Damage

When characters or enemies attack their targets, they deal damage (abbreviated as DMG) based on their own and their target's attributes.
There are eight damage types, seven of them are Elemental, one is Physical.
A single instance of damage cannot exceed 9,999,999.
==General Damage Formula==
For DMG dealt by Talents, Constellations, Weapon passives, and enemy attacks, the DMG calculation factors in the following components:
*ATK, DEF, Max HP, or Elemental Mastery depending on the ability
*Ability scaling
*Base DMG Multiplier
*Additive Base DMG Bonus
*DMG Bonus
*DEF of target
*RES of target
*DMG Reduction of target
*Amplifying Reactions
*CRIT Hit
DMG is calculated as:
:\begin{align} \text{DMG} ={} & \big( \Sigma (\text{Base DMG} \times \text{Base DMG Multiplier}) + \text{Additive Base DMG Bonus}\big) \\ & \times \text{DMG Bonus Multiplier} \\ & \times \text{DEF Multiplier}_\text{Target} \times \text{RES Multiplier}_\text{Target} \\ & \times \text{Amplifying Multiplier} \end{align}
If the damage scores a Critical Hit, then the CRIT DMG multiplier will be applied.
:\text{DMG}_\text{CRIT Multiplier} = \text{DMG} \times (1 + \%\text{CRIT DMG})
===Base DMG===
Base DMG is the amount of DMG resulted from multiplying the ability's scaling with the corresponding stat, before accounting for any damage modifiers.
Unless otherwise specified in the skill attributes, abilities will scale with ATK. Some abilities may scale with more than one stat.
:
\text{Base DMG} = \begin{cases}
\% \text{Ability} \times \text{ATK} & \text{if ability scales with ATK}\\
\% \text{Ability} \times \text{DEF} & \text{if ability scales with DEF}\\
\% \text{Ability} \times \text{Max HP} & \text{if ability scales with Max HP}\\
\% \text{Ability} \times \text{EM} & \text{if ability scales with EM}
\end{cases}
===Base DMG Multiplier===
Base DMG Multiplier is directly multiplicative with Base DMG. It can be obtained through:
===Additive Base DMG Bonus===
Additive Base DMG Bonus is a fixed amount of bonus DMG added to the base DMG.
It can be obtained through:
Spread and Aggravate Elemental Reactions
===DMG Bonus===
DMG Bonus refers to all percentage-based DMG bonuses, which include Elemental and Physical DMG Bonuses listed in the stats screen, as well as all other special percentage-based DMG bonuses which may affect Normal/Charged/Plunging Attack, Elemental Skill, Elemental Burst, all DMG, etc. DMG Reduction of the target effectively reduces DMG Bonus.
:\text{DMG Bonus Multiplier} = (1 + \text{DMG Bonus} - \text{DMG Reduction}_\text{Target})
===DEF===
Defense (abbreviated DEF) reduces incoming damage based on the following formula:
:\text{DEF DMG Reduction}=\frac{\text{DEF}}{\text{DEF} + 5 \times \text{Level}_\text{Attacker} + 500}
The incoming damage will then be multiplied by:
:\text{DEF Multiplier}=1 - \text{DEF DMG Reduction}
Alternatively, for enemies only:
*Enemy Defense is given as:
:\text{DEF}_\text{Enemy} = 5 \times \text{Level}_\text{Enemy} + 500
*Enemy Defense multiplier can be calculated as:
:\text{DEF Multiplier} = \frac{\text{Level}_\text{Character} + 100}
 {k \; (\text{Level}_\text{Enemy} + 100) + (\text{Level}_\text{Character} + 100)}
::where k = \left[ 1 - \% \text{ DEF Reduction} \right] \left[ 1 - \% \text{ DEF Ignored} \right]
===RES===
Targets have different Resistances (abbreviated as RES) to Elemental and Physical DMG. There are ways to increase or decrease these resistances. Total RES is calculated as:
:\%\text{RES} = \%\text{RES Base} + \%\text{RES Bonus} - \% \text{RES Debuffs}
The RES multiplier varies non-linearly with the RES percentage. Depending on the value of \% \text{RES} in the interval below, the corresponding \text{RES Multiplier} is as follows:
Formula 	Interval
1 - \biggl( \frac{\mathsf{RES}}{2} \biggr)	RES < 0
1 - \mathsf{RES} 	0 ≤ RES < 0.75
\frac{1}{4 \times \mathsf{RES} + 1} 	RES ≥ 0.75
For example, an enemy with 10% RES (i.e., 0.1) will have a 1 - 0.1 = 0.9 RES multiplier.
