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'''Damage Resistance''' refers to the [[Weapon Damage|Bullet]], [[Melee Attack|Melee]], and [[Spirit Power|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. [[Unit]]s have a unique "Damage Resistance" stat that is applied to all sources of damage, including [[Trooper]]s.

Most resistances stack multiplicatively; they are not added together. Sources of Resistance Reduction are multiplied together separately first. The total reduction is then subtracted from the total resistance. This has the consequence of resistance reduction being more effective on targets with higher resistance.
{{#ev:youtube|kOg7Q-OLwwQ|360|description=Video explaining Damage Resistance}}

== Resistance types ==
=== Bullet Resist ===
Bullet Resist reduces all incoming [[Weapon Damage]], including from abilities. [[Troopers]], [[Guardians]], [[Neutrals]] and the [[Mid-Boss]] deal weapon damage.

List of abilities that deal weapon damage:
{{AbilityTable|weapondamage}}

=== Spirit Resist ===
Spirit Resist reduces all incoming [[Spirit Damage]]. Most abilities and items deal spirit damage, as well as [[Walkers]], [[Shrines]], and the [[Patron]].

=== Melee Resist ===

Melee Resist reduces all incoming [[Melee Damage]], including from abilities. 

In addition to Melee Resist gained from items, Bullet Resist affects all Weapon Damage, granting another source of resistance against Melee Damage. The only exception is {{HeroIcon|Venator}}'s innate Spirit-scaled Bullet Resist, although this is likely a bug.

List of abilities that deal melee damage:
{{AbilityTable|Melee|hide=Light Melee Scaling,Notes}}

=== Crit Reduction ===
Crit Reduction is a stat that reduces the critical damage (headshots) received by the hero. Not to be confused with [[Weapon Damage#Crit Multiplier|Crit Bonus Scale]], a stat that reduces the critical damage dealt by the hero to other targets.

Crit Reduction is an innate stat to balance heroes with large head hitboxes, and cannot be modified by items or abilities.

== Starting Damage Resistance ==
The following [[Hero|Heroes]] either have starting Damage Resistance values or gain resistance with [[Boon|Boons]] or [[Spirit Power]]. Boon and Spirit scaling resistances stack additively.

Note: Negative values indicate that the hero receives increased damage.

{{#invoke:HeroDataArrays|heroDamageResistTable}}

== 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.

==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 +{{#invoke:ItemData|get_prop|Monster Rounds|NonPlayerBulletResist}}. 
* {{ItemIcon|Escalating Resilience}} increases Bullet Resist by {{#invoke:ItemData|get_prop|Escalating Resilience|BulletResistPerStack}} per [[stack]] per shot when hitting enemy heroes, maxing at {{#invoke:ItemData|get_prop|Escalating Resilience|MaxArmorStacks}} 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}}

* {{ItemIcon|Spirit Rend}} reduces {{#invoke:ItemData|get_prop|Spirit Rend|TechArmorDamageReduction}} spirit resist on bullet hit from its component {{ItemIcon|Spirit Shredder Bullets}}, as well as an additional {{#invoke:ItemData|get_prop|Spirit Rend|MagicResistReduction}} spirit resist reduction per stack on headshots, up to a max of 4 stacks (-33% spirit resist total).
{{Stat navbox}}
[[Category:Damage Calculation]]
@@ Line 35: / Line 35: @@
 {{#invoke:HeroDataArrays|heroDamageResistTable}}
-== Calculation ==
+== Math ==
-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'''.
+Despite being presented in-game as +x% Bullet, Melee, or Spirit Resist, multiple sources of resist stack multiplicatively, not additively.
-=== Calculating Resistance ===
+The formula for resist is: <math>BR_f = \left\lceil 1 - \prod_{i=1}^n (1 - BR_i) \right\rceil</math><br />
-To find your total resistance, use the following formula:
+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>
-<math>\text{Total Resist} = 1 - (1 - R_1) \times (1 - R_2) \dots</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:
-'''Example:'''
+<math>1 - (1 - 0.6) * (1 - 0.4) = 76% \text{ Bullet Resist}</math>
-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%'''.
-=== Calculating Resistance Reduction ===
+==Resistance Reduction==
-'''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 refers to any negative amount of Resist, making the target take increased damage.
-<math>\text{Final Resist} = \text{Total Resistance} - \text{Total Reduction}</math>
+Resistance Reduction is calculated multiplicatively like resistance, but then simply subtracted from the resistance amount.
-'''Example:'''
+<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>
-A target has '''52%''' Total Resistance (as calculated above). You attack them with two sources of Reduction: one providing '''25%''' and another providing '''20%'''.
-'''Step 1: Calculate Total Reduction'''
+For example, using Bullet Resists and Reductions:
-<math>1 - (1 - 0.25) \times (1 - 0.20) = 0.40 \rightarrow \mathbf{40\%}</math>
-'''Step 2: Subtract Reduction from Resistance'''
+* 70% Spirit Resist from Viscous' [[Viscous#(4) Goo Ball|Goo Ball]]
-<math>52\% - 40\% = \mathbf{12\%}</math>
+* 20% Spirit Resist from [[Spirit Armor]]
+* -12% Spirit Resist from [[Spirit Strike]]
+* -12% Spirit Resist from [[Mystic Vulnerability]]
+* -24% Spirit Resist from [[Crippling Headshot]]
-The target has a final effective Resist of only '''12%'''.
+<math>[1 - ((1 - 0.7) * (1 - 0.2))] -[1 - ((1-0.12)*(1-0.12)*(1-0.24))] =  \mathit 35% Spirit Resist</math>
-=== Negative Resistance ===
+The final Resistance can go negative, and this multiplies the damage taken of that type. For example:
-If the Total Reduction is higher than the Total Resistance, the final value will be negative. This acts as a damage amplifier.
-* '''30% Resist:''' You take '''70%''' of incoming damage.
+* 30% resist= 70% of the damage from the weapon or ability.
-* '''0% Resist:''' You take '''100%''' of incoming damage (True Damage).
+* 0% resist = 100% of the damage from the weapon or ability.
-* '''-30% Resist:''' You take '''130%''' of incoming damage.
+* -30% resist = 130% of the damage from the weapon or ability.
-== Effective Health ==
+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==
 {{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.]]