wiki-article concerning Quality

[FactorioGamer22]

Hi there,
first of all: great work!
This nice arcticle let me dive into to Quality

1)
Unfortunately i cannot confirm some numbers presented in the article.
I believe there are some mistakes in the formula given in the "Derivation"-section - (but that might just be a typo cause with the presented formulas one is not able to reproduce the authors correct numbers given in the matrix).

The formulas i used were (which i believe were correct):
Common: (1+P) * (1-Q)
Uncommon: (1+P) * (Q - Q/10)
Rare: (1+P) * (Q/10 - Q/10^2)
Epic: (1+P) * (Q/10^2 - Q/10^3)
Legendary: (1+P) * (Q/10^3)

I have some questions to the author to clarify some premise:
- section "Common"
premise 1: using Assembling Machine 3 with 4 Quality3-modules (results in 10% Quality) and a recycler with also 4 Quality3-modules (results in 10% Quality as well)
premise 2: the recycler is used iterative until approaching asymptotic zero output (feeding its output into its input again and again)
premise 3: the "crafts" shown in the table are the reciprocal of the mathematical odds

My calculations of the outcome (get a legendary item) are:
after 1st recycling: 0,000190000
after 2nd recycling: 0,000240625
after 3rd recycling: 0,00026340625
after 4th recycling: 0,000272376367188

in terms of "crafts" that means:
after 1st recycling: 5.263
after 2nd recycling: 4.156
after 3rd recycling: 3.796
after 4th recycling: 3.671
.......

This gradually approaches somewhat around 3500.

The authors result is 1546 crafts.
Why do we differ that much - where is the mistake?

after the first recycling i get (with P=0 and Q=0.1 for Asembler and Recycler):
Common Uncommon Rare Epic Legendary
0,2025 0,0405 0,006075 0,00081 0,000190000
After each loop i remove the legendary fraction and feed the rest back into the recycler - resulting in the numbers shown above.


2) right above the next section "Usage tip" a Matrix is shown.
In the premise the author writes

An example matrix for P of 50% and Q of 25% for both recycling and assembly

.
- To be precise, the maximum quality a recycler can get is 24.8% (4 legendary T3-Quality) - just to not confuse readers

Would like to discuss the topic with the author.
Greetings

[cooky173]

Hi,

My approach was to consider a fictional factorio workd where you can get/do fractional crafts.

Then taking 1 set of ingredients, crafting them into a set of products, then recycling everything non legendary (once) crafting again, recycling again repeating until there is essentially no ingredient left.

Similar results would come from starting with say, 1000000 sets of ingredients.

I think the difference is that you have assumed the recycling step is repeated without the intermediate recrafting step.

I am trying to take my work into a google sheet (and also allow different steps of production to have different modules).

[cooky173]

I reread your post and think I misunderstood you.

Will try and so the sheet conversion tonight.

Definitely plausible that I made a mistake.

[FactorioGamer22]

Thanks for your reply.
One cannot craft stuff like "superconductors" again after recycling cause u dont get the "ingredients" from recycling (unlike e.g. green circuits).
I posted more details in the "discussion"-section of the wiki. Maybe u can have a look at it and we discuss the topic there?
Greetings

[cooky173]

Ah, I see why you are talking about infinite recycling now.

Yes, my numbers are talking about a product that can be recycled back into ingredients to be crafted again.

That would also be why I am getting fewer crafts than you, as half my rolls to improve quality aren't destroying 3/4ths of the item

[Upserter]

Hi @FactorioGamer22. Just to note that I agree with you that the formulae currently on the wiki in the Derivation section are incorrect, and yours are correct.