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The Battle Equation in Age of Empires Online is a mathematical equation used to determine how many hit points a target will lose when attacked by a building or unit. While the formula for previous entries in the series is known the exact formula for AOEO is presently unknown: the following are speculations based on testing.
The speculated equation is roughly as follows:
HitPointLoss = (BA * ( ( BD * (1 - BDP ) ) ) * (1 - A)
BA x (1 - BDP) x BD x (1 - A)
BA=Base Attack, BDP=Bonus Damage Protection, BD=Bonus Damage, A=Armor
Example using hypothetical units for easy numbers: A Spearmen with 100 damage output (not DPS, but DAMage per hit) and 3.0 bonus damage against cavalry
Vs a Cavalry unit with armor stat of 0.25 against melee-infantry.
BA = 100, BD = 3.0, BDP = 0, A = 0.25
225 = (100 * (3.0 * (1 - 0))) * (1 - 0.25)
255 = 100 * (1 - 0) * 3.0 * (1 - A)
Vs a Cavalry unit with armor stat of 0.25 against melee-infantry AND 0.50 Bonus Damage Protection.