator]] of any quality. One must therefore ensure that high-quality items do not clog up belts and starve production units of lower-quality items.

As fluids do not possess any quality, they are exempt from ingredient quality requirements; the same [[lubricant]] can be used to create [[electric engine unit]]s of any quality.

=== Quality modules ===
{{Main|Quality module}}
[[File:quality_module_animated.png|64px|right]]'''Quality modules''' allow crafting machines to produce items of a higher quality than their ingredients. Each module adds a quality chance to a machine, depending on its tier and quality. See the following table for all quality chances:

{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Module|Quality}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! {{Icon|quality_module}}
| +1% || +1.3% || +1.6% || +1.9% || +2.5%
|-
! {{Icon|quality_module_2}}
| +2% || +2.6% || +3.2% || +3.8% || +5%
|-
! {{Icon|quality_module_3}}
| +2.5% || +3.2% || +4% || +4.7% || +6.2%
|}

When working out the odds of improving quality, a machine starts with the sum of the quality chance of all its modules. When the machine produces an item, it performs a random roll with that chance to succeed. If it succeeds, the product is upgraded 1 level from its ingredients. If the product was upgraded, the machine repeats this process, now with a constant 10% chance of passing, rolling and upgrading until a roll fails.

When using quality ingredients as an input, the base quality is the quality of the recipe. You can only use items with the same quality as input.

Quality modules are only required to ''improve'' quality, crafting will always give the base quality of the used items. Additionally, the odds of improving from a given base quality is the same as improving the same number of tiers from Normal quality.

Where Q is quality chance, the following tables present expected outputs for each level of research.
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Quality module (research)|}} [[Quality module (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Epic quality (research)|}} [[Epic quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 1/100
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+ {{icontech|Legendary quality (research)|}} [[Legendary quality (research)]]
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
! [[File:quality_normal.png|Normal|16px]]
| 1 - Q || Q * 9/10|| Q * 9/100 ||Q * 9/1000 || Q * 1/1000
|-
! [[File:quality_uncommon.png|Uncommon|16px]]
| - || 1 - Q || Q * 9/10|| Q * 9/100 || Q * 1/100
|-
! [[File:quality_rare.png|Rare|16px]]
| - || - || 1 - Q || Q * 9/10|| Q * 1/10
|-
! [[File:quality_epic.png|Epic|16px]]
| - || - || - || 1 - Q || Q
|-
! [[File:quality_legendary.png|Legendary|16px]]
| - || - || - || - || 1
|}
</div>

==== Examples ====
<div style="display:inline-block; margin-right:20px; vertical-align:top;">
{|class="wikitable" style="text-align: center;"
|+ 2× {{Icon|quality_module_2|[[File:quality_normal.png|Normal|16px]]}} → Q = 4%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 96% || 3.6% || 0.4%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 96% || 4%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
|+ 4× {{Icon|quality_module_3|[[File:quality_normal.png|Normal|16px]]}} → Q = 10%
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|-
! [[File:quality_normal.png|Normal|32px]]
| 90% || 9% || 0.9% || 0.09% || 0.01%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 90% || 9% || 0.9% || 0.1%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 90% || 9% || 1%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 90% || 10%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div><div style="display:inline-block; margin-right:20px;">
{|class="wikitable" style="text-align: center;"
! {{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|32px]] !! [[File:quality_uncommon.png|Uncommon|32px]] !! [[File:quality_rare.png|Rare|32px]] !! [[File:quality_epic.png|Epic|32px]] !! [[File:quality_legendary.png|Legendary|32px]]
|+ 4× {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}} → Q = 24.8%
|-
! [[File:quality_normal.png|Normal|32px]]
| 75.2% || 22.32% || 2.232% || 0.2232% || 0.0248%
|-
! [[File:quality_uncommon.png|Uncommon|32px]]
| - || 75.2% || 22.32% || 2.232% || 0.248%
|-
! [[File:quality_rare.png|Rare|32px]]
| - || - || 75.2% || 22.32% || 2.48%
|-
! [[File:quality_epic.png|Epic|32px]]
| - || - || - || 75.2% || 24.8%
|-
! [[File:quality_legendary.png|Legendary|32px]]
| - || - || - || - || 100%
|}
</div>

==== Optimal module usage ====

It is optimal to improve quality on the lead-up to the target output item due to the recycler only giving back 25% of the input items, except for cases where the chosen item has a productivity research available, in which case looping through a recycler is optimal and has no added material cost (ignoring fluids).

