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'''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.
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.


Bullet Resist reduces all weapon (such as bullets/melee) damage, while Spirit Resist reduces all spirit damage.
The Bullet Resistance and Spirit Resistance stats are also sometimes referred to as "Bullet Armor" and "Spirit Armor".


Resistances from [[Level|Power Increase]]s seems to act strangely and requires more research.
== 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.


== Stacking Resistances ==
== Math ==
Resistances from multiple sources are multiplicative with each other.
Despite being presented in-game as +x% Bullet, Melee, or Spirit Resist, multiple sources of resist stack multiplicatively, not additively.  


<math>\mathit{Displayed Resist} = 1 - (1 - \mathit{Resistance 1}) * (1 - \mathit{Resistance 2}) * ... * (1 - \mathit{Resistance N})</math>
The formula for resist is: <math>BR_f = \left\lceil 1 - \prod_{i=1}^n (1 - BR_i) \right\rceil</math><br />
 
where:<br />
For example, multiple sources of Bullet Resist
<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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* 20% Spirit Resist from [[Spirit Armor]]
* 20% Spirit Resist from [[Spirit Armor]]
* -12% Spirit Resist from [[Spirit Strike]]
* -12% Spirit Resist from [[Spirit Strike]]
* -12% Spirit Resist from [[Spirit Strike|Mystic Vulnerability]]
* -12% Spirit Resist from [[Mystic Vulnerability]]
* -24% Spirit Resist from [[Crippling Headshot]]
* -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>
<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.


==Notes==
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.
Resistances can go negative, and this multiplies the damage taken of that type.  


30% resist= 70% 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>


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


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


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.
== 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.


==Graphs==
=== Bullet Resist Reduction ===
''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].
{{Item stat table|Bullet Resist Reduction}}


''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].
=== Melee Resist ===
{{Item stat table|Melee Resist}}


== Sources of Bullet Resistance ==
=== Spirit Resist ===
{{Navbox|list1={{ItemBox|item_name = Monster Rounds}}{{ItemBox|item_name = Restorative Shot}}{{ItemBox|item_name = Berserker}}{{ItemBox|item_name = Swift Striker}}{{ItemBox|item_name = Escalating Resilience}}{{ItemBox|item_name = Point Blank}}{{ItemBox|item_name = Titanic Magazine}}{{ItemBox|item_name = Warp Stone}}|list2={{ItemBox|item_name = Bullet Armor}}{{ItemBox|item_name = Lifestrike}}{{ItemBox|item_name = Improved Bullet Armor}}{{ItemBox|item_name = Colossus}}{{ItemBox|item_name = Phantom Strike}} {{ItemBox|item_name = Siphon Bullets}}|list3={{ItemBox|item_name = Mystic Reach}}{{ItemBox|item_name = Bullet Resist Shredder}}{{ItemBox|item_name = Improved Reach}}{{ItemBox|item_name = Echo Shard}}{{ItemBox|item_name = Refresher}}|title=[[Items]]|titlestyle=text-align:center;background-color:#ffefd7}}
{{Item stat table|Spirit Resist}}


== Sources of Spirit Resistance ==
=== Spirit Resist Reduction ===
{{Navbox|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}}|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:Mechanics]]
[[Category:Damage Calculation]]
[[Category:Damage Calculation]]
Retrieved from "https://deadlock.wiki/Damage_Resistance"