Damage Formula

The whole sum

Every hit one of your units lands on an enemy goes through the same sum:

damage = ATK curve × multiplier × element × Break × critical
       × (1 + DMG UP) × (1 + RES DOWN − enemy RES) × DEF

Each part is one factor, and they all multiply. Inside a factor, buffs of the same kind add up first. That is why stacking a second 50% DMG UP takes you from ×1.5 to ×2, a third more damage rather than half again: it shares a bucket with the first. A buff in a different bucket, such as a RES DOWN on the enemy, multiplies with it instead, so spreading buffs over several buckets usually beats piling them into one.

ATK and the curve

The sum starts from the unit’s ATK before buffs: its own at its level, plus equips, crests and Tasmons. That is the ATK the unit screen shows. ATK UP buffs then all add together and multiply it once, so a unit with 4,000 ATK under two 30% ATK UPs has 4,000 × 1.6 = 6,400. The game cuts the result to a whole number.

That ATK goes through a curve before it does anything:

curve = 700 × ATK ÷ (ATK + 3,500)

Each point of ATK is worth a bit less than the one before, and the curve never reaches 700. A unit with 3,500 ATK gets exactly half of it.

ATK	Curve
1,000	155.6
2,000	254.5
3,500	350.0
4,000	373.3
6,000	442.1
10,000	518.5

So doubling ATK from 2,000 to 4,000 gives about 47% more damage, and from 4,000 to 8,000 only about 30%. A low-ATK unit gets far more from an ATK UP than one that already has a lot. At 6,000 ATK a 10% ATK UP adds about 3.5% damage, while a 10% DMG UP on a unit with no other DMG UP adds the full 10%.

The move’s multiplier

The move sets how big the hit is. A skill or Arts that reads “15000% Water DMG” multiplies by 150. A normal attack is about 100%, though each hit of a unit’s combo carries its own share, so normal-attack numbers come out a little off.

Element and Break

Hitting the element yours beats gives ×1.2, and hitting the one that beats yours gives ×0.8. Fire beats Earth, Earth beats Water, Water beats Fire, and Light and Dark each beat the other. A move with no element skips this.

An enemy in Break takes ×1.25 from every hit.

Critical hits

A critical deals ×1.25 and skips the enemy’s DEF entirely. A Super Critical deals ×3 instead of ×1.25, and also skips DEF. In the Arena and other player-versus-player modes the two are ×1.1 and ×1.5.

CRI DMG UP is not part of this ×1.25. It is a DMG UP that only counts on a critical, so it goes in the DMG UP bucket below with everything else. A hit is a critical when a roll lands under the CRI rate, so at 100% CRI rate every hit crits.

DMG UP

Every buff that says “DMG” on your side goes in one bucket and adds up: plain DMG UP, Physical or Magic DMG UP, “Fire units’ DMG UP”, Arts DMG UP, Skill and Equip DMG UP, CRI DMG UP on a critical, and the race killers (“DMG to Beasts 30% UP”). Only the ones that match the hit count: a Magic DMG UP does nothing for a physical Arts, and a Beast killer does nothing against a Demon. The bucket is then 1 plus the total.

Resistance

On the enemy’s side, every resistance cut goes in a second bucket: “DMG taken UP”, Physical or Magic RES DOWN, and the element RES DOWN that matches your hit. The enemy’s own resistance comes off the same bucket. Most enemies have none, but some bosses resist or take more of one element: an enemy with −40% Earth RES takes 1.4× from Earth hits before any debuff.

So 35% Water RES DOWN, 35% Magic RES DOWN and 30% DMG taken UP on a boss with a natural −10% Water RES make 1 + 0.35 + 0.35 + 0.30 + 0.10 = 2.1 for a Water magic hit.

DEF

Last, the enemy’s DEF cuts the hit by DEF ÷ (DEF + 5,000):

Enemy DEF	Damage that gets through
500	90.9%
1,000	83.3%
2,500	66.7%
5,000	50.0%
10,000	33.3%

DEF has diminishing returns too, which is why it only matters much on enemies with thousands of it. Critical hits skip this step. DEF DOWN and Ignore DEF lower the DEF the hit meets; the calculator takes each off as a percentage of the enemy’s DEF.

A worked example

The community guide measured this one in the game. Vox has 4,651 ATK before buffs and 30% ATK UP from his own Arts, so 6,046 ATK. He uses an 18000% Arts as a critical on a boss in Break, with 224% of DMG UP (80% + 50% CRI DMG UP, 50% Arts DMG UP, 34% DMG UP, 10% CRI DMG UP) and a 30% Water RES DOWN on the boss.

curve      700 × 6,046 ÷ 9,546     = 443.35
multiplier 18,000%                  × 180
critical                            × 1.25
Break                               × 1.25
DMG UP     1 + 2.24                 × 3.24
RES        1 + 0.30                 × 1.30
DEF        skipped on a critical    × 1
                                    = 525,201

The game showed 525,202. It keeps the damage rounded down and rounds the number on screen up, so a popup can read one higher than the damage it dealt.

Where these numbers come from

Every constant here is a row in the game’s battle settings: 7,000 and 3,500 for the curve (the 700 is 7,000 × 0.1), 5,000 for DEF, 1.2 and 0.8 for element, 1.25 for Break, and 1.25 and 3 for criticals. The order of the sum was read from the battle code that works out a hit, and checked against hits logged in the game: the curve, the element factor and the DEF factor matched to the point, and a race killer showed up as its own 30% in the DMG UP bucket.

A few things are still open:

• How DEF DOWN and Ignore DEF combine. The calculator takes both off the DEF as percentages.
• Normal attacks come out about 1.6% lower than the sum says, on every unit tested. Skills and Arts don’t seem to.
• Whether two copies of the same buff stack. The battle code adds every active buff of a kind when it reads them, so any limit is set when a buff goes on. Unit text that allows it says “(Stacks)”.
• Some buffs only count under a condition the game checks in its own scripts: own HP over 80%, an enemy that is Burning, a unit that is equipped by a named character. The calculator lists those and leaves them for you to tick.