Damage Formula

The battle simulator feature is a decent method for inquiring how much damage one unit will do to another, or which units will win in a certain matchup or arrangement, but for the sake of understanding the mechanics of the game and precisely calculating damage dealt from one stack to another, the damage formula is needed.

Damage Formula

UnitR_Losses = Number_of_UnitA * UnitA_attack_power * (accuracy/100) * UnitA_damage_modifier * UnitA_efficiency * (1 - (UnitR_resistance/100)) * UnitR_defensive_abilities / UnitR_hitpoints

• UnitA is the attacking unit
• UnitR is the unit receiving the attack
• UnitA_attack_power may be modified by valor, berserk, battle spells, battle items, etc.
• accuracy is Unit A's accuracy in attacking UnitR; base accuracy is 0.3 on defense and regular attacks and 0.2 on sieges, but often modified by Sun favor, accuracy-related unit abilities (fear, swift, beauty, marksmanship, clumsiness), enchantments, battle spells, heroes, etc.
• UnitA_damage_modifier is typically a random number between 0.2 and 0.8, but the average of 0.5 is usually used
• UnitR_resistance is the resistance of UnitR to the attack type of UnitA's attack; if there is more than one attack type (e.g. FIRE BREATH), the average of these attack types is used; often modified by battle spells, items, hero abilities (mind shield, ice shield, unholy aura), enchantments (Black Sabbath), and uniques
• UnitR_Defensive_Abilities would be non-accuracy-related unit abilities like healing (0.7), scales (0.75), regeneration (0.8), charm (0.5), large shield (0.5), weakness (2.0), etc., which would all be multiplied together

Alternate Version of Damage Formula

Alternatively, this calculation can be broken up into intermediate parts...

Attack = Number_of_UnitA * UnitA_attack_power * accuracy * UnitA_damage_modifier * UnitA_efficiency
Defend = UnitR_hitpoints / (1 - (UnitR_resistance/100))
UnitR_Losses = Attack/Defend

Examples

Regular Attack: 245 Water Elemental attacking Vampire

• accuracy modifiers: 30% (standard accuracy in a regular attack) - 10% (swift) = 20%; therefore, accuracy/100 = 0.2
• resistance modifiers: poison (75%), ranged (95%); (1 - (85/100)) = 0.15

Vampire_Losses = 245 * 400,000 * 0.2 * 0.5 * 1.0 * 0.15 * 0.5 / 4500 = 163.3 => 163 dead Vampire

Using the Damage Formula to your benefit

Using the damage formula, you can know how damage is calculated and therefore determine the easiest ways to increase it.

For example, the damage formula will demonstrate that getting a level 17 warlord, which will increase your damage on a siege by roughly 16% (assuming Sun favor and that some of your units won't suffer the siege attack's 10% accuracy penalty), is far better than getting a level 17 veteran whose level 9 valor increases damage by only 12% on primary attacks (if not less) and not at all on secondary attacks. This formula will also demonstrate that Sun favor's 3% accuracy is also slightly superior to Lucifer favor's 10% AP increase.

Perhaps most importantly, this formula will allow you to decide what battle spells and items you should be using. For example, using candle against 90% melee-resistant Titans will increase the damage done to them by Treant by 100%, whereas using Potion of Valor would produce much less significant gains. The same sorts of comparisons can be used when a green is deciding between using Rust Armor, Sword of Light, Flame Blade, or Eye of the Eagle, when a nether is deciding between Foul Water, Battle Lust, or Flame Blade, or when a Phantasm mage is deciding between Double Time or Sleep.

Damage-Soaking Formula

UnitR_Soaking_Ability = UnitR_hitpoints / (accuracy * (1 - (UnitR_resistance/100)) * UnitR_defensive_abilities * UnitR_netpower)

Using the equation above, which might be called the Damage-Soaking Formula, you can calculate how well certain units are at defending against various attacks.

For example, if you were an Ascendant mage attacking an verdant mage who was known to be using a heavy HE top with an eye+candle (+10% accuracy for HE, -10% resistances for attacker) defensive assignment, you'll have to decide between using an AA, unicorn, KT, dominion, djinni, or treant top, at which point you could compare their ability to take damage from the HE, which we'll assume to also have a 7% accuracy boost from Nature's Lore and a 3% boost from Sun favor.

Unicorn: Ranged-Paralyze Soaking Ability = 2500 / (0.35 * 0.65 * 1 * 375) = 29.30
Archangel: Ranged-Paralyze Soaking Ability = 5000 / (0.45 * 0.75 * 0.7 * 750) = 28.22
Knight Templar: Ranged-Paralyze Soaking Ability = 375 / (0.5 * 0.925 * 0.5 * 60) = 27.03
Dominion: Ranged-Paralyze Soaking Ability = 80000 / (0.45 * 0.25 * 0.7 * 39013) = 26.04
Djinni: Ranged-Paralyze Soaking Ability = 7650 / (0.5 * 0.425 * 1 * 1700) = 21.18
Treant: Ranged-Paralyze Soaking Ability = 4200 / (0.5 * 0.39 * 1 * 423) = 50.92

Unicorn: Ranged-Lightning Soaking Ability = 2500 / (0.35 * 0.8 * 1 * 375) = 23.81
Archangel: Ranged-Lightning Soaking Ability = 5000 / (0.45 * 0.4 * 0.7 * 750) = 52.91
Knight Templar: Ranged-Lightning Soaking Ability = 375 / (0.5 * 0.925 * 0.5 * 60) = 27.03
Dominion: Ranged-Lightning Soaking Ability = 80000 / (0.45 * 0.25 * 0.7 * 39013) = 26.04
Djinni: Ranged-Lightning Soaking Ability = 7650 / (0.5 * 0.175 * 1 * 1700) = 51.43
Treant: Ranged-Paralyze Soaking Ability = 4200 / (0.5 * 0.765 * 1 * 423) = 25.99

Dropping the clear losers, we have...
Archangel Soaking Ability = 28.22 * (13/20.5) + 52.91 * (7.5/20.5) = 37.25
Djinni Soaking Ability = 21.18 * (13/20.5) + 51.43 * (7.5/20.5) = 32.25
Treant: Soaking Ability = 50.92 * (13/20.5) + 25.99 * (7.5/20.5) = 41.80

Usually there will only be 2 or 3 candidates to calculate, and usually the calculations won't be this complicated (lots of accuracy bonuses, candle, two attacks with two damage types each), so calculating this isn't usually this ridiculous. That said, clearly treants are the winners here!