The following tables summarize the number of normal crafts (rounded up) needed to produce 1 legendary output using ideal ratios of quality module 3s to productivity module 3s, with 4 matching quality module 3 in the recycler.

It is important to emphasize that these ratios maximize return per input material. If input capacity isn't a concern and the goal is speed rather than material efficiency, then switch out productivity modules for quality modules as needed. Beware, however, that in many cases material inefficiency nearly keeps pace with the legendary output rate.

<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_rare.png|Rare|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_rare.png|Rare|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 891
|-
| 3 || 0% || 0 || 3 || 533
|-
| 4 || 0% || 1 || 3 || 342
|-
| 4 || 50% || 0 || 4 || 97
|-
| 5 || 50% || 1 || 4 || 67
|-
| 8 || 0% || 4 || 4 || 70
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_epic.png|Epic|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_epic.png|Epic|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 608
|-
| 3 || 0% || 1 || 2 || 356
|-
| 4 || 0% || 1 || 3 || 212
|-
| 4 || 50% || 1 || 3 || 62
|-
| 5 || 50% || 2 || 3 || 40
|-
| 8 || 0% || 5 || 3 || 34
|}
</div>
<div style="display:inline-block; vertical-align:top; margin-right:20px;">
{| class="wikitable" style="border: 2px solid; text-align:center;"
|-
!Max Modules!!Base Prod.!!No. of {{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!No. of {{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}!!Crafts
|-
| 2 || 0% || 0 || 2 || 309
|-
| 3 || 0% || 1 || 2 || 153
|-
| 4 || 0% || 2 || 2 || 80
|-
| 4 || 50% || 3 || 1 || 25
|-
| 5 || 50% || 4 || 1 || 14
|-
| 8 || 0% || 8 || 0 || 7
|}
</div><div style="white-space: nowrap;">For example, suppose the goal is to produce{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}and legendary T3 modules are available. If each electromagnetic plant producing epic quality or below has 1{{Icon|quality_module_3|[[File:quality_legendary.png|Legendary|16px]]}}and 4{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, and the electromagnetic plant with the legendary recipe has 5{{Icon|productivity_module_3|[[File:quality_legendary.png|Legendary|16px]]}}, then on average an input of 280{{Icon|Electronic_circuit|[[File:quality_normal.png|Normal|16px]]}}and 28{{Icon|Advanced_circuit|[[File:quality_normal.png|Normal|16px]]}}is expected to produce 1{{Icon|Processing_unit|[[File:quality_legendary.png|Legendary|16px]]}}.</div>

;Derivation

Derivation of the tables above was as follows:
Starting with 1 set of common ingredients, with an assembly quality chance of Q and total productivity bonus of P, the statistical expected number of product is as follows:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + P) * (1 - Q) || (1 + P) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + P) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + P) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + P) * (Q * 10<sup>-3</sup>)
|-
| (1 + P) * (1 - Q) || (1 + P) * Q * 9/10|| (1 + P) * Q * 9/100 || (1 + P) * Q * 9/1000 || (1 + P) * Q * 1/1000
|}

In a similar vein, the same calculations can be done for recycling products, except that there is, in effect, -75% productivity bonus, where only a quarter of the items are returned.

{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
| (1 + -0.75) * (1-Q) || (1 + -0.75) * (Q * (10<sup>0</sup> - 10<sup>-1</sup>))|| (1 + -0.75) * (Q * (10<sup>-1</sup> - 10<sup>-2</sup>)) || (1 + -0.75) * (Q * (10<sup>-2</sup> - 10<sup>-3</sup>)) || (1 + -0.75) * (Q * 10<sup>-3</sup>)
|-
| 0.25 * (1-Q) || 0.25 * Q * 9/10|| 0.25 * Q * 9/100 || 0.25 * Q * 9/1000 || 0.25 * Q * 1/1000
|}

For example, recycling an uncommon ingredient with a Q of 25%:
{| class="wikitable" style="text-align:center; vertical-align:middle;"
|+
!{{Diagonal split header|Input|Output}} !! [[File:quality_normal.png|Normal|20px]] !! [[File:quality_uncommon.png|Uncommon|20px]] !! [[File:quality_rare.png|Rare|20px]] !! [[File:quality_epic.png|Epic|20px]] !! [[File:quality_legendary.png|Legendary|20px]]
|-
|style="background:#424242"| [[File:quality_uncommon.png|Uncommon|16px]] || - || 0.1875 || 0.05625 || 0.005625 || 0.000625
|}

Combining these results allows a 'Transition Matrix' to be developed (see Stochastic Matrix on wikipedia) which after iteration can generate the expected number of legendary products from 1 set of common ingredients via matrix multiplication. An example matrix for P of 50% and Q of 25% for both recycling and assembly is copied below. Note that since legendary products are the goal, they are not recycled.