For a table of enemy RES, see Resistance#Enemy RES.
==Elemental Reaction Damage==
Elemental Reactions may be categorized into three groups:
* Transformative Reactions that deal additional elemental damage, calculated separately, when triggered
* Amplifying Reactions that increase damage by adding a damage multiplier ("Amplifying Multiplier") to the hit that triggered the reaction
* Catalyze Reactions that increase damage by adding an Additive Base DMG Bonus to the hit that triggered the reaction
Note that triggering multiple reactions in quick succession can cause the reaction's pop-up text to be hidden by the game, even though the reaction occurred and dealt damage successfully.
===Transformative Reaction Damage===
The transformative reactions are Overloaded, Shattered, Electro-Charged, Superconduct, Swirl, Burning, Bloom, Hyperbloom, and Burgeon.
The damage dealt by such reactions scales with the triggering party's level and Elemental Mastery (EM), and is reduced by the target's Resistances. Unlike normal damage, this damage is not based on the triggering party's ATK, cannot score CRIT Hits by default, and ignores target's DEF.Transformative Reactions do have a DMG multiplier based on DEF:\text{DEF Multiplier}_\text{Transformative} = \frac{99999999}{99999999 + \text{DEF}_\text{Target}}However, the difference it causes is so extremely minuscule that it is usually ignored.
Certain effects such as the 4-piece set bonuses of the Crimson Witch of Flames and Thundering Fury Artifact sets can also increase the reaction damage (% Reaction Bonus).
Additionally, the stats of the party that applies the initial element do not affect the reaction damage; the only party taken into account is the one that applies the second element (or third element with Hyperbloom, Burgeon) which triggers the reaction.
Transformative Reaction DMG is calculated as:
:\begin{align}\text{DMG}_\text{Transformative} = & \text{ Reaction Multiplier} \times \text{Level Multiplier}_\text{Attacker}
\\ & \times (1 + \% \text{ EM Bonus}_\text{Transformative} + \% \text{ Reaction Bonus})
\\ & \times \text{RES Multiplier}_\text{Target}
\end{align}
:\text{Reaction Multiplier} = \begin{cases}\begin{align}
0.25 &\text{, for Burning } \\
0.6 &\text{, for Swirl } \\
1.5 &\text{, for Superconduct } \\
2.0 &\text{, for Electro-Charged } \\
2.0 &\text{, for Bloom } \\
2.75 &\text{, for Overloaded } \\
3.0 &\text{, for Burgeon } \\
3.0 &\text{, for Hyperbloom } \\
3.0 &\text{, for Shatter } \\
\end{align}\end{cases}
If the damage scores a Critical Hit, the CRIT DMG multiplier is also applied.This is currently only achievable with Nahida's 2nd Constellation.
:\text{DMG}_\text{CRIT} = \text{DMG} \times (1 + \%\text{CRIT DMG})
The amount of EM can also increase the damage of transformative reactions by a certain percentage (% EM Bonus). (See Elemental Mastery for more details.) EM Bonus is calculated as:
:\% \text{EM Bonus}_\text{Transformative} = 16 \times \frac{\text{EM}}{\text{EM} + 2000} \times 100 \%
It is possible for transformative reactions that further apply an element (Swirl and Burning) to further trigger amplifying reactions. For example, when is applied to a target affected by , a Pyro Swirl is triggered and this can hit nearby targets that are affected by . In this case, the amplifying reaction adds an additional multiplier ("Amplifying Multiplier") to the outgoing damage dealt to the target affected by Hydro, as calculated in the next section.
For the base damages of transformative reactions per Level, see Elemental Reaction/Level Scaling.
===Amplifying Reaction Damage===
The amplifying reactions are Vaporize and Melt. Amplifying reactions add extra multipliers to the damage of the attack that triggered the reaction based on the triggering element and the elemental mastery of the triggering character.
Certain effects such as the 4-piece set bonus of the Crimson Witch of Flames Artifact set can further increase the damage ("Reaction Bonus").
