# Damage Formula

## General Formula for Damage​

$\text{DMG} = (\Sigma(\text{Base DMG} \times \text{BaseDMGMultiplier}) + \text{AdditiveBaseDMGBonus}) \\ \times (1 + \text{DMGBonus} - \text{DMGReduction} {\text{Target}}) \\ \times \text{CRIT} \times \text{EnemyDefMult} \times \text{EnemyResMult} \\ \times \text{AmplifyingReaction} + \text{TransformativeReaction} + \text{Proc} \\$

See the sections below for the breakdown of each individual part of the formula.

## Base Damage​

$\text{Base DMG} = \begin{cases} \text{Talent\%} \times \text{ATK} & \text{if, Talent scales with ATK} \\ \text{Talent\%} \times \text{DEF} & \text{if, Talent scales with DEF} \\ \text{Talent\%} \times \text{Max HP} & \text{if, Talent scales with Max HP} \\ \text{Talent\%} \times \text{EM} & \text{if, Talent scales with EM} \end{cases}$
$\text{ATK} = (\text{AttackCharacter} + \text{AttackWeapon}) \times (1 + \text{AttackBonus}) + \text{FlatAttack}$
$\text{DEF} = \text{DefenseCharacter} \times (1 + \text{DefenseBonus}) + \text{FlatDefense}$
$\text{Max HP} = \text{HealthCharacter} \times (1 + \text{HealthBonus}) + \text{FlatHealth}$
Formula VariableExplanation
Talent%The scaling percentage of the Talent.
AttackCharacterCharacter's Base ATK.
AttackWeaponWeapon's Base ATK.
AttackBonusSum of all percentage-based ATK Bonuses from weapons, artifacts, and other sources.
FlatAttackSum of all non-percentage-based ATK Bonuses from artifacts, and other sources.
DefenseCharacterCharacter's Base DEF.
DefenseBonusSum of all percentage-based defense bonuses from artifacts, weapons, and other sources.
HealthCharacterCharacter's Base HP.
HealthBonusSum of all percentage-based HP bonuses from artifacts, weapons, and other sources
EMSum of all Elemental Mastery from ascension stat, weapons, artifacts, and other sources.
DMGBonusSum of all percentage damage increases from goblets, weapons, set bonuses and other buffs. Excludes Xingqiu's C4 and Yoimiya's Elemental Skill.
BaseDMGMultiplierApplies to certain character Talents only. See the Special Multiplier section for full details.

Talents and Constellations

Talents:

Constellations:

Weapons
Artifacts
Reactions

## Critical Hits​

$\text{CRIT} = \begin{cases} 1 + \text{CRITDamage} & \text{if, CRIT} \\ 1 & \text{otherwise} \end{cases}$
$\text{AverageCrit} = 1 + \text{clamp}\{0\%, \text{CRITRate}, 100\% \} \times \text{CRITDamage}$
Formula VariableExplanation
CRITRateThe total CRIT Rate, including the 5% base CRIT Rate and bonuses from weapons, artifacts, etc.
CRITDamageThe total CRIT DMG, including the 50% base CRIT DMG and bonuses from weapons, artifacts, etc.

## Enemy Defense​

$\text{EnemyDefMult} = \frac {\text{Level}_{\text{Character}} + 100} {(\text{Level}_{\text{Character}} + 100) + (\text{Level}_{\text{Enemy}} + 100) \times (1 - \text{DefReduction}) \times (1 - \text{DefIgnore})}$
Formula VariableExplanation
LevelCharacterThe player character's level.
LevelEnemyThe enemy's level.
DefReductionThe total defense (but not resistance) reduction from various defense reduction effects.
DefIgnoreThe total defense ignore from effects from certain constellations.
• DefReduction is hard capped at 90%

Constellations

### Defense Reduction Sources​

Talents and Constellations

Talents:

Constellations:

## Enemy Resistance​

$\text{EnemyResMult} = \begin{cases} 1 - \frac{\text{Resistance}}{2} & \text{if, } \text{Resistance} \lt 0 \\ 1 - \text{Resistance} & \text{if, } 0 \le \text{Resistance} \lt 0.75 \\ \frac{1}{4 \times \text{Resistance} + 1} & \text{if, } \text{Resistance} \ge 0.75 \end{cases}$
$\text{Resistance} = \text{BaseResistance} - \text{ResistanceReduction}$
Formula VariableExplanation
BaseResistanceThe enemy's base resistance to the Element of the attack being used. Enemy Resistances database contains all enemy base Elemental resistances.
ResistanceReductionThe total resistance reduction of the relevant Element from effects such as Superconduct and Viridescent Venerer.

## Base DMG Multiplier​

Unlike other bonuses, these are directly multiplicative with base Talent scaling. They can be considered a multiplier of the Talent motion value.

