How much damage an attack does, and what raises or lowers it. Every unit's results are on Unit Damage & Counters.
The formula
ATK is the attacker's strength after all modifiers, and DEF is the defender's. The result rounds up when the attacker is stronger, and down otherwise. An even fight deals 6, so it takes three attacks to kill a 20 HP unit. The game shows strength to one decimal but uses the unrounded value.
| DEF โATK โ | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 3 | 6 | 4 | 3 | 3 | 2 | 2 | 2 | 1 | 1 | 1 | 1 | 1 | 1 |
| 4 | 8 | 6 | 4 | 4 | 3 | 3 | 2 | 2 | 2 | 2 | 1 | 1 | 1 |
| 5 | 10 | 8 | 6 | 5 | 4 | 3 | 3 | 3 | 2 | 2 | 2 | 2 | 2 |
| 6 | 12 | 9 | 8 | 6 | 5 | 4 | 4 | 3 | 3 | 3 | 2 | 2 | 2 |
| 7 | 14 | 11 | 9 | 7 | 6 | 5 | 4 | 4 | 3 | 3 | 3 | 3 | 2 |
| 8 | 16 | 12 | 10 | 8 | 7 | 6 | 5 | 4 | 4 | 4 | 3 | 3 | 3 |
| 9 | 18 | 14 | 11 | 9 | 8 | 7 | 6 | 5 | 4 | 4 | 4 | 3 | 3 |
| 10 | 20 | 15 | 12 | 10 | 9 | 8 | 7 | 6 | 5 | 5 | 4 | 4 | 4 |
| 11 | 22 | 17 | 14 | 11 | 10 | 9 | 8 | 7 | 6 | 5 | 5 | 4 | 4 |
| 12 | 24 | 18 | 15 | 12 | 11 | 9 | 8 | 8 | 7 | 6 | 5 | 5 | 4 |
| 13 | 26 | 20 | 16 | 13 | 12 | 10 | 9 | 8 | 8 | 7 | 6 | 5 | 5 |
| 14 | 28 | 21 | 17 | 14 | 12 | 11 | 10 | 9 | 8 | 7 | 7 | 6 | 5 |
| 15 | 30 | 23 | 18 | 15 | 13 | 12 | 10 | 9 | 9 | 8 | 7 | 7 | 6 |
Effective strengths often land between these integers. For example, a Hoplite attacking a Horseman in melee is ATK 9, which is 6 ร 1.5 for the anti-mounted bonus, against DEF 6, for 9 damage.
Effective strength
Modifiers are percentages that add together. The attacker and the defender each add up their own.
- Anti-trait bonuses are the unit's own effects against the opponent's traits, e.g. Pikeman +100% against Mounted in melee, Crossbowman +50% against Melee, and Ballista +100% when attacking Infantry. They are the counters listed on the Unit Counters page.
- Promotions and general ratings are each promotion's strength, attack and defense percentages, listed on Promotions. A general adds further bonuses from his ratings.
- Terrain and position covers melee attacking across a river at โ50%, attacks between land and water at โ50%, each unit's own modifiers for urban tiles and vegetation, and +10% for fighting in your own family's territory.
- State covers a siege unit that moved this turn, which defends at โ25%, attacking from hiding at +10%, and the bonuses some units get against damaged targets or targets led by a general.
Current HP does not change strength, so a Pikeman on 1 HP hits as hard as a fresh one.
Example: Hoplite against Horseman
| Hoplite base strength | 6 |
| + Anti-Mounted II (melee, vs Mounted) | +50% |
| Hoplite effective attack | 9 |
| Horseman defense (no modifiers) | 6 |
| Damage of 6 ร 9 / 6, rounded up | 9 HP |
The Horseman drops from 20 to 11 HP. When the Horseman attacks back it is 6 against 9, because the anti-mounted bonus also works when the Hoplite defends in melee: 6 ร 6 / 9 is 4 damage.
Striking back
- Ranged attacks draw no return damage at all.
- Melee defenders deal a flat 1 damage back per attack, and 1 more against a routed attacker.
- Tactician generals raise that to 100% of the unit's own attack damage.
- Cities defend at 8 + 0.5 ร citizens, and units capture at 50% HP.
Attack patterns (Pierce, Cleave, Splash, Circle)
Some units also hit nearby tiles when they attack. These extra hits use the same damage formula at a lower strength, and the attacker takes no damage back from them.
- Pierce belongs to the Spearman and Pikeman line, and it hits the main target plus the tile behind it.
- Cleave belongs to the Axeman and Maceman line, and it hits the main target plus the two tiles beside it.
- Splash belongs to the Catapult and Trebuchet, and it hits a cluster of 7 tiles.
- Circle belongs to the Macedonian Companion and certain elephants, and it hits all 6 adjacent tiles.
An extra hit's strength is a small percentage of the unit's base strength. For example, Pierce I adds +25% Pierce damage on top of a flat +1.
Rout and routed units
A unit at 0 HP routs: it retreats one tile and cannot attack until you rally it. The final blow never does more damage than the unit's remaining HP.
- A unit that cannot retreat, because it is surrounded or on water, is destroyed instead.
- Zone of control never stops an attack, a rout or a push.
- A routed unit heals 5 HP per turn from the next turn, once it is safe.
Combat constants
| Constant | Value | Meaning |
|---|---|---|
STRENGTH_MULTIPLIER | 10 | Strength inside the game is 10 times the displayed value. |
ACTIVE_HEAL | 5 | HP healed per turn when the unit neither moves nor attacks. |
IDLE_HEAL | 1 | HP healed per turn after moving but not attacking. |
UNIT_HEAL_COST | 1 | Cost per HP healed (in Training or Civics, depending). |
COUNTER_CITY_DAMAGE | 1 | Damage delivered to a city per attack against its garrison. |
COUNTER_ROUT_DAMAGE | 1 | Damage applied to a routed unit if attacked again. |
CITY_STRENGTH_BASE | 80 | Base garrison strength for an undamaged city. |
CITY_STRENGTH_PER | 5 | Bonus strength per city level. |
CITY_HEAL_PERCENT_PER_TURN | 5% | City HP healed per turn while at peace. |
CITY_CAPTURE_DAMAGE_PERCENT | 50% | City damage taken on capture. |
Related pages
- Unit Damage & Counters: stats and counters for every combat unit.
- Unit Counters: which unit type beats which.
- Promotions: every modifier you can add to strength.