Factorio Forums

1) Because the example chosen is 10%, it could be interpreted that the chance to skip qualities is multiplicative: Q^N, Q being the % base quality chance, and N being the number of steps.
In fact the chance to skip to the next level is always 10%. So the formula is actually Q*(0.1^N-1)
I suggest mentioning in the text that the next level is always 10% of the previous level.
I also suggest changing the example to use 4 quality1 modules, total 4% chance -> 0.4, 0.04, 0.004
Or 4 legendary quality2 modules, total 20% chance -> 2, 0.2, 0.02

2) A second way the table is misleading is that it's actually the chance to get this level of quality or higher.
The numbers for the exact qualities would be uncommon: 9%, rare: 0.9%, epic: 0.09%, legendary: 0.01%
For simplicity I would just show a ">=" sign in the header of the table before each quality icon (except legendary).

I also strongly recommend rephrasing the last sentence in that tip from
> There is also a small chance of skipping steps …
to
> There is also a 10% chance of skipping steps …

If used in addition to not starting with the 10% from the modules, this change should be "good enough" to give people the right kind of understanding to extrapolate.

I also suggest changing the example to use 4 quality1 modules, total 4% chance -> 0.4, 0.04, 0.004

I very much agree. There are two percentages in play here: %quality and %extrauplift. As you say, the formula is %quality*(%extrauplift^N-1). The current help text uses an example where %quality incidentally happens to be the same as %extrauplift, which obviously makes same readers reasonably assume that %quality=%extrauplift always. Especially since the current help text fails to post the actual general formula, so the reader has no chance to infer the correct calculation from the text with confidence.

Are you sure that this isn't actually a bug, and that 4 normal quality mk1's aren't supposed to result in chances :
~96%, 4%, 0.16%, 0.006 4%, 0.000 0256% ?

@BlueTemplar From https://factorio.com/blog/post/fff-375 : "On top of that, the quality increase can be not only one level at a time, but you can get lucky and get more steps at a time, each additional step has 10 times lower chance of happening, so for our previous examples, out of the 1000 gears, 9 would be uncommon and 1 rare. "

So the 1/10 for the additional uplifts is according to the design document, apparently.

But I do agree that using the quality% instead of 10% for the additional uplifts would be more intuitive.

BlueTemplar wrote: ↑Sat Nov 09, 2024 5:08 pm Are you sure that this isn't actually a bug, and that 4 normal quality mk1's aren't supposed to result in chances :
~96%, 4%, 0.16%, 0.006 4%, 0.000 0256% ?

Definitely not. Achieving 100% quality is not supposed to be 100% legendary, but only actually give you 0% 88.8% 10% 1% 0.1% quality chances. In other words, you are guaranteed uncommon or better, but straight out skipping qualities remains unlikely.

You'd need 1000% for a guarantee two jump two levels at a time, and that's fine, too.

Hmm, but isn't the maximum achievable (in vanilla) far short of this : +6.2% × 5 = +31% ?

Which would result in the following :
~55.49% — 31% — 9.61% — 2.98...% — 0.924...%

(And which itself of course could be tweaked.)

Don't you think that higher qualities being fixed like this is also kind of weird (in addition of being more complicated, and in this case, misleading) ?

If we take into account what was written in the FFF-375

On top of that, the quality increase can be not only one level at a time, but you can get lucky and get more steps at a time, each additional step has 10 times lower chance of happening, so for our previous examples, out of the 1000 gears, 9 would be uncommon and 1 rare.

If we take 31% quality like you said, i think the true chances are:

Common: 69%
Uncommon: 27.9%
Rare: 2.79%
Epic: 0.279%
Legendary: 0.031%

Because it has 10% to upgrade AFTER it already got a higher rarity

Or in text:
31% of the results will be uncommon
Of these 31% you will have a 10% chance to get rare -> so 31% * 90% = 27.9% uncommon and 31% * 10% = 3.1% rare
Of these 3.1% you will again have 10% chance to get next rarity -> 3.1% * 90% = 2.79% rare and 3.1% * 10% = 0.31% epic
and so on

Yes, my math was for IF the chance for multiple upgrades was the same as for the first upgrade, but compounded.

And I think I might have indeed forgotten subtracting the upgrade chances for subsequent quality upgrades past the first one for the final result ? So 31% chances for the uncommons to upgrade into rares too, but which is then substracted from total uncommon odds, since these items aren't uncommon any more !

Hmm, maybe that's why it was designed like this ? So that they can show a clear table of final odds, even if the underlying math is more complicated ? (Normal to uncommon is more than 10% if you consider some of the uncommons then becoming rare !)