PoE2 "Increased damage with hits against enemies" (eg Hindered Capabilities) and "targets take increased damage" (eg shock,) multiplicative or additive?
I'm having trouble parsing out which "increased damage" effects are additive and which multiplicative. I recently read that increased damage taken by enemies, as in the shock ailment, acts as a multiplier. Is this accurate? Do multiple sources of such add or multiply? The way I'm trying to make sense of it now is that it acts as a multiplicative factor which grows additively if the game takes your post-calculation damage dealt and applies it to the enemy as the base damage to which defenses and debuffs apply, and then this (eg shock) debuff sums sources in the usual way for modifiers with the "% increased damage" language. Is that correct? If not, do you know the correct model for reasoning like this or is the language opaque and one just has to learn the specific rules for each mechanic?
What about Hindered Capabilities, "30% increased Damage with Hits against Hindered enemies"? It reads to me like it applies at the source of the damage (you) and is additive with other "increased damage" effects. Do I have that right, or is it multiplicative? If the latter does it add or multiply with eg. shock?
Thanks for the help!
Comments
It's right. As with all other increase mods that have their own application terms. Increased attack speed is a multiplier with increased damage and increased crit. More or less.
Increased damage taken is the same. So all instances of increased damage taken are additive with each other and multiplicative with your stack of axis
Damage taken is a multiplier that is additive with effects like shock.
I believe "increased damage taken by target" is the only time the word "increase" is used despite being a multiplier. Someone correct me if I'm wrong. (Unless you want to count "increase/decrease target resistance/armor)
If it says a target take increased damage like shock then it's multiplicative, anything else it's additive. Which is why shock is very powerful and this works for enemies too, so if you are shocked then you just taking 20% more damage of everything and in poe 1, shock was one of the deadliest things and shock immunity was basically mandatory because it was 50% more damage
This is a combination of two rules that interact in a way that is logical, but not necessarily obvious.
When your outgoing damage is calculated, all the "increased" modifiers are summed together.
However, when a target takes damage, the first step of THAT calculation is "figure out the total incoming damage", which obviously means by that step, all of YOUR increased modifiers have already been multiplied with everything else to get you a total outgoing number.
So the process repeats, with all of the *targets "increased and reduced" damage taken effects being summed together, and then all of the "take more damage" and "take less damage" effects being multiplied separately.
modifiers to "reduced/increased damage" are additive with themselves
modifiers to "enemies take reduced/increased damage" are additive with themselves
but these two are multiplicative with each other
Increased damage dealt and increased damage taken fundamentally function the same way, they're just applied at different steps of damage calculation. PoE uses "increased" to signify that a modifier is summed with other applicable effects. This means that all your effects like "increased lightning damage", "increased damage with hits against hindered enemies", and "increased spell damage" would be summed together to calculate how much your base damage is increased by during damage calculation. Separately, effects that apply to the damage taken by a target are also summed, such as shock, increased damage taken, and wither. Because these effects are applied during a separate step of damage calculation, they are effectively multiplicative with your other sources of damage scaling (since they apply after your outgoing damage was calculated) but they are still "increased" modifiers and therefore are summed with one-another for the sake of damage calculation.
To put it another way (ignoring defenses and irrelevant other effects):
Base damage * sum_of_increased_damage * more_damage1 * more_damage2 ... = Outgoing Damage
Outgoing Damage * sum_of_increased_damage_taken = Damage taken by the enemy.
It’s best to think of it as Shock is multiplicative. The passive skill is not.
The reason is that “increased damage done” is a stat that sums together. 30% increased damage vs burning and 30% increased damage for attacks = 60% increased damage with an attack vs a burning target
and “increased damage taken” is also stat that sums together. 30% shock and 30% shock mean 60% increased damage taken
But the damage formula is
(Base * sum(gain)) * product(more) * sum(increased) = hit dmg
Hit dmg determines affliction threshold calcs and such.
And final dmg is
Hit dmg * resistances or armor reduction * increased or decreased dmg taken
Since you simply get far less sources of “increased damage taken” to apply to enemies it’s easy enough to think of it as a multiplier since you probably only have one. And if you have 2 then 1.3*1.3 = 1.69 which is close enough to 1.6 that it’s not the end of the world if you multiply them together to do your math even if you shouldn’t.(and if you’re treating them as a multiplier you’re probably just doing napkin math anyway so the error is even less important) But 10 stacks of 10% increased and 2 30% increase is 160% increased (and if you multiplied them together improperly you would get 338% total increased which over estimates by almost double)