Damage Formula

Here is the formula used to calculate damage in a battle. This applies to both allies and enemies damage calculation.

## Base Damage

Base Damage is the damage shown in Skill Preview

```
Base Damage = (Attacker's Base ATK + Flat ATK UP)* (Base Multiplier + SMU - SMD) * Tile Multiplier

```

Flat ATK UP
The sums of the Attacker's Flat (non-percentage) ATK UP Buffs ().
Base Multiplier
Multiplier mentioned in unit skill
SMU - Skill Multiplier UP
Sums of Attacker's Skill Multiplier UP Buffs ()
SMD - Skill Multiplier DOWN
Sums of Attacker's Skill Multiplier DOWN Debuffs ()
Tile Multiplier
Some skills has lower Skill Multiplier for non-center tile. For example, Rhea's **Severe Thunderstorm Warning** only has 25% normal Skill Multiplier for the surrounding tiles.
## Incoming Damage (Damage before Defense / Resists)

```
Incoming Damage = Base Damage * C * (1 + ATK UP) * (1 - ATK DOWN) * (1 + Anti-Type) * (1 - Damage Reduction)

```

C - Critical
Equal 1.5 if the hit is critical and 1 otherwise.
ATK UP
The sums of the Attacker's ATK UP Buffs ().
ATK DOWN
The sums of the Attacker's ATK DOWN Debuffs (). Capped at 100%.
Anti-Type
The sums of the Attacker's Anti-Type (Light, Heavy or Flying) Buffs and Debuffs corresponding to the target's Type (). Can be negative.
Damage Reduction
The sums of the Defender's DR (Damage Reduction) Buffs and Debuffs (). Capped at 100%.
## Receiving Damage (Damage after Defense / Resists)

### For Physical (normal) Damage

```
Physical Receiving Damage = Incoming Damage - (Target's Base DEF + Flat DEF UP) * (1 + DEF UP) * (1 - DEF DOWN) * (1 - DP + DPR)
Additional Physical Damage = Physical Receiving Damage * AD effects

```

Flat DEF UP
The sums of the Target's Flat (non-percentage) DEF UP Buffs ().
DEF UP
The sums of the Target's DEF UP Buffs ().
DEF DOWN
The sums of the Target's DEF DOWN Debuffs ().
DP - Defense Penetration
The sums of the Attacker's Defense Penetration Buffs and Debuffs (). Capped at 100%. Can be negative.
DPR - Defense Penetration Resist
Equal the percentage of current HP of the Defender multiplied by Defense Penetration Resist buff (). Cannot exceed DP.
AD - Additional Damage
Additional Damage when a certain condition is met. ().
If attacking unit has any amount of DEF PEN, negative DEF values are set to 0.
### For Elemental Damage

```
Resist = (1 - Max(MR, Base Resist - Resists debuffs) + Resist buffs) (of the corresponding Element)
Elemental Receiving Damage = Incoming Damage * Resist
Additional Elemental Damage = Elemental Receiving Damage * AD effects * Resist

```

MR - Minimum Resist
Sum of Minimum Resist buffs of the respective Elemental Damage taken (). Elemental Resists cannot be lower than Minimum Resist. Start at 0%, but doesn't apply if there is no Minimum Resist buffs (i.e. Resists can be negative if there is no Minimum Resist buffs).
Elemental Resist buffs/debuffs
Resist buffs/debuffs of the respective Elemental Damage taken ().
RR - Resist Reversal
Is -1 if Resist Reversal buff of the respective Elemental Damage taken () is applied and 1 otherwise. Unknown interaction with Minimum Resist.
AD - Additional Damage
Additional Damage when a certain condition is met. ().
## Final Damage

```
Final Damage = (Receiving Damage + Additional Damage) * (1 + DTI) * (1 + Enmity) * (1 + Merciless) * (1 + ADF) * (1- ADD)

```

DTI - Damage Taken Increase
The sums of The Target's Damage Taken Increased debuffs ().
Enmity
The sums of the Attacker's Enmity Buffs. The lower Atttacker's HP, The more damage is dealt ().
Merciless
The sums of the Attacker's Merciless Buffs. The lower Target's HP, The more damage is dealt ().
ADF - Area Damage Focus
Has no effect if the maximum number of targets is 1.

If the maximum number of targets is more than 1:

```
ADF = (M - N) / M * (Sum of Attacker's Area Damage Focus Buffs)

```

Where M is the the maximum number of targets and N is the actual number of targets in Area of Effect.

ADD - Area Damage Dispersion
If the maximum number of targets is 1, ADD is 0.

If the maximum number of targets is more than 1:

```
ADD = N / M * (Sum of Defender's Area Damage Dispersion Buffs / Debuffs)

```

Where M is the the maximum number of targets and N is the actual number of targets in Area of Effect.

If ADD is higher than 100%, no damage will be received. ADD can be negative, in which case it will increase damage dealt instead.

## Barrier, Minimize Damage, Nullify Damage

* [Minimize Damage] Buffs will set the Receiving Damage to 1 directly
* [Nullify Damage] Buffs will set the Final Damage to 0 directly.
* Nullified Attacks are not counted as being hit for 4\* Missions and "when hit effects".
* [Barrier] buff is applied after  [Minimize Damage] buff.
* The damage cap for a single instance is 2,147,483,848.