{| class="wikitable" style="border:2px solid; text-align:center;"
! !!style="border-left:2px solid"| I<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! I<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! I<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
!style="border-left:2px solid"| P<sub>[[File:quality_normal.png|Normal|10px]]</sub> !! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub> !! P<sub>[[File:quality_rare.png|Rare|10px]]</sub> !! P<sub>[[File:quality_epic.png|Epic|10px]]</sub> !! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|- style="border-top:2px solid"
! I<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 1.125 || 0.3375 || 0.03375 || 0.003375 || 0.000375
|-
! I<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 1.125 || 0.3375 || 0.03375 || 0.00375
|-
! I<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 1.125 || 0.3375 || 0.0375
|-
! I<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 1.125 || 0.375
|-
! I<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1.5
|- style="border-top:2px solid"
! P<sub>[[File:quality_normal.png|Normal|10px]]</sub>
|style="border-left:2px solid"| 0.1875 || 0.5625 || 0.005625 || 0.0005625 || 0.0000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_uncommon.png|Uncommon|10px]]</sub>
|style="border-left:2px solid"| 0 || 0.1875 || 0.05625 || 0.005625 || 0.000625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_rare.png|Rare|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0.1875 || 0.05625 || 0.00625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_epic.png|Epic|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0.1875 || 0.0625
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|-
! P<sub>[[File:quality_legendary.png|Legendary|10px]]</sub>
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 0
|style="border-left:2px solid"| 0 || 0 || 0 || 0 || 1
|}

To iterate this matrix (M) apply the matrix to itself. For example, M<sup>6</sup> would indicate 6 iterations, corresponding to 3 crafting steps and 3 recycling steps. To see how much 1 ingredient set produces after a given iteration, x, multiply an input vector by M<sup>x</sup>. The vector format follows that of the matrix labels, so with the table arranged as above, left multiply a row vector of ingredient(s) by the matrix. In order to see the expected product of 1 set of normal ingredients, the vector will have '1' in the first column and '0's everywhere else. Likewise, a set of uncommon ingredients will correspond to '1' in the second column of the vector.

It is important to note that since the recycling step has a material loss of 75% most recycling loops will be well behaved and converge quickly.<br>
Extreme productivity from research breaks this pattern and will prevent convergence, but this simply means that there is a positive material cycle, so 1 set of ingredients will produce infinite legendary crafts, on average. The closer the total productivity is to 400%, the slower the convergence of the matrix iteration and the higher you need to calculate x in M<sup>x</sup>.


== Usage tips ==
=== Using quality to increase production ===
There are four ways in which quality can increase the output of a single production machine:
* Increasing the quality of the machine itself will improve its base crafting speed.
* Increasing the quality of [[speed module]]s will increase the effect of their speed improvements.
* Increasing the quality of [[productivity module]]s will increase their productivity bonus without reducing crafting speed. Since extra items obtained from the productivity bonus do not take extra time to produce, this will also increase the number of items produced over time.
* Increasing the quality of [[beacon]]s will increase their transmission efficiency. If they contain speed modules, then the effect of these modules is increased.

These four options share a powerful synergy, as they react multiplicatively with one another. This makes it possible to achieve very high production rates with very few machines when compared to only using normal quality items. For example, imagine a setup where [[electronic circuit]]s are made using one [[electromagnetic plant]] with five [[productivity module 3]]s, which is surrounded by 12 [[beacon]]s with two [[speed module 3]]s, each. With normal quality, this will achieve an output rate of almost 45 items per second (almost enough to saturate one non-layered [[express transport belt]]). However, if the electromagnetic plant and all beacons and modules have legendary quality, the output rate becomes slightly more than 600 items per second (enough to saturate two and a half [[turbo transport belt]]s with four layers of items). This is more than 13 times as many items as without quality.

