Factorio Forums

Hello,
I believed I had a good grasp of the mechanics of quality. However, I recently decided to calculate on paper how quickly I could produce legendary level 3 modules using only common ingredients and without a recycler. This made me question whether I had miscalculated something.
My math is as follows:

Let's say I have a rare assembler 3 with a speed of 2.0.

The recipe for a level 3 module takes 60 seconds.

However, in this assembler, it will be crafted twice as fast, taking only 30 seconds.

let's say I have 4 uncomon level 3 quality modules, which gives me a total quality increase chance of 12.8%

according to my calculations:

60s / 2 / (0.1284) = 111 758 seconds. which equals 31 hours.

I'm confused about the 1 legendary module per 31 hour. Am I calculating it correctly?

You get 2 items per minute with cance to be not common 0,128. 120 items per hour (12% are green quality, 1,2% rare, 0,12 epic and 0,012% legendary) and you get 0,0144 legendary items per hour. So to get 1 item you need 70hours.
Somebody can do better math but it takes a lot

A quality increase chance of 12.8% or p=0.128 means:

p(normal+) = p^0
p(uncommon+) = p^1
p(rare+) = p^2
p(epic+) = p^3
p(legendary)=p^4

or

p(legendary) = 0.128^4 = 0.000268435

To get 1 legendary item average, you need 1/p = 3725.29 crafts

You say 1 craft takes 30 seconds, so you need 3725.29 * 30s= 111758.7s = 31.044 hours

However, it's not guaranteed to get this item within 31 hours. For this, there is this table: