Fighting

How a battle is decided: the attack against the defence, the morale, then the losses of both sides.

1. Attack points

Every attacking unit adds its attack to the infantry total A_inf or, if it is cavalry, to the cavalry total A_cav. A unit upgraded in the Smithy to level L attacks with

a′ = a + (a + 300 × u / 7) × (1.007^L − 1)

where a is its base attack and u its crop upkeep. The alliance's Metallurgy bonus multiplies the attacker's totals.

2. Defence points

Every defending unit (the village's own and every reinforcement) adds its defence against infantry to D_inf and its defence against cavalry to D_cav, upgraded in the Armoury with the same formula. The defender's Metallurgy bonus multiplies them.

3. Wall and base defence

The wall multiplies both defences by m = f^W (rounded to three decimals), with W the wall level and f 1.030 for the Romans' City Wall, 1.020 for the Germanic Tribes' Earth Wall and 1.025 for the Dacians' Palisade. Every village also defends with a base of (2 × R² + 10) × m points, R being its Residence or Palace level. A village with no troops at all defends with 10 × m × W plus that base.

4. The totals

A = A_inf + A_cav (the Germanic Tribes' Brewery adds its percentage during a celebration)

D = (A_cav / A) × D_cav + (A_inf / A) × D_inf

The defence is split in the attack's own proportions: cavalry is met by the defence against cavalry, infantry by the defence against infantry. The attacker wins when A > D.

5. Morale

When the attacker has more inhabitants than the defender the defence counts more:

morale = 1 / max(0.667, (P_def / P_att)^(0.2 × min(1, A / D)))

6. Losses

The exponent M is 1.5; in battles with 1,000 units or more it drops to 2 × (1.8592 − N^0.015), never below 1.2578 (N = every unit taking part).

Normal attack. The winner loses (loser’s points / winner’s points)^M of its troops, the loser everything (the defence counts with its morale).
Raid. With x = (loser’s points / winner’s points)^M, the winner loses x / (1 + x) and the loser 1 / (1 + x): both sides keep troops.
Loot. The surviving attackers carry home up to their capacity each.
Chiefs. Each surviving chief of a won normal attack takes 20–30 loyalty (two: 40–60, three: 60–80, four: 80–100); at 0 the village changes hands.

7. Rams and catapults

With σ(x) = x^1.5 / 2 for x ≤ 1 and (2 − x^−1.5) / 2 above, the damage of n rams or catapults is

damage = 4 × σ(A / D) × ⌊n / (stonemason × stronger buildings)⌋ × u / morale

where u = 1.0205^S for the Smithy level S of the siege unit, the Stonemason's Lodge and the artifacts of stronger buildings divide the damage, and the catapults' morale is (P_att / P_def)^0.3 between 1 and 3. The building loses levels while the damage (minus 0.5) still covers the level it is at.

8. Scouting

Scouts attack with 35 points each and defend with 20 each (upgraded as above); the scouting artifacts multiply them. Only scouts take part; the attacker's scouts die in the proportion of the losses formula when the defender has scouts of his own.

Worked example

100 Legionarii (attack 40, capacity 50) attack 50 Sica Warriors (defence 40 against infantry) in a Dacian village with no wall and no Residence; both players have the same population.

A = 100 × 40 = 4,000
D = 50 × 40 + 10 = 2,010 (all infantry: the defence against infantry counts)
Losses of the attacker: (2,010 / 4,000)^1.5 = 0.356 → 36 Legionarii die; all the Sica Warriors die.
Loot: 64 × 50 = 3,200 resources at most.

With a Palisade at level 10 (m = 1.025^10 = 1.28): D = 2,000 × 1.28 + 10 × 1.28 = 2,573, the attacker loses (2,573 / 4,000)^1.5 = 0.516 → 52 Legionarii, and carries at most 2,400.

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