It should be noted that quality beacons are the only one of these factors that may increase energy consumption over time, as the transmission effect is also applied to the energy cost of speed modules. However, this is offset or even negated by the reduced energy consumption of the beacons themselves (which is also affected by quality), especially with high beacon counts wherein the transmission effect is subject to diminishing returns. For speed modules, productivity modules, and the machine itself, only the speed increase, productivity bonus, and base crafting speed are affected, respectively.

The increased transmission effect of high-quality beacons is also notable because unlike when increasing the number of beacons, there are no diminishing returns for increasing their quality (aside from the exponentially increasing cost of producing those higher-quality beacons in the first place). This means that, despite a legendary beacon only being 1.66 times as powerful as a normal-quality beacon, one would need 0.36 times as many legendary beacons as normal ones to achieve the same effect. Aside from making more powerful beacon setups, this can also be used to save space by achieving the same effect with fewer beacons, thereby leaving more room for machines and belts.

Higher-quality machines are also particularly useful for producing quality items as, unlike speed modules, machine quality does not reduce the chance of increasing a product's quality.

=== Using quality to save space ===
Another use for quality is decreasing the amount of buildings needed to perform the same production. This is particularly useful in a [[space platform]], where small, compact designs are rewarded with increased speed, as well as needing fewer rockets to build the platform.

== Relevant Factorio Friday Facts ==
* [https://www.factorio.com/blog/post/fff-375 FFF 375 - Quality]
* [https://www.factorio.com/blog/post/fff-376 FFF 376 - Research and Technology]

== Trivia ==
* Quality is not technically exclusive to player-made entities; Though this does not occur naturally, quality is also allowed on enemies, asteroids, and even the [[player]] character.
** Some enemies with qualities above normal can even be created in regular sandbox gameplay: Big biters, behemoth biters, and big premature wriggler pentapods born from spoiled [[biter egg]]s, [[captive biter spawner]]s, and [[pentapod egg]]s inherit the quality of the spoiled items, with the latter two being possible to craft with quality modules. Furthermore, a starved captured biter spawner will retain its quality upon converting into a hostile biter spawner, with said quality even being inherited by the biters that it will spawn. Should these biters chose to expand, they may also create quality spitters and worms.

== History ==
{{history|2.0.7|
* Introduced in [[Space Age]]{{SA}} expansion.
}}

{{C|Main}}

Talk:Quality

2024-12-11T13:47:55Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

Talk:Quality

2024-12-11T13:30:43Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine.<br>
-- [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it.
:-- [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

::I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

::[[File:Screenshot 2024-11-21 094640.png|thumb]]
::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

:::Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.

:::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

::::Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
::::Not sure whether i should delete my post and move it to this discussion.

::::Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

::::At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

::::The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
::::[[File:Screenshot 2024-11-23 002509.png|thumb]]
::::-- [[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

:::::I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

:::::https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
:::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

::::::With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

::::::<math>\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}</math>

::::::where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

::::::<math>\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}</math>

::::::As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

::::::I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

::::::I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

::::::-- [[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

:::::::I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
:::::::1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
:::::::2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
:::::::3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
:::::::3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

:::::::I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

:::::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

::::::::I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.
::::::::I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

::::::::Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.
::::::::Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

::::::::Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.
::::::::I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

:::::::::Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

:::::::::I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

:::::::::But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.
:::::::::Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

:::::::::Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

:::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

::::::::::I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

::::::::::For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The table presents rates per minute, averaged over an hour of in-game time.

::::::::::{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
::::::::::The figures are rather close. Not sure why it was off though.

::::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?

-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

:Could you perhaps post a more fleshed out example?

:My gut reaction is that this will make for a cumbersome table given how many effects there are. Plus, there are items with multiple quality effects, how would the table handle this?
:-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 16:23, 10 December 2024 (UTC)

::I think it would be a lot less cumbersome than any other format it could be put in. As for items with multiple effects per quality level, the extra effects would simply be listed in the relevant cell on a new line.

::Here is an example of what I would put on the page, if all are happy with it. Items would be arranged in alphabetical order for easy perusal.

::What do you think?

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-
| [[File:small_electric_pole.png|15px]] Small electric pole ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-
| [[File:laser_turret.png|15px]] Laser turret ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:assembling_machine_2.png|15px]] Assembling machine 2 ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-
| [[File:construction_robot.png|15px]] Construction robot||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

|}
::-- [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]])

::: Looks good to me. Having a reference with actual items and their numbers would be nice.
::: Imo, we shouldn't ''replace'' the current list though. Having the quality effect rules stated explicitly is useful. Best to simply have both the list and the table.

