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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 Icon Type SwordIcon Type LanceIcon Type AxeIcon Type BowIcon Type DaggerIcon Type Beast physical weapon type, while the Res is used for Icon Type MagicIcon Type StaffIcon Type Dragonstone 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 Icon Class Colorless Staff Staff, halving their damage output. It is defined as 0.5 (50%) for Icon Class Colorless Staff 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, Icon Class Red Sword Wo Dao+, Skilliconspecial Godlike Reflexes and Domain of Flame Domain of Flame are , as they respectively depends on Special activation, Special cooldown count value, and turn order. Skilliconweapon Shining Bow+, Status Effect Exposure Exposure and Gambit 4 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 Skilliconspecial Aegis, Status Effect Reduces damage when initiating Reduces damage when initiating, Domain of Ice Domain of Ice and Close Call 4 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 Shield Pulse 3, Flow Flight 3 Flow Flight 3 and Icon Class Green Axe 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 Status Effect Triangle Adept 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 Status Effect Cancel Affinity 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 Status Effect Hexblade 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 Icon Class Red Sword Astra Blade, use the actual stats (with consideration of Temporary buffs and debuffs), not .
  • Skills such as Wrathful Staff 3 Wrathful Staff 3 or similar on Icon Class Colorless Staff Staff users change to 1.
    • Effects that cancel such skills, like Mystic Boost 3 Mystic Boost 3, reset it to 0.5.
  • Skills that "Reduce 'Reduce damage by percentage'" affects the part of the expression.

Examples[ | ]

Simple combat[ | ]

Damage Calculation Simple combat

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

Enemy attack

Player attack

Advantage, Effectiveness and Special[ | ]

Damage Calculation Advantage Effectiveness Special

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

Enemy attack

Player Forecast

Player Attack

Staff user[ | ]

Damage Calculation Staff

A combat with a Icon Class Colorless Staff Staff user and . Marth Altean Prince Face FC Marth: Altean Prince is afflicted by the Status Effect Exposure Exposure Status effect.

Player attack

Fixed Damage and Reduction[ | ]

Damage Calculation Damage DR

A combat with and . Icon Class Green Axe 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[ | ]

Damage Calculation Damage DR 2

A combat with and . Divine Breath W Divine Breath and Dragons Wrath 4 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[ | ]

Damage Calculation Full case

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

Player Forecast

Player Attack

References[ | ]

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