$\text{BaseDMGMultiplier} = \begin{cases} 2 & \text{if, World-Shaker triggered} \\ 1.5 & \text{if, Evilsoother triggered} \\ \text{Talent \%} & \text{if, Niwabi Fire-Dance or Hanega: Song of the Wind triggered} \\ 1 & \text{otherwise} \end{cases}$
Formula VariableExplanation
World-ShakerElectro Traveler's Constellation 6 ability applies a 2 buff to some attacks of their Elemental Burst.
Hanega: Song of the WindWanderer's Elemental Skill applies a scaling buff to his Normal Attacks.
EvilsootherXingqiu’s Constellation 4 ability applies a 1.5 buff to his Elemental Skill.
Niwabi Fire-DanceYoimiya's Elemental Skill applies a scaling buff to her Normal Attacks.

## Amplifying Reaction​

Equals to $1$ if no amplifying reaction is triggered, otherwise:

$\text{AmplifyingReaction} = \text{ReactionMultiplier} \times \biggl(1 + \frac{2.78 \times \text{EM}}{1400 + \text{EM}} + \text{ReactionBonus}\biggr)$
$\text{ReactionMultiplier} = \begin{cases} 2 & \text{if, triggering Vaporize with {\color{4688ff}Hydro} or Melt with {\color{f68f9a}Pyro}}\\ 1.5 & \text{if, triggering Vaporize with {\color{f68f9a}Pyro} or Melt with {\color{7ba4d3}Cryo}}\end{cases}$
Formula VariableExplanation
EMThe character's total Elemental Mastery.
ReactionBonusReaction damage bonuses such as the Crimson Witch 4-Piece set bonus and from Mona's C1 (for Vaporize).

## Transformative Reaction​

\begin{align*} \text{TransformativeReactions} = & \ \text{ReactionMultiplier} \times \text{LevelMultiplier} \times \biggl(1 + \frac{16 \times \text{EM}}{2000 + \text{EM}} + \text{ReactionBonus} \biggr) \\ & \times \text{EnemyResistanceMultiplier} \end{align*}
$\text{ReactionMultiplier} = \begin{cases} 3 & \text{if, triggering {\color{fd9e0d}Burgeon} and {\color{df96fe}Hyperbloom}}\\ 2 & \text{if, triggering {\color{cd7b8d}Overloaded} and {\color{00eb50}Bloom}}\\ 1.5 & \text{if, triggering Shattered}\\ 1.2 \times \text{ECTriggers} & \text{if, triggering {\color{df96fe}Electro-Charged}}\\ 0.6 & \text{if, triggering {\color{5bcba3}Swirl}}\\ 0.5 & \text{if, triggering {\color{b1aeff}Superconduct}}\\ 0.25 & \text{if, triggering {\color{fd9e0d}Burning}}\\ 0 & \text{otherwise} \end{cases}$
Formula VariableExplanation
ECTriggersThe number of times Electro-Charged triggers, and depends on the Elemental Gauge strength of the Hydro and Electro Elements applied to the enemy.
EMThe character's total Elemental Mastery.
ReactionBonusIncludes reaction damage bonuses from the 4-Piece set bonuses of Thundering Fury and Viridescent Venerer, Mona's C1, and Nilou's A4.
LevelMultiplierPlayer level multiplier at Lv. : 1446.85
Enemy/environment level multiplier at Lv. : 1202.81
EnemyResistanceMultiplierUses the Enemy Resistance formula above, but for the Element of the Transformative Reaction (Pyro for Overloaded, Physical for Shattered, Electro for Electro-Charged, Cryo for Superconduct, the Element being Swirled for Swirl, and Dendro for Bloom, Bugeon, and Hyperbloom).

$\text{AdditiveReaction} = \text{ReactionMultiplier} \times \text{LevelMultiplier} \times \biggl(1 + \frac{5 \times \text{EM}}{1200 + \text{EM}} + \text{ReactionBonus}\biggr)$
$\text{ReactionMultiplier} = \begin{cases} 1.25 \ \text{if, triggering {\color{00eb50}Spread}}\\ 1.15 \ \text{if, triggering {\color{df96fe}Aggravate}} \end{cases}$
Formula VariableExplanation
EMThe character's total Elemental Mastery.
ReactionBonusIncludes reaction damage bonus from 4-Piece set bonus of Thundering Fury.
LevelMultiplierPlayer level multiplier at Lv. : 1446.85
Enemy/environment level multiplier at Lv. : 1202.81

## Proc​

The damage dealt by weapon and ability procs when they trigger, such as Prototype Archaic or Xiangling's constellation 2. This is dealt as a separate instance of damage from the attack that triggered it.

To calculate this damage, substitute the proc percentage (e.g. 240% for Prototype Archaic R1) for Talent in the damage formula. Note that weapon proc effects always deal Physical damage, and are therefore affected by Physical damage bonuses and Physical resistance, even if an Elemental attack is used to trigger them.

Characters
Weapons