::: Unrelated to the topic, to sign your talk page comments use <code><nowiki>~~~~</nowiki></code>. This generates the user name tag with a timestamp automatically. The user stamp along with indentation helps keep the message chain clear.

:::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 12:54, 11 December 2024 (UTC)

:::: Cool, so am I ok to start adding this in at the bottom of the Quality Effects section (i.e. below the current bulletpoint list)? Or should it go in its own section below Quality Effects?

:::: Also, thanks for the bit about signing the talk page comments; I wasn't sure if it was something that got added in automatically or not when I last replied.

:::: [[User:MadKingAyres|MadKingAyres]] ([[User talk:MadKingAyres|talk]]) 13:30, 11 December 2024 (UTC)

Talk:Quality

2024-12-11T11:46:13Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine.<br>
-- [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it.
:-- [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

::I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

::[[File:Screenshot 2024-11-21 094640.png|thumb]]
::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

:::Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.

:::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

::::Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
::::Not sure whether i should delete my post and move it to this discussion.

::::Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

::::At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

::::The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
::::[[File:Screenshot 2024-11-23 002509.png|thumb]]
::::-- [[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

:::::I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

:::::https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
:::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

::::::With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

::::::<math>\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}</math>

::::::where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

::::::<math>\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}</math>

::::::As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

::::::I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

::::::I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

::::::-- [[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

:::::::I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
:::::::1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
:::::::2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
:::::::3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
:::::::3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

:::::::I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

:::::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

::::::::I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.
::::::::I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

::::::::Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.
::::::::Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

::::::::Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.
::::::::I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

:::::::::Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

:::::::::I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

:::::::::But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.
:::::::::Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

:::::::::Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

:::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

::::::::::I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

::::::::::For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The table presents rates per minute, averaged over an hour of in-game time.

::::::::::{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
::::::::::The figures are rather close. Not sure why it was off though.

::::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?

:Could you perhaps post a more fleshed out example?

:My gut reaction is that this will make for a cumbersome table given how many effects there are. Plus, there are items with multiple quality effects, how would the table handle this?
:-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 16:23, 10 December 2024 (UTC)

::I think it would be a lot less cumbersome than any other format it could be put in. As for items with multiple effects per quality level, the extra effects would simply be listed in the relevant cell on a new line.

::Here is an example of what I would put on the page, if all are happy with it. Items would be arranged in alphabetical order for easy perusal.

::What do you think?

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-
| [[File:small_electric_pole.png|15px]] Small electric pole ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-
| [[File:laser_turret.png|15px]] Laser turret ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:assembling_machine_2.png|15px]] Assembling machine 2 ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-
| [[File:construction_robot.png|15px]] Construction robot||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

|}

Talk:Quality

2024-12-11T00:25:30Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine.<br>
-- [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it.
:-- [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

::I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

::[[File:Screenshot 2024-11-21 094640.png|thumb]]
::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

:::Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.

:::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

::::Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
::::Not sure whether i should delete my post and move it to this discussion.

::::Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

::::At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

::::The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
::::[[File:Screenshot 2024-11-23 002509.png|thumb]]
::::-- [[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

:::::I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

:::::https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
:::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

::::::With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

::::::<math>\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}</math>

::::::where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

::::::<math>\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}</math>

::::::As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

::::::I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

::::::I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

::::::-- [[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

:::::::I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
:::::::1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
:::::::2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
:::::::3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
:::::::3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

:::::::I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

:::::::-- [[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

::::::::I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.
::::::::I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

::::::::Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.
::::::::Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

::::::::Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.
::::::::I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

:::::::::Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

:::::::::I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

:::::::::But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.
:::::::::Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

:::::::::Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

:::::::::-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

::::::::::I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

::::::::::For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The table presents rates per minute, averaged over an hour of in-game time.

::::::::::{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
::::::::::The figures are rather close. Not sure why it was off though.

::::::::::--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?

:Could you perhaps post a more fleshed out example?

:My gut reaction is that this will make for a cumbersome table given how many effects there are. Plus, there are items with multiple quality effects, how would the table handle this?
:-- [[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 16:23, 10 December 2024 (UTC)

::I think it would be a lot less cumbersome than any other format it could be put in. As for items with multiple effects per quality level, the extra effects would simply be listed in the relevant cell on a new line.

::Here is an example of what I would put on the page, if all are happy with it. Items would be arranged either in alphabetical order for easy perusal.

