Combat Formula

  Definitions

Combat Pair

In a single combat round, one type of your units can target only one type of the enemy's units. These 2 unit types are a 'Combat Pair'.

Attacker

The unit type that will be attacking. When acting as an attacker, units only deal damage and never take damage.

Defender

The unit type that will be attacked. When acting as a defender, units only take damage and never deal damage.

How to apply the equation

This equation applies to a single round of combat between a combat pair. Both sides execute the equation at the same time so it's fair:

1. If the enemy is within range, calculate the deaths incurred by your side(You are defender, they are attacker.)
2. If your units are within range, calculate the deaths on the enemy's side (You are attacker, they are defender.)
3. Subtract the deaths from their respective sides.
4. End of the round. If there are survivors on both sides, the combat continues.

Note that in real combat with different types of units, combat pairs change as units move closer to each other.

The Equation

Nd = (Na * Ab * R * A * (1 - D/1000)) / Ld)
Where: Nd - Maximum number of defenders killed
Na - The number of attackers
A - Attack value of attackers
Ab - Attack bonus (see below)
D - Defenders defense value
R - Ranged damage modifier
Ld - Amount of Life of the defender unit type

The attack, defense and life values can be looked up in the game. The Range damage modifier and attack bonus is explained below.
The maximum number of defenders killed is the number of defender that could possibly die in this combat round. Obviously if there are less defenders than the maximum number killed, then all defenders of that unit type are dead at the end of the round.
Decimal values are rounded up to the nearest integer. If a unit loses even 1 hit point, that unit is counted as dead and removed from combat in future rounds.

Ranged Damage Modifier

Ranged units do half the damage that melee units do. Here are the modifiers:
R = 0.5 for ranged units (Archer, Ballista, Catapult)
R = 1.0 for melee units (All other units)

Attack Bonus

Depending on the unit type being attacked, there may get be bonus to the attacker's attack value. This table obviously applies to the attackers because defenders don't attack, ie don't look up the defender's attack bonus. Lookup the attacking unit type across the top and match it to the defending unit type along the left.

Defender Type	Attacker Type
	Worker	Warrior	Scout	Pikeman	Swordsman	Archer	Cavalry	Cataphract	Transporter	Ballista	Battering Ram	Catapult
Worker*	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96	0.96
Warrior, Swordsman, Transporter, Ballista, Battering Ram, Catapult	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Scout*	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97	0.97
Pikeman	1.00	1.00	1.00	1.00	1.10	1.00	1.00	1.00	1.00	1.00	1.00	1.00
Archer	1.00	1.00	1.00	1.00	1.00	1.00	1.20	1.20	1.00	1.00	1.00	1.00
Cavalry	1.00	1.00	1.00	1.80	1.00	2.00	1.00	1.00	1.00	2.00	1.00	2.00
Cataphract	1.00	1.00	1.00	1.80	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00

I've highlighted the positive bonuses in red. For example, all ranged units do double damage to cavalry, pikemen do 80% more damage to mounted units.

Scouts and workers have strange attack bonuses. It seems like the game doesn't like defense values less than 50. If you round up worker and scout defenses to 50, then their modifiers can be set to 1.00