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Damage Resistance: Difference between revisions

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{{Stub}}
'''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.
'''Damage Resistance''' refers to the Bullet and Spirit Resist statistics which reduce incoming damage taken.


Bullet Resist reduces all weapon (such as bullets/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.


Resistances from [[Level|Power Increase]]s seems to act strangely and requires more research.
The Bullet Resistance and Spirit Resistance stats are also sometimes referred to as "Bullet Armor" and "Spirit Armor".


== Stacking Resistances ==
== Starting Damage Resistance ==
Resistances from multiple sources are multiplicative with each other.
Most [[Hero|Heroes]] have no starting damage resistance. However, there are a few exceptions:


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


For example, multiple sources of Bullet 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.


=== Spirit Damage Resistance ===
* {{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.
=== Headshot Critical Damage Resistance ===
* {{PageRef|name=Seven}} has 35% headshot critical damage resistance.
* {{PageRef|name=Mo & Krill}} have 20% headshot critical damage resistance (Mo's head only).
== 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]]  
* 60% Bullet Resist from Viscous' [[Viscous#(4)_Goo_Ball|Goo Ball]]  
* 40% Bullet Resist from the [[Colossus]] [[Items|Item]] results in:
* 40% Bullet Resist from the [[Colossus]] [[Items|Item]] results in:


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


==Resistance Reduction==
==Resistance Reduction==
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<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 - 0.7) * (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:


==Notes==
* 30% resist= 70% of the damage from the weapon or ability.
Resistances can go negative, and this multiplies the damage taken of that type.  
* 0% resist = 100% of the damage from the weapon or ability.
* -30% resist = 130% of the damage from the weapon or ability.


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


-30% resist = 130% of the damage from the weapon or ability.
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>


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}}
==Graphs==
[[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 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].


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


=== Bullet Resist Reduction on enemies ===
=== Bullet Resist Reduction ===
{{Item stat table|Bullet Resist Reduction}}
{{Item stat table|Bullet Resist Reduction}}
=== Melee Resist ===
{{Item stat table|Melee Resist}}


=== Spirit Resist ===
=== Spirit Resist ===
{{Navbox
{{Item stat table|Spirit Resist}}
|list1={{ItemBox|item_name = Pristine Emblem}}{{ItemBox|item_name = Frenzy}}
 
|list2={{ItemBox|item_name = Healing Booster}}{{ItemBox|item_name = Spirit Armor}}{{ItemBox|item_name = Restorative Locket}}{{ItemBox|item_name = Improved Spirit Armor}}{{ItemBox|item_name = Colossus}}{{ItemBox|item_name = Unstoppable}}
=== Spirit Resist Reduction ===
|list3={{ItemBox|item_name = Mystic Vulnerability}}
{{Item stat table|Spirit Resist Reduction}}
{{ItemBox|item_name = Cold Front}}
{{ItemBox|item_name = Escalating Exposure}}
{{ItemBox|item_name = Mystic Reverb}}
{{ItemBox|item_name = Refresher}}|title=[[Items]]|titlestyle=text-align:center;background-color:#ffefd7}}


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