::What do you think?

::{| class="wikitable"
|+ Quality Effects
|-
! Item !! [[File:quality_normal.png|15px]] Normal !! [[File:quality_uncommon.png|15px]] Uncommon !! [[File:quality_rare.png|15px]] Rare !! [[File:quality_epic.png|15px]] Epic !! [[File:quality_legendary.png|15px]] Legendary
|-
| [[File:small_electric_pole.png|15px]] Small electric pole ||
* 5x5 supply area
* Wire reach - 7.5 tiles
* Health - 100

||
* 7x7 supply area
* Wire reach - 9.5 tiles
* Health - 130

||
* 9x9 supply area
* Wire reach - 11.5 tiles
* Health - 160

||
* 11x11 supply area
* Wire reach - 13.5 tiles
* Health - 190

||
* 15x15 supply area
* Wire reach - 17.5 tiles
* Health - 250
|-

|-
| [[File:laser_turret.png|15px]] Laser turret ||
* Range - 24 tiles
* Health - 1000

||
* Range - 26.4 tiles
* Health - 1300

||
* Range - 28.8 tiles
* Health - 1600

||
* Range - 31.2 tiles
* Health - 1900

||
* Range - 36 tiles
* Health - 2500
|-
| [[File:assembling_machine_2.png|15px]] Assembling machine 2 ||
* Crafting speed - 0.75
* Health - 350

||
* Crafting speed - 0.975
* Health - 455

||
* Crafting speed - 1.2
* Health - 560

||
* Crafting speed - 1.425
* Health - 665

||
* Crafting speed - 1.875
* Health - 875
|-
| [[File:construction_robot.png|15px]] Construction robot||
* Max flying reach - 571m
* Health - 100
* Energy capacity - 3MJ

||
* Max flying reach - 1152m
* Health - 130
* Energy capacity - 6MJ

||
* Max flying reach - 1728m
* Health - 160
* Energy capacity - 9MJ

||
* Max flying reach - 2305m
* Health - 190
* Energy capacity - 12MJ

||
* Max flying reach - 3457m
* Health - 250
* Energy capacity - 18MJ
|-

|}

Talk:Quality

2024-12-10T13:25:45Z

MadKingAyres: /* Consider adding table of items and effects of each quality level? */ new section

== Template for quality-affected stats ==

Writing this here because I need to write it somewhere.

I went ahead and made a template for when the same property varies based on quality. (Example: {{Quality|Small number|Not so small number|Decent number|Big number|Insane number}}.) Not sure if this is how we're gonna handle it (I've never been one to make good decisions :b), so it won't bother me if we wind up doing something completely different. I've already added it to the [[electromagnetic plant]] infobox (not sure if that was a good idea...), so you can see it there in practice if you need to. However, I don't really want to take it any further if I'm the only one who thinks this is a good idea. So, any thoughts? - [[User:Tecanec|tecanec]] ([[User talk:Tecanec|talk]]) 13:07, 28 October 2024 (UTC)
: Thanks for the initial implementation and the example usage! I made some adjustments and I think it's good to go now :D -- [[User:Bilka|Bilka]] ([[User talk:Bilka|talk]]) - <span style="color:#FF0000">Admin</span> 21:51, 28 October 2024 (UTC)

== Optimal module usage ==
How exactly is the optimal module usage calculated? I know the list only applies to it's usage in Assembler 3's, but with the new special buildings from other planets, chemical plants, and other various machines, I feel like it would be much better to break down what exactly the formula is in a general sense so we can apply it to every machine, instead of only getting the answers for a single machine. [[User:Brin|Brin]] ([[User talk:Brin|talk]]) 00:07, 13 November 2024 (UTC)

: Agreed with this - even for one machine, it seems incredibly un-useful to present these stats on the page as absolute truth without showing any workings. I'd rather have this section removed from the wiki than blindly trust it. [[User:Sachertorte|Sachertorte]] ([[User talk:Sachertorte|talk]]) 18:29, 17 November 2024 (UTC)

I created an excel sheet to do the iterative calculations to work out the number of crafts required to take 1 set of common inputs to 1 set of legendary outputs, using the statistical products. It is a bit complicated, using Markov chains and matrix multiplication. I'm not in a position to upload the sheet, but a screenshot is included showing the transition probabilities and workflow (for a 50% productivity machine with common quality 3 modules in it and the recycler

[[File:Screenshot 2024-11-21 094640.png|thumb]]
--[[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 23:55, 20 November 2024 (UTC)

Have done a further revision to add some derivation - maybe getting too technical for the wiki page, but figured it was better to write it down somewhere and let people more familiar with wiki format to either clean it up or put it in a more appropriate place.--[[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 07:07, 22 November 2024 (UTC)

Cause i had no access to wiki and couldnt contact Cooky173 i added a post concerning this page: https://forums.factorio.com/viewtopic.php?f=50&t=122540
Not sure whether i should delete my post and move it to this discussion.

