units: 1

Final damage dealt by a creature stack in combat:

DMGf = DMGb × (1 + I1 + I2 + I3 + I4 + I5) × (1 − R1) × (1 − R2 − R3) × (1 − R4) × (1 − R5) × (1 − R6) × (1 − R7) × (1 − R8)  [× L1 in HotA]

Base damage (DMGb)

• Stack ≤ 10: sum of a random roll in [min_dmg, max_dmg] per creature.
• Stack > 10: roll 10 random values, sum, multiply by N/10 (N = stack size), round down.

Offense modifiers (increase)

• I1 — Attack-Defense difference. If attacker's total attack > defender's total defense: +5% per point of difference (capped at +300%, i.e. ×4). I1 = 0 when negative.
• R1 — If defense > attack: −2.5% per point (capped at −70%, i.e. ×0.30). R1 = 0 when positive. I1 and R1 are mutually exclusive.
• I2 — Secondary skills: Archery (ranged) gives +0/10/25/50%, Offense (melee) gives +0/10/20/30% at none/basic/adv/expert.
• I3 — Specialty bonus for Archery/Offense specialists (Orrin, Gundula, Crag Hack, Corkes): I3 = 0.05 × hero_level × I2. Adela's Bless specialty: I3 = 0.03 × hero_level ÷ creature_level.
• I4 — Lucky strike: 1.00 if triggered, 0 otherwise. Chance scales with luck (+1→4.17%, +2→8.33%, +3→12.5%).
• I5 — Creature abilities: Dread Knight death blow = 1.00, hate bonus (e.g. Angels vs Devils) = 0.50, jousting (Cavalier/Champion) = 0.05 × hexes travelled, elemental double damage = 1.00.

Defense modifiers (reduce)

• R2 — Armorer skill: 0/5/10/15% at none/basic/adv/expert.
• R3 — Armorer specialty (Mephala, Neela, Tazar): R3 = 0.05 × hero_level × R2.
• R4 — Magic shields: Shield (melee) = 15/30%, Air Shield (ranged) = 25/50% at basic/adv-expert.
• R5 — Range penalty (50% at 10+ hexes) or melee penalty (50% for ranged units in melee).
• R6 — Obstacle penalty (50% when shooting through intact siege walls).
• R7 — Mind spells: retaliation after Blind (50% basic, 25% advanced), Forgetfulness (50% ranged damage).
• R8 — Creature specials: Psychic Elemental vs mind-immune (50%), Magic Elemental vs spell-immune (50%), petrified target (50%), paralyzed retaliation (25%).

Luck (HotA only)

• L1 — Replaces I4 in HotA: lucky strike = 2.00, normal = 1.00, unlucky = 0.50. Negative luck introduces unlucky strikes.

Source: heroes.thelazy.net — Damage · AI/Fight Value