The additional amplifying multiplier is as follows:
:\begin{align}\text{Amplifying Multiplier} = {} &\text{Reaction Multiplier} \\ &\times (1 + \% \text{EM Bonus}_\text{Amplifying} + \% \text{Reaction Bonus}) \end{align}
:\text{Reaction Multiplier} = \begin{cases}\begin{align}
2.0 &\text{, for Melt if } \color{red}\text{Pyro} \color{black}\text{ triggers} \\
1.5 &\text{, for Melt if } \color{skyblue}\text{Cryo} \color{black}\text{ triggers}\\
2.0 &\text{, for Vaporize if } \color{blue}\text{Hydro} \color{black}\text{ triggers} \\
1.5 &\text{, for Vaporize if } \color{red}\text{Pyro} \color{black}\text{ triggers}
\end{align}\end{cases}
This amplifying multiplier increases damage:
:\text{DMG}_\text{Amplified} = \text{DMG} \times \text{Amplifying Multiplier}
where "DMG" may be the damage dealt by Talents, Constellations, enemy attacks, or a Swirl reaction as calculated in the earlier section.
The level of EM can also increase the damage of amplifying reactions by a certain percentage ("% EM Bonus"). (See Elemental Mastery for more details.) This can be approximated as follows:
:\% \text{EM Bonus}_\text{Amplifying} = 2.78 \times \frac{\text{EM}}{\text{EM} + 1400} \times 100 \%
Talents that only apply the elemental status will deal no damage upon triggering an amplifying reaction.
===Catalyze Damage Bonus===
The Spread and Aggravate reactions add Additive Base DMG Bonus to attacks. Similar to transformative reactions, the damage bonus scales with the triggering party's level and Elemental Mastery.
The Additive Base DMG Bonus is calculated as:
:\begin{align}\text{Additive Base DMG Bonus}_\text{Quicken} = {} &\text{Reaction Multiplier} \times \text{Level Multiplier}_\text{Character}
\\ & \times (1 + \% \text{EM Bonus}_\text{Quicken} + \% \text{Reaction Bonus})
\end{align}
:\text{Reaction Multiplier} = \begin{cases}\begin{align}
1.15 &\text{, if } \color{purple}\text{Aggravate} \color{black}\text{ is triggered} \\
1.25 &\text{, if } \color{green}\text{Spread} \color{black}\text{ is triggered}
\end{align}\end{cases}
:\% \text{EM Bonus}_\text{Catalyze} = \frac{5 \times \text{EM}}{\text{EM} + 1200} \times 100 \%
===Swirl/Burning-Induced Reaction Damage===
Unlike most transformative reactions, Swirl and Burning can apply their corresponding elements, and are therefore able to trigger further reactions. DMG will be affected as follows:
For Amplifying Reactions:
:\text{Amplified Swirl/Burning DMG} = \text{Original Swirl/Burning DMG} \times \text{Amplifying Multiplier}
For Aggravate:
:\begin{align} \text{Aggravated Swirl DMG} = {} &(\text{Swirl Factor} + \text{Additive Base DMG Bonus}_\text{Aggravate}) \\ &\times [\text{RES Multiplier}]_\text{Target} \end{align}
:\begin{align} \textsf{where} \quad \text{Swirl Factor} = {} & \text{Reaction Multiplier} \\ &\times \text{Level Multiplier}_\text{Attacker} \\ &\times (1 + \% \text{EM Bonus}_\text{Transformative} + \% \text{Swirl Bonus}) \end{align}
For Transformative Reactions, the same damage calculations in the previous sections is applied.
===Reaction Modifiers===
The following abilities or equipments provide reaction bonuses. These bonuses are additive with the bonuses provided by Elemental Mastery.
