Damage Resistance: Difference between revisions

Revision as of 04:13, 13 November 2024

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 diminishingly with each additional resistance source having reduced effect. Resistance Reduction is applied to the final resistance, and if stacked separately and diminishingly.

The Bullet Resistance and Spirit Resistance stats are also sometimes referred to as "Bullet Armor" and "Spirit Armor".

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 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: $B R_{f} = ⌈ 1 - \prod_{i = 1}^{n} (1 - B R_{i}) ⌉$
where:
$\begin{aligned} B R_{f} & = final bullet resist, \\ n & = number of bullet resist sources, \\ B R_{n} & = bullet resist value \end{aligned}$

For example, multiple sources of Bullet Resist:

60% Bullet Resist from Viscous' Goo Ball
40% Bullet Resist from the Colossus Item results in:

$1 - (1 - 0.6) * (1 - 0.4) = 76 % Bullet Resist$

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.

$D i s p l a y e d R e s i s t = [1 - (1 - R e s i s t a n c e 1) * (1 - R e s i s t a n c e 2) * . . . * (1 - R e s i s t a n c e N)] - [1 - (1 - R e s R e d u c t . 1) * (1 - R e s R e d u c t . 2) * . . . * (1 - R e s R e d u c t . N)]$

For example, using Bullet Resists and Reductions:

70% Spirit Resist from Viscous' 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

$[1 - (1 - 0.7) * (1 - 0.2)] - [1 - (1 - 0.12) * (1 - 0.12) * (1 - 0.24)] = 35 % S p i r i t R e s i s t$

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.

Even Resistance from Level#Power Increases is multiplicative. For example, Bebop's base Resistance is 0%, while he gains 1.25% Resist per Power Increase. After 14 Power Increases, Bebop's total resistance will be $0.1 + 1 - (1 - 0.0125)^{14} = 26.2 %$

Effective Health

“Alright buddy, give 'em hell!”

This page is under construction. To avoid edit conflicts, please consult the edit history and the talk page.

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 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 Desmos graph.

Sources of Damage Resistance

Bullet Resist

List of items
Name	Cost	Category	Stat change
Close Quarters	500	Weapon	+4% Bullet Resist
Berserker	1,250	Weapon	+8% Bullet Resist
Swift Striker	1,250	Weapon	-5% Bullet Resist
Escalating Resilience	3,000	Weapon	+2% Bullet Resist
Warp Stone	3,000	Weapon	+30% Bullet Resist
Point Blank	3,500	Weapon	+15% Bullet Resist
Frenzy	7,250	Weapon	+8% Bullet Resist
Melee Lifesteal	500	Vitality	+3% Bullet Resist
Bullet Armor	1,250	Vitality	+26% Bullet Resist
Return Fire	1,750	Vitality	+20% Bullet Resist
Lifestrike	3,500	Vitality	+10% Bullet Resist
Improved Bullet Armor	4,250	Vitality	+50% Bullet Resist
Colossus	6,000	Vitality	+40% Bullet Resist
Siphon Bullets	6,000	Vitality	+18% Bullet Resist
Unstoppable	6,000	Vitality	+15% Bullet Resist
Mystic Reach	500	Spirit	+7% Bullet Resist
Improved Reach	3,500	Spirit	+13% Bullet Resist
Echo Shard	6,000	Spirit	+16% Bullet Resist
Refresher	6,000	Spirit	+16% Bullet Resist

Monster Rounds increases Bullet Resist vs. NPCs by +30%.
Escalating Resilience increases Bullet Resist by 2% per stack per shot when hitting enemy heroes, maxing at 40% Bullet Resist.

