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Damage calculation
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Please help improve this if you can. The Discussion page may contain suggestions.
Reason: "Use official terminology from What's In Store for the 2.10.0 Update (Notification)"
Contents
Notation[edit  edit source]
The and notation is used to mean the Floor and ceiling functions in these formulae. For example, and .
The notation is used to mean truncation in these formulae. This means that , it is effectively dropping all numbers after the decimal point. To make the formulae more readable, this notation will only be used when floor is not sufficient to provide a visual shorthand for truncation.
The positive part of Positive and negative parts notation is used to set a number to 0 if it is negative.
Damage is calculated in these steps:^{[1]}
 Base Damage
 Adjusted Damage
 Final Damage
Base Damage calculation[edit  edit source]
Simple hit[edit  edit source]
The damage calculation for a simple hit is:
Variable  Description 

Atk  The Attack stat of the attacking unit.
Includes the might (Mt) of the equipped weapon, and any stat changes, such as bonuses, penalties, combat boosts, combat reductions, or boosts. 
Mit  The Mitigation stat of the defending unit.
Physical attacks are mitigated by Def, while magical attacks are mitigated by Res. 
Positive part. In short, this is used in damage calculation formulas to say "if the number is negative, set it to 0, otherwise, keep it". 
 Note: Damage is never negative.
Example 

Example: A sword unit with an Atk of 15 attacks another red unit with a Def of 11.

Weapontriangle advantage[edit  edit source]
Here the formula adds in weapontriangle advantage ("Atk+20%"):
Variable / Notation  Description 

Adv  The weapon triangle advantage a unit receives due to weapontriangle advantage or disadvantage. It is currently always 0.2 if advantage, 0 if neither, −0.2 if disadvantage. 
Aff  Affinity from sources such as Triangle Adept and Ruby Sword and Trilemma+'s Triangle Adept status effect. The default is 0, and only the highest value applies. Example values include 0, 15 (such as from Triangle Adept 2), 20 (such as from Ruby Sword+), etc.
Note: Cancel Affinity 3 reverses the affinity provided by skills or status effects. In the situations where affinity is reversed, make Aff negative. 
Example 

Example: A red sword unit with Atk 15 attacks a blue unit with Def 11. The red unit has a disadvantage, so Adv is negative.

Important is that although weapontriangle advantage is "Atk+20%" and Triangle Adept 3 will "boost Atk by 20%", these modifiers all affect the same component and do not act independently, thus, is incorrect while is correct.
To illustrate this point, take the example of a red unit with 54 Atk attacking a green unit with a Mitigation of 34.^{[2]}
Example 

Damage: 
Note: Affinity does not stack. Triangle Adept does not stack with the gemstone weapons. Only the highest value is applied.
Effectiveness[edit  edit source]
The formula including the weapontriangle and factoring effective damage in is
Variable  Description 

Eff  The effectiveness multiplier a unit receives when using a
weapon effective against an enemy. Either 1 for normal attacks or 1.5 for effective attacks. 
Note that effectiveness is first instead of weapontriangle advantage. To illustrate this, take a look at the following example.
Example 

In this example, Merric: Wind Mage attacks Lance Flier and deals 57 damage.^{[3]} Environment:

Note that the formula cannot be simplified to . This can be proven with the next example:
Example 

In this example, Marth: Altean Prince attacks Green Manakete and deals 88 damage.^{[4]} Environment:

Boosted Damage[edit  edit source]
Some Specials can also add boosted damage. When a Special is capable of doing so, its description will say that it boosts damage. This boosted damage is also referred to as "special damage bonus" (奥義ダメージ)^{[5]}. The formula looks like this:
Currently only Specials use boosted damage in the game. Other extra damage skills use dealt damage instead, described later. Note that BoostedDamage is added within the first set of parentheses that have positive part applied to them. This means, unlike the calculations that come afterwards, boosted damage from specials will need to "make up" negative damage.
Variable  Description 

BoostedDamage  The damage added as a result of the Special. 
Calculating Boosted Damage[edit  edit source]
This section describes how to calculate the boosted damage for various Specials. Some specials, like Blue Flame, tell the amount directly in the skill description.
Statbased Specials[edit  edit source]
Luna[edit  edit source]
The formula above applies for similar skills such as Moonbow or Aether, simply replace 0.5 with the appropriate value.
Note that despite Luna stating that it treats foe’s Def/Res "as if reduced by 50% during combat", it does not actually do this, because the activation of Luna also does not change whether or not the condition "If foe's Def ≥ foe's Res+5" for Shining Bow+ or Light Brand is true or not.^{[6]}^{[7]} In addition, the activation of Luna on a foe does not change the amount added to damage dealt for Lunar Brace.^{[citation needed]}
It is currently mathematically accurate to say adding 50% of foe's Def/Res to damage is identical to reducing foe's Def/Res by 50%, but only for the purpose of Base Damage calculation:
Variable  Description 

Mit  Use the Def or Res stat, depending on the situation. 
Example 

In this example, Lucina: Future Witness attacks Hector: General of Ostia while triggering Luna, and this results in 42 damage.^{[8]} Environment:

Astra[edit  edit source]
Astra does not use boosted damage.
Defensive terrain effects[edit  edit source]
Adjusted Damage calculation[edit  edit source]
Dealt Damage[edit  edit source]
Staff calculation[edit  edit source]
Damagereducing skill effects[edit  edit source]
Final Damage calculation[edit  edit source]
References[edit  edit source]
 ↑ Notifications: What's In Store for the 2.10.0 Update
 ↑ Media:Damage_Calculation_Triangle_Adept.webm
 ↑ Media:Damage_Calculation_Merric.webm
 ↑ Media:Damage_Calculation eff damage.png
 ↑ https://guide.fireemblemheroes.com/enUS/eve013/
 ↑ Media:Damage_Calculation_Shining_Moonbow.webm
 ↑ Media:Damage_Calculation_Wrath_Aether_Light_Brand.webm
 ↑ Media:Damage_Calculation_Luna.webm