Ok, so by my understanding of the math a percentage is a ratio: 5% = 5 / 100 = 0.05, so 5% of 100 = 0.05 x 100 = 5 = (100 / 100) x 5.
In the tooltips, damage is either given as X%(+) or X%(x), but its not clear whether we are multiplying by the percentage or the percentage value: if it was the percentage value, then say I have 4000 weapon damage, and am using the inner calm aspect.
10 / 100 = 0.1, and 0.1 x 4000 = 400.
But then, 400 x 4000 = 1,600,000 or 1.6M damage.
Now since I cannot get close to 1.6M base damage by equipping the aspect of Inner Calm, I can only assume that the game does not multiply by the percentage value (400), but by the actual percentage (0.1) and therefore all multipliers under 100% actually reduce damage.
You multiply by INTEGER values (or float). So a percentage like 140 means divide by 100 (140/100) = 1.4, then add 1 to it (1 + 1.4) = 2.4. This is now the multiplier.
Add a 1 to the percent… Dmg + Dmg*.1 = Dmg*1.1
If you had 400% (which is equal to 4), you’d still add a 1 to get the increase, so Dmg*(4+1)=Dmg*5 which gives you additional 400% of base damage
Additive bonuses listed as a percentage are lumped together as decimals, 1 is added to represent base damage, and then the base is multiplied by that.
800 damage with a +40% bonus and a +20% bonus is 800 * (1+ .4 +.2) = 800 * (1.6) = 1280.
A multiplicative bonus (shown in tooltips with [ x ] after it) is turned into a decimal and 1 added to it (to include the base amount,) and then multiplied.
800 with a 20% [ x ] bonus is 800 * (1 + .2) = 800 * (1.2) = 960.
So for the example of all of the above working at the same time,
(800 * (1 + .4 + .2) ) * (1 + .2) =
(800 * (1.6) ) * (1.2) =
1280 * 1.2 = 1536
Also I’m not sure if each [ x ] bonus that applies is multiplied separately or if they are lumped together additively. I assume since they are called out as [ x ] each is separate. (So +10% [ x ] and +20% [ x ] stack as * 1.1 * 1.2.)
Some conditional additive bonuses take an extra step; iirc Critical Hit damage is additive and on its own is 50%; so if you have +120% critical damage, the critical multiplier becomes .5 + 1.2 = 1.7. (Note that this is WITHOUT counting in the 1 additive multiplier that represents the base damage; I am ONLY talking the crit portion here.)
EDITED because reminded by below comment, I forgot multiplication is commutative.
Additive are just a multiplier… Just like everything else, they get added together, converted and then the order of operations make no difference when multiplying.
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Yes, my bad…order doesn’t matter once you’ve reduced each bucket to a single multiplier.
Thanks, that clears a lot up.
Although…
I suppose then the question is, if we are adding 1 to the decimal value, how is that different to an additive bonus?
4000 x (1 + 0.2) = 4000 x 1.2 = 4800 = 4000 + (0.2 x 4000)
All additive bonuses are added together as decimals and added to 1, then multiplied by the base.
Each multiplicative bonus is added to 1 as a decimal then multiplied by the base.
Example on why this is different:
800 base
Two 20% additives
One 20% [ x ]
800 * (1 + .2 + .2) * (1 + .2) = 800 * 1.4 * 1.2 = 1344
800 base
Three 20% additives
800 * (1 + .2 + .2 + .2) = 800 * 1.6 = 1280
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The exact one. Additive damage is still multiplicative, but it would just be a bucket. And each multiplicative damage is another separate bucket.
The idea is that initially the additive damage is very strong because if you have 150% critical damage and it increases to 300%. There was an increase of 100%. But at the end of the game we have 1500% critical damage and we gain another 150%, it passes it will be a 10% increase. The same goes for skills and the main attribute. The more we have, the smaller the increase.