## Formulae[ | ]

Damages are calculated as follow^{[1]}:

The Combat Forecast's^{[2]} damages use a shortened formula:

**Notation**

- is used as a placeholder for "the result so far".
- is used to represent the Floor functions, that is rounding the result down. For example, .
- is used to mean the Positive parts, which set negative values to 0.

A detailed explanation of the remaining terms is provided below.

#### Atk

The is the result of the attacker's visible Atk stat before entering the combat, plus all the Temporary buffs and debuffs affecting it. This second value is visible through the Combat Forecast (any temporary buffs and debuffs greater than 99 are displayed as 99, but are used properly).

#### Def

The is the result of the defender's visible Def or Res stat before entering the combat, plus all the Temporary buffs and debuffs affecting it. The Def is used when the attacker has a physical weapon type, while the Res is used for magical weapon type.

#### AdvantageMod

The is the result of the Weapon-triangle mechanism of the attacker's weapon type over the defender's weapon type. It is equal to 0.2 (20%) when there is a dis/advantage, 0 otherwise.

Note the ± sign in front of it. The actual operator depends on whether there is an advantage or a disadvantage: + in case of advantage, - in case of disadvantage.

#### EffectiveMod

The is the result of the effectiveness of the attacker over the defender's weapon type or move type. It is equal to 0.5 (50%) in case of effectiveness, 0 otherwise. Being effective against both weapon type and move type *does not* increase this modifier any more.

#### TerrainMod

The is the effect of Defensive terrains applied on the defender. It is equal to 0.3 (30%) when the defender is on a defensive terrain, 0 otherwise.

#### StaffMod

The is the particular effect that unconditionally affects all attackers that use a Staff, halving their damage output. It is defined as 0.5 (50%) for Staff users, 1 otherwise.

#### SpecialDamage

The is the result of the additional damages granted during the activation of an Offensive Special.

Specials that "Boosts damage by percentage" use as the source of boosting.

#### FixedDamage

The is the result of all effects that "Deals damage during combat". It is effectively the sum of all such effects targeted on the defender.

Note that the rounding operation is applied *after* the summation, therefore the decimal demages of individual effect are also summed.

can actually be divided into two categories: and .

includes all effects that depends on factors that can change during a combat. This concerns the following effects:

- Effects that depends on turn order, i.e. "During first attack", "After foe's attack", etc.
- Effects that depends on Specials and its current cooldown count, i.e. "When Special triggers", "When cooldown count is 0", etc.
- Effects that depends on the current HP, i.e. "Deals damage = 10% foe's HP", "When unit's HP > 25%", etc.

All other effects are categorized as . Note that effects that depends on the maximum value (of Special cooldown count and HP) or the start of combat's value are categorized as .

For examples, Wo Dao+, Godlike Reflexes and Domain of Flame are , as they respectively depends on Special activation, Special cooldown count value, and turn order. Shining Bow+, Exposure and Gambit 4 on the other hands are considered , as they respectively are dependent of the Def stat, unconditional, and dependent on the maximum cooldown count value.

#### PercentReduction

The is the result of all effects that "Reduce damage by percentage" on the defender. The individual effects should not be summed, but rather multiplied. It is defined as when at least one effect exists, 0 otherwise. In this expression, is the Product function applied on all such effects, while is the individual reduction percentage.

By example, if there is one effect that reduces damage by 30% on the defender, will be . If there are two such effects, will be , which corresponds to a 51% of damage reduction.

Effects that "Reduces damage by percentage" are usually written as is, or as "Reduces damage by *X*%", followed by a period, comma, or a conjunction. A few examples are Aegis, Reduces damage when initiating, Domain of Ice and Close Call 4.

#### FixedReduction

The is the result of all other effects that "Reduces damage". It is defined as the sum of all such effects on the defender.

Note that the rounding operation is applied *after* the summation, therefore the decimal part of individual effect are also summed.

Effects that "Reduces damage" are usually written as "Reduces damage by *X*", where *X* can be a number, and "Reduces damage by *X*% of ...". A few examples are Shield Pulse 3, Flow Flight 3 and Wyvern Ono.

### Procedural formula[ | ]

The formula can also be understood has a serie of operations, which are listed below:

Note that the formulae have been factorized whenever possible, which required the introduction of the ceil function , which rounds the result up.

## Notes[ | ]

There are some effects that can change the default behaviour listed above. Some examples are listed here:

- The Triangle Adept status effect and other skills with similar behaviour all change the value of . The highest effect applied on the attacker is added to the modifier, therefore changing it from 0.2 to 0.4.
- When such an effect is active on the defender, and the Cancel Affinity status effect or another similar effect is on the attacker, the Triangle Adept effect is substracted to the multiplier, instead of added. It therefore changes from 0.2 to 0.
- The Time Traveler skills
*does not*affect , but are considered and instead. - See also Weapon-triangle for more informations.

- The Hexblade status effect and other similar effects can change the targeted stat of .
- Skills that "Deals damage" based on "Atk minus Def" or "Atk minus Res", such as Astra Blade, use the actual stats (with consideration of Temporary buffs and debuffs),
*not*. - Skills such as Wrathful Staff 3 or similar on Staff users change to 1.
- Effects that cancel such skills, like Mystic Boost 3, reset it to 0.5.

- Skills that "Reduce 'Reduce damage by percentage'" affects the part of the expression.
- Hardy Fighter 3 allows Defensive Specials to trigger twice. It is therefore not affected by effects such as Halves non-Special damage reduction}, which targets non-Special percent based damage reduction.

## Examples[ | ]

### Simple combat[ | ]

A very simple combat. The only particularity is Marth: Altean Prince being on a Defensive terrain.

**Enemy attack**

**Player attack**

### Advantage, Effectiveness and Special[ | ]

A combat accounting for Weapon-triangle mechanisms and Effectiveness. Sharena: Princess of Askr is equipped with the Effective against dragons Status effect, and activates her Glimmer Special.

**Enemy attack**

**Player Forecast**

**Player Attack**

### Staff user[ | ]

A combat with a Staff user and . Marth: Altean Prince is afflicted by the Exposure Status effect.

**Player attack**

### Fixed Damage and Reduction[ | ]

A combat with and . Wyvern Ono deals damage equal to 20% of the unit's Def, and reduce damage by the same amount.

**Player attack**

**Enemy forecast**

**Enemy attack**

### Situational Damage and Percent Reduction[ | ]

A combat with and . Divine Breath and Dragon's Wrath 4 both deals damage equal to 25% of unit's Atk minus foe's Res during first attack, and reduce damage of first attack by 25%.

**Enemy Forecast**

**Enemy Attack**

**Player Forecast**

**Player Attack**

### Complete case[ | ]

A complete case where almost every part are included (except and ). Naga: Dragon Divinity has an advantage and is effective against Tiki: Dragon Scion. She also possess as in the previous case. Tiki: Dragon Scion is located on a Defensive terrain, is afflicted by the Exposure Status effect, therefore sustaining , is in the range of Domain of Ice's , and activates her Special Escutcheon, which in turn triggers Shield Pulse 3's .

**Player Forecast**

**Player Attack**