Ability 	Icon	Amount 	Reaction
Baizhu: 4th Ascension Passive 	 	Up to +100% 	, ,
Baizhu: 4th Ascension Passive 	 	Up to +40% 	,
Kaveh: Constellation 4 	 	+60% 	
Mona: Constellation 1 	 	+15% 	, ,
Nilou: 4th Ascension Passive 	 	Up to +400% 	
Crimson Witch of Flames: 4-Piece Bonus	 	+40% 	, ,
Crimson Witch of Flames: 4-Piece Bonus	 	+15% 	,
Flower of Paradise Lost: 4-Piece Bonus	 	+40%/+50%/+60%/+70%/+80%	, ,
Thundering Fury: 4-Piece Bonus 	 	+40% 	, , ,
Thundering Fury: 4-Piece Bonus 	 	+20% 	
Viridescent Venerer: 4-Piece Bonus 	 	+60% 	
==True DMG==
True DMGTerm introduced in Version 2.3. is DMG that ignores the target's DEF, RES, and Damage Reduction, but does not ignore shields. However, True DMG can be increased by Melt and Vaporize, but not Spread and Aggravate.
Note that True DMG is not to be confused with HP Loss, as HP Loss is not considered damage at all.
Notable sources of True DMG include:
* Certain Ley Line Disorders
* Electrogranum Coordinated Attacks
* Thunderstones
* Kamuijima Cannons
* Mountainators
* Unique Rock Pillars
* Xenochromatic Creature abilities
==Other Damage-Modifying Effects==
Other than those specified above, there are certain less common mechanics that will affect damage:
* Bow users have damage dropoff on their aimed shots based on the amount of time that an arrow travels in the air. The damage dropoff multiplier is applied multiplicatively with the entire damage formula.
* Dehya's Elemental Skill multiplicatively reduces DMG that characters receive. This also applies to Transformative Reaction DMG and True DMG.
* La Signora has a mechanic that prevents her from taking a single instance of DMG that exceeds a percentage of her Max HP. DMG exceeding that threshold will be nullified.
==Snapshotting==
Snapshotting refers to the ability of certain abilities to retain their buffs from the time they are cast. For example, Xiangling's Pyronado will be buffed for its whole duration when cast inside Bennett's Fantastic Voyage field, even if one walks outside the field or the field expires.
==Sample Calculation==
Consider the following sequence of events:
# is Level 70 with the following Attributes: Attack is 1500, Elemental Mastery is 150, Crit DMG is 80% and is 40%.
# applies on a Level 75 Fatui Agent.
# with 4 piece Viridescent Venerer the enemy. This decreases the Fatui Agent's Hydro RES by 40% (i.e., 0.4).
# The Fatui Agent's status wears off.
# with Constellation 2, Explosive Frags, deals , thus applying on the Fatui Agent and decreasing their DEF by 23%.
# casts Level 6 Stellaris Phantasm, triggering Vaporize for no damage and clearing the status.
# deals to the Fatui Agent, triggering Illusory Bubble, which gives a 52% DMG Bonus and deals Critical and Vaporize.
We can calculate the damage dealt by Mona in the final step as follows:
:\begin{align} \text{DEF Multiplier}_\text{Fatui Agent} & {} = \frac{70+100}{[1-0.23_\text{Klee}](75+100)+70+100} \\ & = 0.55783 \end{align}
:\begin{align} \text{RES}_\text{Fatui Agent} & {} = [0.1]_\text{Base RES} - [0.4]_\text{Sucrose} \\ & = -0.3 < 0 \end{align}
:\begin{align} \therefore \text{RES Multiplier}_\text{Fatui Agent} & {} = 1-\left(\frac{-0.3}{2}\right) \\ & = 1.15 \end{align}
:\begin{align} \text{EM Bonus}_\text{Amplifying} & {} = 2.78 \times \frac{150}{150 + 1400} \\ & = 0.26903 \end{align}
:\begin{align} \therefore \text{Amplifying Multiplier} & {} = [2]_\text{Vaporize} \times [1+0.26903_\text{EM Bonus}] \\ & = 2.53806 \end{align}
:\begin{align} \text{DMG}_\text{CRIT} & {} = 1500 \times [6.19]_\text{Stellaris} \\ &\quad \times [1+0.4_\text{Hydro Bonus}+0.52_\text{Stellaris}]_\text{DMG Bonuses} \\ &\quad \times 0.55783_\text{DEF Multiplier} \times 1.15_\text{RES Multiplier} \\ &\quad \times 2.53806_\text{Amplifying Multiplier} \\ &\quad \times [1+0.8]_\text{Critical} \\ & = 52246.50 \end{align}
Therefore, Stellaris Phantasm will deal .
==Notes==
==Change History==
==References==
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