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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.
'''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 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.
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.
{{#ev:youtube|kOg7Q-OLwwQ|360|description=Video explaining Damage Resistance}}


== Resistance types ==
The Bullet Resistance and Spirit Resistance stats are also sometimes referred to as "Bullet Armor" and "Spirit Armor".
=== 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:
== Starting Damage Resistance ==
{{AbilityTable|weapondamage}}
Most [[Hero|Heroes]] have no starting damage resistance. However, there are a few exceptions:


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


=== Melee Resist ===
* {{PageRef|name=Bebop}} has {{#invoke:HeroData|get_hero_var|Bebop|BulletResist|3}}% bullet damage resistance.
* {{PageRef|name=McGinnis}} has {{#invoke:HeroData|get_hero_var|McGinnis|BulletResist|3}}% bullet damage resistance.
* {{PageRef|name=Dynamo}} has no starting bullet damage resistance, but he gains 1% on each level-up.


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


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.
* {{PageRef|name=Kelvin}} and {{PageRef|name=Lash}} have {{#invoke:HeroData|get_hero_var|Lash|TechResist|3}}% spirit damage resistance.
* {{PageRef|name=Pocket}} and {{PageRef|name=Trapper}} have {{#invoke:HeroData|get_hero_var|Pocket|TechResist|3}}% spirit damage resistance (they take 15% more spirit damage).
* {{PageRef|name=Bebop}} has no starting spirit damage resistance, but he gains 1% on each level-up.


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


=== Crit Reduction ===
* {{PageRef|name=Seven}} has 35% headshot critical damage 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.
* {{PageRef|name=Mo & Krill}} have 20% headshot critical damage reduction (Mo's head only).


== Starting Damage Resistance ==
== Melee Resist ==
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.
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.


Note: Negative values indicate that the hero receives increased damage.
== Math ==
Despite being presented in-game as +x% Bullet, Melee, or Spirit Resist, multiple sources of resist stack multiplicatively, not additively.  


{{#invoke:HeroDataArrays|heroDamageResistTable}}
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>


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


=== Calculating Resistance ===
<math>1 - (1 - 0.6) * (1 - 0.4) = 76% \text{ Bullet Resist}</math>
To find your total resistance, use the following formula:


<math>\text{Total Resist} = 1 - (1 - R_1) \times (1 - R_2) \dots</math>
==Resistance Reduction==
Resistance Reduction refers to any negative amount of Resist, making the target take increased damage.


'''Example:'''
Resistance Reduction is calculated multiplicatively like resistance, but then simply subtracted from the resistance amount.
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 ===
<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>
'''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.


<math>\text{Final Resist} = \text{Total Resistance} - \text{Total Reduction}</math>
For example, using Bullet Resists and Reductions:


'''Example:'''
* 70% Spirit Resist from Viscous' [[Viscous#(4) Goo Ball|Goo Ball]]
A target has '''52%''' Total Resistance (as calculated above). You attack them with two sources of Reduction: one providing '''25%''' and another providing '''20%'''.
* 20% Spirit Resist from [[Spirit Armor]]
* -12% Spirit Resist from [[Spirit Strike]]
* -12% Spirit Resist from [[Mystic Vulnerability]]
* -24% Spirit Resist from [[Crippling Headshot]]


'''Step 1: Calculate Total Reduction'''
<math>[1 - (1 - 0.7) * (1 - 0.2)] -[1 - (1-0.12)*(1-0.12)*(1-0.24)] =  \mathit 35% Spirit Resist</math>
<math>1 - (1 - 0.25) \times (1 - 0.20) = 0.40 \rightarrow \mathbf{40\%}</math>


'''Step 2: Subtract Reduction from Resistance'''
The final Resistance can go negative, and this multiplies the damage taken of that type. For example:
<math>52\% - 40\% = \mathbf{12\%}</math>


The target has a final effective Resist of only '''12%'''.
* 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.


=== Negative Resistance ===
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.
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.
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
* '''0% Resist:''' You take '''100%''' of incoming damage (True Damage).
<math>0.1 + 1 - (1-0.0125)^{14} = 26.2%</math>
* '''-30% Resist:''' You take '''130%''' of incoming 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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=== Bullet Resist ===
=== Bullet Resist ===
{{Item stat table|Bullet Resist}}
{{Item stat table|Bullet Resist}}
* {{ItemIcon|Monster Rounds}} increases Bullet Resist vs. NPCs by +{{#invoke:ItemData|get_prop|Monster Rounds|NonPlayerBulletResist}}.  
* {{ItemIcon|Monster Rounds}} increases Bullet Resist vs. NPCs by +30%.  
* {{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.
* {{ItemIcon|Escalating Resilience}} increases Bullet Resist by 2% per [[stack]] per shot when hitting enemy heroes, maxing at 40% Bullet Resist.


=== Bullet Resist Reduction ===
=== Bullet Resist Reduction ===
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{{Item stat table|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}}
{{Stat navbox}}
[[Category:Damage Calculation]]
[[Category:Damage Calculation]]
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