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# Math problems with passives

## Question

So, testing out Dual Pistols and the math isn't adding up:

For Pistols, all of the recovery/action speed applies to reloading. It starts with a base of 5 seconds to reload, and the modifiers don't add up either of the ways I can figure out to do them.

1. Add all modifiers together and then figure the problem:

A. Base of 5 second reload.

B. Modifiers: -21% from Dex, +10% from Sharpshooter, -30% from Dual Wield(not the style), -20% from Gunner, -15% from Dual Wield(style)

C. Adding the modifiers up reaches -76%. 5 seconds minues 76% (5 x .24) = 1.2

2. Figure each modifier individually.

B. Same modifiers.

C. Math: 5 x .79 = 3.95. 3.95 x 1.1 = 4.345. 4.345 x .7 = 3.0415. 3.0415 x .8 = 2.4332. 2.4332 x .85 = 2.068 rounded to 2.07.

So the 2 options are 1.2 second reload, or 2.07 second reload. In game, my reload sits at 2.7 before I put in the final Dual Wield style skill point, and 2.5 after that. That is nowhere near where it should be. Even if 2.5, half of the base, is a cap, I should have gotten there well before the final Dual Wield 15%. Especially using the first formula of adding the modifiers.

So somewhere the math is wrong, or the numbers presented to us are wrong.

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Just started a new playthrough, and I found at least one source of the problem.

When I first put on a pistol, it calculated correctly for my Dex bonuses.

When I dual wielded by putting on a blunderbuss it calculated the 30% dual wield incorrectly.

With my dex at -21% and Dual wield at -30% it should go from 5.0 to 2.765/2.8. But the in-game display puts it at 2.9. Even with rounding at both of the previous calculations, it should be 2.8. So i'm missing .1 second reload time.

And that's only if you do them in order of modifier. If you add the modifiers together THEN multiply, I should be at 2.45.

I will keep updating as I level and get new passives.

Level 4 as a dual-class. First time leveling picked only Gunner, 20% reload speed. From the 2.9 listed on my gun before leveling, 20% should take it to 2.32. In game it takes it from 2.9 to 2.6.

From the 2.6 it was with just Gunner added, Two Weapon Style should take it to 2.21. In game, after leveling with both of them the gun is at 2.4.

So the total math: 5.0 second base Reload Time. -21% from Dex, -30% Dual Wield, -15% Two Weapon Style, -20% Gunner.

5.0 x .79 = 3.95.

3.95 x .7 = 2.765/2.77

2.77 x .85 = 2.35

2.35 x .8 = 1.88

So after all is said and done, I should be at 1.88 reload speed. In game I am at 2.4. I am missing more than half a second.

To add to this, the Modal for Pistols is a -50%. From the 2.4 I was at, activating the modal puts me to 1.6. It should be 1.2.

Edited by Kragtor
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Bonuses and penalties don't combine that simply. See this thread: https://forums.obsidian.net/topic/95847-attackaction-speed-thread/ Notably, modifiers are not strictly additive or multiplicative, and penalties are weighted in such a way that they matter more (when combined with bonuses). There are also diminishing returns to stacking on bonuses.

If you're used to pillars of eternity 1, this is a sea change from how things used to be, which was a little more straightforward IMO (though still not like how you put in either scenario like in the OP).

final recovery = 5 / speed_coeff

steps_sum = (1.21 - 1) /*dex*/ + (1.3 - 1) /*2w*/ + (1.15 - 1) /*2w style*/ + (1.2 - 1) /*gunner*/ + (1 - 1 / .9) /*sharpshooter penalty*/

steps_sum = .21 + .3 + .15 + .2 -.11

steps_sum = .75

speed_coeff = steps_sum + 1

=>

final recovery = 5 / 1.75 = ~2.85s, which is in the right ballpark of what you see in-game (though i imagine some more context would get it all the way to the exact values).

Edited by thelee
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If i'm reading this right, with my new calculations where I didn't take the malus Sharpshooter should be the totals of the speed added together, then the base 5.0 divided by that modifier total.

So:

sum of modifiers: .21 + .3 + .15 + .2

Sum of modifiers: .86

modifier total: 1.86

5.0 / 1.86 = 2.68.

So, if that math is right it should be 2.68 in game.

In fact, it is 2.4.

If I add the -50% from the modal:

1.86 becomes 2.36

5.0 / 2.36 = 2.12. The result in game is 1.6.

So, neither the math as displayed in game nor the math in that thread appears correct in this situation, unless I messed up. But I spent quite a bit of time making sure I followed the formula you set out.

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Hey Kragtor,

Thanks for the post, I'll have the devs look into the numbers of dual wielding pistols to see if there's any discrepancy.

Best,

-Caleb

I like big bugs and I cannot lie...

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If i'm reading this right, with my new calculations where I didn't take the malus Sharpshooter should be the totals of the speed added together, then the base 5.0 divided by that modifier total.

