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Melee Resist is a special case of Bullet Resist that stacks diminishingly alongside it to reduce all incoming melee damage. This includes all 'melee' abilities such as {{HeroIcon|Viscous}}' {{AbilityIcon|Puddle Punch}} ability.
Melee Resist is a special case of Bullet Resist that stacks diminishingly alongside it to reduce all incoming melee damage. This includes all 'melee' abilities such as {{HeroIcon|Viscous}}' {{AbilityIcon|Puddle Punch}} ability.


== Math ==
== Calculation ==
Despite being presented in-game as +x% Bullet, Melee, or Spirit Resist, multiple sources of resist stack multiplicatively, not additively.  
While items often display resistance as a flat percentage (e.g., +20% Resist), multiple sources of resistance do not simply add together. Instead, they stack '''multiplicatively'''.


The formula for resist is: <math>BR_f = \left\lceil 1 - \prod_{i=1}^n (1 - BR_i) \right\rceil</math><br />
=== Calculating Resistance ===
where:<br />
To find your total resistance, use the following formula:
<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:
<math>\text{Total Resist} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>
* 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>
'''Example:'''
If you have two sources of resistance, one providing '''40%''' and another providing '''20%''':
# Convert percentages to decimals: 0.40 and 0.20.
# Subtract from 1: (1 - 0.40) = '''0.60''' and (1 - 0.20) = '''0.80'''.
# Multiply the remainders: 0.60 × 0.80 = '''0.48'''.
# Subtract from 1: 1 - 0.48 = '''0.52'''.
# Your Total Resist is '''52%'''.


==Resistance Reduction==
=== Calculating Resistance Reduction ===
Resistance Reduction refers to any negative amount of Resist, making the target take increased damage.
'''Resistance Reduction''' (often called "shred") acts as a counter to resistance. It is calculated separately using the same multiplicative formula, and then subtracted from the target's resistance.


Resistance Reduction is calculated multiplicatively like resistance, but then simply subtracted from the resistance amount.
<math>\text{Final Resist} = \text{Total Resistance} - \text{Total Reduction}</math>


<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>
'''Example:'''
A target has '''52%''' Total Resistance (as calculated above). You attack them with two sources of Reduction: one providing '''25%''' and another providing '''20%'''.


For example, using Bullet Resists and Reductions:
'''Step 1: Calculate Total Reduction'''
<math>1 - (1 - 0.25) \times (1 - 0.20) = 0.40 \rightarrow \mathbf{40\%}</math>


* 70% Spirit Resist from Viscous' [[Viscous#(4) Goo Ball|Goo Ball]]
'''Step 2: Subtract Reduction from Resistance'''
* 20% Spirit Resist from [[Spirit Armor]]
<math>52\% - 40\% = \mathbf{12\%}</math>
* -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 target has a final effective Resist of only '''12%'''.


The final Resistance can go negative, and this multiplies the damage taken of that type. For example:
=== Negative Resistance ===
If the Total Reduction is higher than the Total Resistance, the final value will be negative. This acts as a damage amplifier.


* 30% resist= 70% of the damage from the weapon or ability.
* '''30% Resist:''' You take '''70%''' of incoming damage.
* 0% resist = 100% of the damage from the weapon or ability.
* '''0% Resist:''' You take '''100%''' of incoming damage (True Damage).
* -30% resist = 130% of the damage from the weapon or ability.
* '''-30% Resist:''' You take '''130%''' of incoming damage.


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.
== Effective Health ==
 
==Effective Health==
{{Construction}}
{{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.]]
[[File:Resistance-graph.png|thumb|A graph showing how despite the resistance percentage not growing additively, it scales the player's effective health additively.]]
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