Editing Damage Resistance

'''Damage Resistance''' refers to the Bullet, Melee, and Spirit Resist statistics which reduce incoming damage taken. Bullet Resist reduces all weapon and melee damage, Melee Resist reduces only melee damage, while Spirit Resist reduces all spirit damage.

Most resistances stack diminishingly with each additional resistance source having reduced effect. Resistance Reduction is applied to the final resistance, and if stacked separately and diminishingly.

The Bullet Resistance and Spirit Resistance stats are also sometimes referred to as "Bullet Armor" and "Spirit Armor".

== Melee Resist ==
Melee Resist is a special case of Bullet Resist that is stacked diminishingly along with Bullet Resist to reduce all incoming melee damage. This includes all "melee" abilities such as [[Viscous#Abilities|Viscous]] Puddle Punch ability.

== Math ==
Despite being presented in-game as +x% Bullet, Melee, or Spirit Resist, multiple sources of resist stack multiplicatively, not additively. 

The formula for resist is: <math>BR_f = \left\lceil 1 - \prod_{i=1}^n (1 - BR_i) \right\rceil</math><br />
where:<br />
<math>
\begin{align}
  BR_f &= \text{final bullet resist,} \\
  n &= \text{number of bullet resist sources,} \\
  BR_n &= \text{bullet resist value} \\
\end{align}
</math>

For example, multiple sources of Bullet Resist:
* 60% Bullet Resist from Viscous' [[Viscous#(4)_Goo_Ball|Goo Ball]] 
* 40% Bullet Resist from the [[Colossus]] [[Items|Item]] results in:

<math>1 - (1 - 0.6) * (1 - 0.4) = 76% \text{ Bullet Resist}</math>

==Resistance Reduction==
Resistance Reduction refers to any negative amount of Resist, making the target take increased damage.

Resistance Reduction is calculated multiplicatively like resistance, but then simply subtracted from the resistance amount.

<math>\mathit{Displayed Resist} = [1 - (1 - \mathit{Resistance 1}) * (1 - \mathit{Resistance 2}) * ... * (1 - \mathit{Resistance N})] - [1 - (1 - \mathit{ResReduct.1}) * (1 - \mathit{ResReduct.2})* ... * (1 - \mathit{ResReduct.N})]</math>

For example, using Bullet Resists and Reductions:

* 70% Spirit Resist from Viscous' [[Viscous#(4) Goo Ball|Goo Ball]]
* 20% Spirit Resist from [[Spirit Armor]]
* -12% Spirit Resist from [[Spirit Strike]]
* -12% Spirit Resist from [[Mystic Vulnerability]]
* -24% Spirit Resist from [[Crippling Headshot]]

<math>[1 - (1 - 0.7) * (1 - 0.2)] -[1 - (1-0.12)*(1-0.12)*(1-0.24)] =  \mathit 35% Spirit Resist</math>

The final Resistance can go negative, and this multiplies the damage taken of that type. For example:

* 30% resist= 70% of the damage from the weapon or ability.
* 0% resist = 100% of the damage from the weapon or ability.
* -30% resist = 130% of the damage from the weapon or ability.

Items like [[Headshot Booster]] grant a flat added bullet damage, this bonus damage is not multiplied by weapon damage but is subject to resistance reduction/increase in damage.

Even Resistance from [[Level#Power Increases]] is multiplicative. For example, [[Bebop]]'s base Resistance is {{#invoke:HeroData|get_hero_var|Bebop|BulletArmorDamageReduction}}%, while he gains 1.25% Resist per Power Increase. After 14 Power Increases, Bebop's total resistance will be
<math>0.1 + 1 - (1-0.0125)^{14} = 26.2%</math>

==Effective Health==
{{Construction}}
[[File:Resistance-graph.png|thumb|A graph showing how despite the resistance percentage not growing additively, it scales the player's effective health additively.]]
''Include graph of effective health as a function of Damage Reduction.'' In the mean time, feel free to refer to this [https://www.desmos.com/calculator/97vhqmutyz Desmos graph].

''Include graph of effective damage increase from using 15%, 30%, and 45% Resistance Reduction as a function of the target's original Damage Reduction.'' In the mean time, feel free to refer to this [https://www.desmos.com/calculator/u7dkpebmm7 Desmos graph].

== Sources of Damage Resistance ==
=== Bullet Resist ===
{{Item stat table|Bullet Resist}}
* {{ItemIcon|Monster Rounds}} increases Bullet Resist vs. NPCs by +30%. 
* {{ItemIcon|Escalating Resilience}} increases Bullet Resist by 2% per [[stack]] per shot when hitting enemy heroes, maxing at 40% Bullet Resist.

=== Bullet Resist Reduction ===
{{Item stat table|Bullet Resist Reduction}}

=== Melee Resist ===
{{Item stat table|Melee Resist}}

=== Spirit Resist ===
{{Item stat table|Spirit Resist}}

=== Spirit Resist Reduction ===
{{Item stat table|Spirit Resist Reduction}}

{{Stat navbox}}
[[Category:Mechanics]]
[[Category:Damage Calculation]]