So:

sum of modifiers: .21 + .3 + .15 + .2

Sum of modifiers: .86

modifier total: 1.86

5.0 / 1.86 = 2.68.

So, if that math is right it should be 2.68 in game.

In fact, it is 2.4.

If I add the -50% from the modal:

1.86 becomes 2.36

5.0 / 2.36 = 2.12. The result in game is 1.6.

So, neither the math as displayed in game nor the math in that thread appears correct in this situation, unless I messed up. But I spent quite a bit of time making sure I followed the formula you set out.

Curious; MaxQuest and co seemed pretty confident that they had the right equations. It'd be interesting to see if this means that something has actually changed between the last backer beta and release.

Edited by thelee
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If i'm reading this right, with my new calculations where I didn't take the malus Sharpshooter should be the totals of the speed added together, then the base 5.0 divided by that modifier total.

So:

sum of modifiers: .21 + .3 + .15 + .2

Sum of modifiers: .86

modifier total: 1.86

5.0 / 1.86 = 2.68.

So, if that math is right it should be 2.68 in game.

In fact, it is 2.4.

If I add the -50% from the modal:

1.86 becomes 2.36

5.0 / 2.36 = 2.12. The result in game is 1.6.

So, neither the math as displayed in game nor the math in that thread appears correct in this situation, unless I messed up. But I spent quite a bit of time making sure I followed the formula you set out.

So I think the formula that MaxQuest is obsolete.

Your numbers seem a lot more consistent with multiplicative "rate" bonuses for speed.

I can reproduce them if I assume something like:

5s base * (1/1.21) * (1/(1 + .3 + .15)) * (1/1.2) = 2.4s, with rounding (2.37s specifically)

2.37s base * 1/1.5 = 1.6s with rounding (1.58s specifically)

this may just be a coincidence though, because i can't really reproduce any of the other numbers in this thread, unless you've not been explicit about various action speed/recovery adjustments you have.

EDIT: ignore this post, see below

Edited by thelee
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OK, I think I figured it out. The problem is that how the "coefficient" is computed is not completely obvious and apparently a little inconsistent.

So to elaborate the problem is actually that dual wielding is not a .3 modifier in the equation. In-game it reduces recovery time by 30%, which means in reality it increases the rate of your recovery by 1.428x (eg 1 / (1 - .3)), and that's what the coefficient is (this is mentioned in a random post in the linked thread about action speed). Similarly you get dual-wielding style, while the game says it's 15% faster, it's actually computed like 1/.85 to get a coeff of 1.176 (eg 1 / (1 - .15)). Similarly, the -50% reload speed modifier is probably actually implemented as a +100% to your action rate, for a coeff of 2. Similarly, gunner is probably implemented like 1/.8 with a coeff of 1.25x.

So instead of 21 + .3 + .15 + .2  you'd get .21 + .428 + .176 + .25 or

5 / 2.064 = 2.42s.

5 / (2.064 + 1) = 1.63s

think this might explain what's going on. Add in sharpshooter penalty and alternately take out the two-weapon style and you get reload times of 2.54s or 2.79s which (if the game truncates trailing after the first decimal) matches your original post.

EDITed to add: it probably requires a lot of paying attention to how the game phrases specific modifictions to your recovery/attack speed. The internal metric is "how quickly you advance through action frames" (or what we should call "action rate"). So when the game says "-15% to weapon recovery" for two-weapon style, there's no concept of weapon recovery internally, so it has to convert it into an effect on your "action rate," which the game designers did so by doing 1 / .85 to produce a coefficient for your "action rate" of 1.176. When the game says "-20% reload speed" similarly there's no concept fo this internally so it has to be converted into an effect on your "action rate" which is 1/.8 to get a coefficient of 1.25.

Edited by thelee
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So, instead of finding a way to display it in-game so that it makes sense with simple math, they confuse everyone that doesn't have some kind of math degree.

I feel like they should have found a way to make this more accessible to the laymen, so that there is one less reason to throw your hands up and not play the game. Because between the super complicated math that they tell us nothing about, there is also potentially caps on action speed/recovery that are not mentioned anywhere.

Obsidian, please be transparent so we can understand what our decisions actually do to our characters.

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So, instead of finding a way to display it in-game so that it makes sense with simple math, they confuse everyone that doesn't have some kind of math degree.

I feel like they should have found a way to make this more accessible to the laymen, so that there is one less reason to throw your hands up and not play the game. Because between the super complicated math that they tell us nothing about, there is also potentially caps on action speed/recovery that are not mentioned anywhere.

Obsidian, please be transparent so we can understand what our decisions actually do to our characters.

Well at least it actually shows you the real value on your equipped weapons now, that alone is a huge improvement over the first game IMO, even if the math used to get there is not intuitive.

At least I can get an attack speed bonus and immediately confirm that it at least reduces it to some extent.