Bullet Resist Reduction

List of items
Name	Cost	Category	Stat change
Hunter's Aura	3,000	Weapon	-8% Bullet Resist Reduction
Crippling Headshot	6,000	Weapon	+24% Bullet Resist Reduction
Bullet Resist Shredder	1,250	Spirit	-12% Bullet Resist Reduction
Withering Whip	1,250	Spirit	-12% Bullet Resist Reduction

Melee Resist

List of items
Name	Cost	Category	Stat change
Point Blank	3,500	Weapon	+20% Melee Resist
Titanic Magazine	3,500	Weapon	+30% Melee Resist
Restorative Locket	1,250	Vitality	+25% Melee Resist
Bullet Resist Shredder	1,250	Spirit	+15% Melee Resist
Torment Pulse	3,000	Spirit	+15% Melee Resist

Spirit Resist

List of items
Name	Cost	Category	Stat change
Pristine Emblem	3,500	Weapon	+12% Spirit Resist
Titanic Magazine	3,500	Weapon	+12% Spirit Resist
Silencer	6,000	Weapon	+15% Spirit Resist
Healing Booster	1,250	Vitality	+6% Spirit Resist
Spirit Armor	1,250	Vitality	+22% Spirit Resist
Majestic Leap	3,000	Vitality	+6% Spirit Resist
Improved Spirit Armor	4,250	Vitality	+45% Spirit Resist
Colossus	6,000	Vitality	+40% Spirit Resist
Phantom Strike	6,000	Vitality	+15% Spirit Resist
Cold Front	1,250	Spirit	+10% Spirit Resist
Mystic Vulnerability	1,250	Spirit	+6% Spirit Resist
Ethereal Shift	3,000	Spirit	+40% Spirit Resist
Spirit Snatch	3,500	Spirit	+8% Spirit Resist
Mystic Reverb	6,000	Spirit	+14% Spirit Resist
Refresher	6,000	Spirit	+8% Spirit Resist
Escalating Exposure	7,250	Spirit	+15% Spirit Resist

Spirit Resist Reduction

List of items
Name	Cost	Category	Stat change
Crippling Headshot	6,000	Weapon	+24% Spirit Resist Reduction
Spirit Strike	500	Spirit	-12% Spirit Resist Reduction
Mystic Vulnerability	1,250	Spirit	-12% Spirit Resist Reduction
Spirit Snatch	3,500	Spirit	-12% Spirit Resist Reduction
Escalating Exposure	7,250	Spirit	-12% Spirit Resist Reduction

@@ Line 1: / Line 1: @@
-{{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==
+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.
-Damage Resistance refers to the Bullet and Spirit Resist statistics which reduce incoming damage dealt.
-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".
-% Damage Resistance simply reduces damage taken by 50%, doubling the ''effective'' health pool.
+== 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.
-Resistances from multiple sources are multiplicative with each other.
+== Math ==
+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 />
+<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, 60% Bullet Resist from Viscous' [[Viscous#(4)_Goo_Ball|Goo Ball]] combined with 40% Bullet Resist from the [[Colossus]] [[Items|Item]] results in:
+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% Bullet Resist</math>
+<math>1 - (1 - 0.6) * (1 - 0.4) = 76% \text{ Bullet Resist}</math>
 ==Resistance Reduction==
-Resistance Reduction refers to any negative amount of Bullet Resist, making the target take increased damage. Though, it isn't applied in the same way.
+Resistance Reduction refers to any negative amount of Resist, making the target take increased damage.
-Resistance Reduction is simply added (as negative numbers) from the otherwise final Resistance.
+Resistance Reduction is calculated multiplicatively like resistance, but then simply subtracted from the resistance amount.
-==Formula==
+<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>
-<math>\mathit{Displayed Resist} = 1 - (1 - \mathit{Resistance 1}) * (1 - \mathit{Resistance 2}) * ... * (1 - \mathit{Resistance N}) + \mathit{Resistance Reductions}</math>
-==Example==
 For example, using Bullet Resists and Reductions:
-* 60% Bullet Resist from Viscous' [[Viscous#(4)_Goo_Ball|Goo Ball]]
-* 40% Bullet Resist from [[Colossus]]
-* -5% Bullet Resist from [[Swift Striker]]
-* -12% Bullet Resist from [[Bullet Resist Shredder]]
-<math>1 - (1 - 0.6) * (1 - 0.4) + (-0.05 - 0.12) = 59% Bullet Resist</math>
+* 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]]
-==Graphs==
+<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.
+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>
+==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/zcyaumcpjr 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 +30%.
+* {{ItemIcon|Escalating Resilience}} increases Bullet Resist by 2% per [[stack]] per shot when hitting enemy heroes, maxing at 40% 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}}
+{{Stat navbox}}
+[[Category:Mechanics]]
+[[Category:Damage Calculation]]