Talk:Quality

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:

			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? - 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 -- Bilka (talk) - Admin 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. 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. 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

--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.--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.

--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 --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:

${\frac {1000\,\left[(p+1)\,q_{r}-p+3\right]^{4}}{(p+1)^{2}\,q_{r}\,\left[10\,(p+1)\,q_{r}-p+3\right]^{3}}}$

where $p$ is the total productivity bonus of the crafting machines, and $q_{r}$ is the quality bonus of the recyclers. There is also a more general formula when the quality bonus of the assemblers, $q_{a}$, is non zero, but it is much uglier (and it breaks formatting, sorry):

${\frac {1000\left((p+1)q_{a}\left(q_{r}-1\right)-(p+1)q_{r}+p-3\right)^{4}}{(p+1)\left(-q_{r}\left((p+1)q_{a}\left(q_{a}\left((p+1)q_{a}\left((p+1)(p+15997)q_{a}-4(p(p+3194)+6409)\right)+6(p-3)(p(p+474)+969)\right)-4(p-3)^{2}(p+57)\right)+((p-8)p+18)p^{2}\right)+1000(p+1)^{4}\left(q_{a}-1\right){}^{4}q_{r}^{4}-100(p+1)^{3}\left(q_{a}-1\right){}^{3}q_{r}^{3}\left((3p+151)q_{a}-3p+9\right)+6(p+1)^{2}q_{r}^{2}\left(q_{a}\left(q_{a}\left(5(p+1)(p+797)q_{a}^{2}-2(p(10p+3207)+6289)q_{a}+30p(p+114)+5470\right)-20(p-3)(p+27)\right)+5(p-3)^{2}\right)+4q_{a}\left(10(p+1)q_{a}-p+3\right)^{3}+27q_{r}\right)}}$

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.

--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. --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 statements. Wikis are open to public editing which brings with a healthy amount of doubt from visiting users. Having the derivation is rather valuable in the face of that.