How damage works · Raid Optimizer

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In short

A hit starts as your stat × the skill's multiplier, then every modifier multiplies it: the target's DEF, a crit, affinity, [Weaken] and so on.
DEF is a curve, not a subtraction. It can remove at most 85% of a hit, and each extra point does less than the last.
[Decrease DEF] and "ignore DEF" attack the same curve from different sides, and they stack.
Poison and HP Burn take a share of the target's max HP. DEF, crits and ATK do not touch them, and bosses cap them.
Each hit of a multi-hit skill rolls its own crit and its own small random variation.

The chain, step by step

Every damaging hit, yours or the enemy's, goes through the same stages. Each one is a multiplication, so a 25% bonus at one stage is always worth 25% of whatever the other stages have already produced.

Damage = stat × skill multiplier × DEF factor × hit type × affinity × [Weaken] / [Strengthen] × other bonuses × small random roll

Stat × skill multiplier. Most skills use ATK, some use HP, DEF or SPD, and a few combine two (for example "DEF + ATK"). The skill text tells you which. Skill books raise the multiplier.
DEF factor. The target's DEF, after debuffs and after any "ignore DEF", is turned into a factor between 1 and 0.15.
Hit type. A critical hit multiplies by 1 + C.DMG ÷ 100, a crushing hit by 1.3, a glancing hit by 0.7, a normal hit by 1. These are exclusive: one hit gets one type. See Affinities.
Affinity. Hitting an enemy you are weak against multiplies by 0.8. A strong matchup has no flat bonus; its benefit comes through the hit type.
Buff and debuff multipliers. [Weaken] on the target (15% or 25%) multiplies the hit; [Strengthen] on the target (15% or 25% less) reduces it. Both are on the effects list.
Other bonuses. Masteries, gear sets, relics and blessings add their own multipliers, all in the same way. One example: a mastery that adds 6% damage against enemies with more max HP than you multiplies the hit by 1.06.
Random roll. Real hits vary by about ±10% around the figure you compute, in steps of 1%. It averages out; it does not move the mean.

Note We checked this in real fights: the centre of each hit, computed with these multipliers, matched the in-game damage to five significant figures. Adding the bonuses together instead of multiplying them missed by about 1%, which is enough to tell the two readings apart.

Reading "4.2×ATK"

A skill that deals "4.2 × ATK" means each hit starts at 4.2 times your current ATK (after buffs). A champion with 4,500 ATK starts a hit at 18,900. Things to know when reading skill text:

It is per hit. A skill that attacks three times runs the whole chain three times, each with its own crit and its own random roll.
Which stat matters. A skill scaling with DEF or HP gains nothing from [Increase ATK].
Books change the multiplier. A damage book multiplies the skill's number, so a +5% book turns 4.2 into 4.41.
Some skills use the target's max HP ("deals damage equal to 4% of the target's MAX HP"). Those are explained below.

DEF: the curve, and the two ways around it

The target's DEF is turned into the share of the hit that survives:

Damage kept = 0.15 + 0.85 × e^{−DEF ÷ 1500}

At 1,000 DEF about 59% gets through; at 2,500 about 31%; at 5,000 about 18%. The floor is 15%: no amount of DEF takes more than 85% off a hit. Two things shrink the DEF number before it goes into the curve:

[Decrease DEF] (30% or 60%) lowers the target's DEF stat. A 60% debuff on 2,500 DEF leaves 1,000.
Ignore DEF (from a skill's text, a gear set such as Cruel with 5%, a mastery) treats the remaining DEF as lower by that percentage. Several sources add up to a maximum of 100%, and at 100% the DEF factor is exactly 1.

They combine in that order: the debuff changes the stat, then "ignore" takes a share of what is left. 2,500 DEF with [Decrease DEF] 60% and 50% ignore becomes 2,500 × 0.4 × 0.5 = 500.

A worked example

An attacker with 3,000 ATK has [Increase ATK] 50% on, so uses 4,500. Its skill is "4.2 × ATK", so a hit starts at 18,900. The target has 2,500 DEF and [Weaken] 25% (neutral affinity, 150 C.DMG for the crit column, random roll left out).

Target situation	DEF used	DEF factor	Normal hit	Critical hit
Plain	2,500	31%	about 7,300	about 18,300
[Decrease DEF] 60%	1,000	59%	about 13,900	about 34,600
[Decrease DEF] 60% and 50% ignore DEF	500	76%	about 17,900	about 44,800

The debuff nearly doubles the damage. The ignore on top adds another 29%. Compare that with ATK: going from 3,000 to 4,500 ATK is a flat +50%, so against a tanky target a good DEF debuff can be worth more than a big ATK buff.

Careful Doubling DEF does not halve the damage. Going from 1,000 to 2,000 DEF takes the damage kept from 59% to 37%, but going from 5,000 to 10,000 only takes it from 18% to 15%.

Poison and HP Burn

These damage-over-time debuffs are written as a share of the target's max HP, not of your ATK.

[Poison] comes as 5% or 2.5% of max HP per tick, and up to 10 poisons can sit on a target at once. [HP Burn] is 3% of max HP and only one can be on a target.
They tick at the start of the bearer's turn. A poison placed for 3 turns ticks 3 times.
DEF does not reduce them, they cannot crit, and neither [Weaken] nor [Increase ATK] makes them hit harder. [Block Damage] on the target does stop them.

On a boss, a fixed share of max HP would be enormous, so bosses limit it. The Nightmare and Ultra-Nightmare Clan Boss caps one 5% poison tick at 50,000 and a 2.5% tick at 25,000. It caps [HP Burn] as well, by the rarity of the champion who placed it: 75,000 for Epic and above, 50,000 for Rare. Lower difficulties and other bosses have their own limits, so check the boss before counting on percentages.

Damage based on max HP

Skills and masteries such as Warmaster and Giant Slayer that deal "a % of the target's MAX HP" are also limited on bosses: a single hit of this kind cannot exceed 75,000 against the Clan Boss when it comes from an Epic, Legendary or Mythical champion (50,000 from a Rare, 15,000 from the lowest rarities). That is why they pay about the same on every Clan Boss difficulty. The cap is applied before DEF, so DEF still takes its share afterwards.

Reflects, counters and shared damage

[Reflect Damage] (15% or 30%) sends that share of the damage that actually reached your HP back at the attacker. Reflected damage is fixed: no DEF, no crit and no affinity.
Counterattacks are a normal hit with the champion's basic attack at 75% strength.
[Ally Protection] redirects a share of a hit to the protector, and the protector's DEF then reduces it.

Tip When you compare two builds, change one thing at a time and recompute the whole chain. Because everything multiplies, the same +10% is worth more on a champion that already hits hard.

Next: how debuffs land, which decides whether the DEF debuff above is on the target at all.