Now that i looked at your numbers in the spreadsheat i wonder why there is a "crafting round 2"? It seems like the output of the recycling round 1 is not the same as the input to recycling round 2.

At least for items that were not recycled into its ingredients (like iron or superconductors) the calculation should imo base on 1 crafting plus (theoretically) infinite recycling of the non-legendary items.

The situation differs when recycling results into components of the item (like green circuits). Then it can be proven that using the results of 1 recycling should better be used for next crafting than for further recycling. To calculate these odds then becomes way more complex.
[[File:Screenshot 2024-11-23 002509.png|thumb]]
--[[User:FactorioGamer22|FactorioGamer22]] ([[User talk:FactorioGamer22|talk]]) 23:12, 22 November 2024 (UTC)

I converted my spreadsheet to google sheets. I think its working and I think I made mistakes when generating the tables in the wiki. Need to crunch the data again and fix.

https://docs.google.com/spreadsheets/d/13HH2twPdDAOo0L1jNLODH1rbGHgyowZjcVNXBhBAaDA/edit?usp=sharing
--[[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 12:29, 24 November 2024 (UTC)

With a little bit of linear algebra I have found an explicit formula for the number of batches of ingredients required per legendary product. When there is no quality module in the assemblers(/foundries/whatever), the formula is rather simple:

<math>
\frac{1000 \, \left[(p+1) \,q_r-p+3\right]^4}{(p+1)^2 \,q_r\, \left[10 \,(p+1)\, q_r-p+3\right]^3}
</math>

where <math>p</math> is the total productivity bonus of the crafting machines, and <math>q_r</math> is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, <math>q_a</math>, is non zero, but it is much uglier (and it breaks formatting, sorry):

<math>
\frac{1000 \left((p+1) q_a \left(q_r-1\right)-(p+1) q_r+p-3\right)^4}{(p+1) \left(-q_r \left((p+1) q_a \left(q_a \left((p+1) q_a \left((p+1) (p+15997) q_a-4 (p (p+3194)+6409)\right)+6 (p-3) (p (p+474)+969)\right)-4 (p-3)^2 (p+57)\right)+((p-8) p+18) p^2\right)+1000 (p+1)^4 \left(q_a-1\right){}^4 q_r^4-100 (p+1)^3 \left(q_a-1\right){}^3 q_r^3 \left((3 p+151) q_a-3 p+9\right)+6 (p+1)^2 q_r^2 \left(q_a \left(q_a \left(5 (p+1) (p+797) q_a^2-2 (p (10 p+3207)+6289) q_a+30 p (p+114)+5470\right)-20 (p-3) (p+27)\right)+5 (p-3)^2\right)+4 q_a \left(10 (p+1) q_a-p+3\right)^3+27 q_r\right)}
</math>

As a check, these formulas give the same results as the spreadsheet of Cooky173. However these results are different than the ones currently shown on the page.

I believe there are currently too much information on the page. Many lines of the giant table are not so useful, as no one should try to upcycle for legendary products without at least epic modules, as the figures show. Regarding the formulas: the general one does not have its place on the page, but the one with only productivity could be useful I think. Going full productivity is almost always the best choice anyway, even when it is not truly optimal, since it lets you use beacons with speed modules to build at scale.

I am newly registered here and I don't have experience writing for wikis, so I would like your opinions before modifying the page.

--[[User:Kaloether|Kaloether]] ([[User talk:Kaloether|talk]]) 22:27, 26 November 2024 (UTC)

I think you might be right about the tables being unnecessary clutter. I guess thinking about it from the perspective of the wiki, people are probably going to want to know the following:
1) When they are starting out on Nauvis, what is the best way to get uncommon and rare items (e.g. pre-recycling)
2) Once they have have access to recyclers, what is the best way to get rare/epic items (maybe with and without Tier 3 modules)
3) Once they have unlocked legendary items, what is the most efficient way to get legendary items.
3 is the question I've really set about answering in a simple way and yea - if you are at the point of making legendary everything you are just going to be using legendary modules - if not immediately, very soon. This is where you can also go down the rabbit hole of recycling products with outrageous prod. bonuses like Blue circuits and Low density structures as more efficient pathways to legendary copper, steel, plastic, green and red circuits.

I don't really know how to answer all of this, but I'll try and update my spreadsheet at least to work better at lower levels of available quality and to enable doing smart things like always use productivity in the last step of the production chain.

--[[User:Cooky173|Cooky173]] ([[User talk:Cooky173|talk]]) 09:14, 27 November 2024 (UTC)

I cleaned up the page in terms of HTML/CSS which made the tables easier to parse at a glance. I also made them inline-blocks, so they can be inspected horizontally side-by-side. I believe these things should alleviate the concern about clutter a whole lot.<br>
I'm concerned I may have misinterpreted some things about those tables so I'd appreciate if someone could look over my changes and confirm that I didn't get something wrong. I didn't change the numbers, but I did change the labels and some wording. Likewise, if someone could check the tables in the derivation section. I changed the formulas in those as I believe they were simply incorrect; or otherwise, I just couldn't understand what they signified. The current formulas give the same numbers as shown in the stochastic matrix, so I expect it's fine. I just worry that instead of the original tables being wrong, I misunderstood the original formula.

Last thing, I removed the bullet points that began the optimal module usage subsection. It had conflicting information with the tables, as far as I could tell.<br>
Since the tables have mathematical support rather than an appeal to authority, I thought it was better to lean on them. In fact, I thought it'd be good to expand on the stochastic matrix and show example usage to make the connection between it and the tables clear. But the sentiment on this seems split.

Something that might be considered, given the discussion above, is to keep the "facts" simple on the Quality page, but move the math and derivations to another page, which the quality page can then reference as needed.<br>
I personally appreciate the clarity of the tables as opposed to an unsupported statement(s). Wikis are open to public editing which comes with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.

--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 07:25, 8 December 2024 (UTC)

Cooky173 Thanks for the spreadsheet link. It was very helpful! I double checked the math and everything is on order as far as I could tell.

I updated the tables on the page since those were made with a slightly incorrect matrix, it seems. I also added all the other potential buildings players might be interested in.

But the tables are rather long. I'm new to this wiki, so I'm not sure how much flexibility we have with CSS.<br>
Ideally we'd split the tables into "tabs", where each tab corresponds to buildings with certain max module slots. That would make the tables far more tidy. Leaving the CSS for this in the page itself seems like poor design though, so I'm not ready to commit to making that.

Short of that, we can simply change out the tables to only show the maximal Prod to Quality module setups.

--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:15, 8 December 2024 (UTC)

I thought it might be useful to confirm the math with practical results from in-game so I ran an artificial test in the game to see how close the math gets to the real game figures.

For both setups I had 800 basic recycling loops running using electromagnetic plants to create legendary blue circuits. The tables presents rates per minute, averaged over an hour of in-game time.

{| class="wikitable" style="text-align:center"
|-
!Quality Modules per Building !! Green Circuit Consumption !! Green Circuit Production !! Legendary Blue Circuit Production !! Legendary Blue Circuit per Craft !! Theoretical Production !! Theoretical per Craft
|-
|1-1-1-1-0||168267||74340||329||329 / ((168267-74340)/20) = 0.070054||354||0.075563
|-
|2-4-5-5-0||216267||80225||345||345 / ((216267-80225)/20) = 0.050720||367||0.053889
|}
The figures are rather close. Not sure why it was off though.

--[[User:Raw Salad|Raw Salad]] ([[User talk:Raw Salad|talk]]) 14:35, 8 December 2024 (UTC)

== Consider adding table of items and effects of each quality level? ==

I think it would help immensely for quick reference if the Quality Effects section was replaced with a table showing the effects of different qualities on each item.

Something like this (please ignore the incorrect effects, this is just an example layout) with the item icons in the Item column.

{| class="wikitable"
|+ Quality Effects
|-
! Item !! Normal !! Uncommon !! Rare !! Epic !! Legendary
|-
| Small electric pole || +1 tile reach || +2 tile reach || +3 tile reach || +4 tile reach || +5 tile reach
|-
| Laser turret || 130% health|| 160% health || 190% health || 210% health || 250% health
|}

If others agree, I can start putting this together and it can just be added to?