Damage formula

This page provides highly detailed information about the game. If you are looking to learn more about combat it's recommended to check land warfare first.

The damage formula is used to calculate strength and morale losses when a source unit attacks a target unit. Units attack up to one target every day. No other losses are applied. Both land and naval combat use the same damage formula.

Most of the damage formula and combat modifiers are shown in tooltips but some information requires manual verification.

Damage formula

• Base damage: Affected by dice rolls, terrain and general martial skill.
• Damage modifiers: Affected by unit's strength, unit types, traditions, technology, trade, tactics, etc.
• Morale damage modifiers: Affected by unit's current morale and unit types.
• Strength damage modifiers: Affected by unit types and tactics.

Base damage

The first step is to calculate the base damage for all units in the army.

• Dice roll: Random value between 1 and 6 is rolled every 5 days for each side.
• Terrain penalty: Terrain causes up to -4 penalty for the attacker.
• General bonus: The side with a better general gets a bonus (Martial skill difference / 2).

 general_bonus = max(0, (source_martial - target_martial) / 2)
 base_damage = min(0.36, 0.096 + 0.024 * (dice_roll - terrain_penalty + general_bonus))

Without any modifiers, the base damage is from 0.12 to 0.24. This means the best roll of 6 causes units to deal double damage when compared to the worst roll of 1.

Every general bonus increases the base damage (and total damage) by 10%-20% depending on the roll. A good general is a great way to mitigate a bad roll because lower rolls see a bigger benefit.

Similarly the terrain penalty lowers the base damage (and total damage) by 10%-20% depending on the roll. However a damage reduction has a bigger impact than a damage increase. For example -4 penalty on a roll of 1 means units will do only 20% of their normal damage.

Total damage

The second step is to calculate total damage for each unit. Base damage is multiplied by modifiers from both source and target units.

Modifier	Type	Description	Multiplier
Strength	Source cohort	Weakened cohorts deal less damage.	0.0 - 1.0
Discipline	Source type & source global	Loyalty gives discipline. Main sources are military traditions, technology and trade.	1.0 - 2.0
Loyalty	Source cohort	Personal loyalty increases damage done. On tooltips this is shown as discipline.	1.0 - 1.1
Terrain	Source type	Only applies when fighting in a specific terrain. Main source is military traditions.	1.0 - 1.33
Versus	Source type & target type	Unit types may get a damage bonus or penalty against other unit types.	0.5 - 1.5
Offense vs. Defense	Source type & target type	Offense is directly reduced by defense. Main source is military traditions.	0.75 - 1.25
Damage done	Source global	Naval only. Main sources are military traditions, technology and trade.	0.9 - 1.5
Damage taken	Target global	Naval only. Main sources are military traditions, technology and trade.	0.65 - 1.15
Tactics	Source tactic & target tactic	Damage bonus when countering a tactic. Damage penalty when getting countered.	0.9 - 1.25
Experience	Target unit	Experienced units take less damage.	0.625 - 1.0

 offense_vs_defense = 1.0 + offense_bonus - defense_bonus
 tactics = countering ? (1.0 + tactic_damage * tactic_effectiveness) : (countered ? 0.9 : 1.0)
 loyalty = is_loyal ? 1.1 : 1.0
 experience = 1.0 - 0.3 * experience_percent * (morale_damage_taken + strength_damage_taken) / 2.0
 total_damage = base_damage * strength * discipline * loyalty  * terrain * versus * offense_vs_defense * tactics * experience * damage_done * damage_taken

Strength damage

The third step is to calculate strength losses from the total damage.

Modifier	Type	Description	Multiplier
Strength damage done	Source type	Naval only. For heavier ships.	1.0 - 1.4
Strength damage taken	Target type	For heavier units and ships.	0.5 - 1.0
Tactics	Source tactic & target tactic	Some tactics increase casualties	0.5 - 1.2
Daily multiplier	Global	Constant multiplier to scale losses.	0.2 for land, 0.5 for naval

 strength_damage = total_damage * strength_damage_done * strength_damage_taken * tactics * daily_multiplier
 manpower_damage = strength_damage * 1000

Morale damage

The fourth step is to calculate morale losses from the total damage.

Modifier	Type	Description	Multiplier
Morale	Source unit	Morale directly affects damage.	0.0 - 4.0
Morale damage done	Source type	Naval only. For lighter ships.	1.0 - 1.15
Morale damage taken	Target type	For infantry and most ships.	0.7 - 1.25
Daily multiplier	Global	Constant multiplier to scale losses.	1.5 for land, 2.0 for naval
Base multiplier	Global	Constant multiplier to scale losses.	0.5

 morale_damage = total_damage * morale * morale_damage_done * morale_damage_taken * daily_multiplier * base_multiplier

In most combat situations, the morale runs out much faster than the strength. This is because the daily multiplier is much higher for morale. Fighting with high morale units is the best way to win fights quickly. Units with a low morale still deal full strength damage.

Example tooltip (Land)

Example tooltip for land combat

Example of a tooltip from land combat. The tooltip is split to 5 sections. Overall the information of the tooltip can be confusing because it shows information for both current round and the previous round.

Unit information

• Unit type: Psiloi, Greek name for Archers.
• Unit name: Polyrrinia's 1st Chiliostys.
• Unit strength: 985 men (0.985 strength)
• Unit morale: 3.05

Inflicted losses

• Target: The previously attacked unit was Kydonia's 1st Chiliostys. In most cases this shows which unit was attacked last round. But it may also show older info if no target have been within range.
• Caused losses: Amount of losses that would be done this round to the previously attacked cohort. The actual target may be different which would result in different amount of losses.

Base damage

• Roll: Dice roll was 6 on the previous round. This may change which affects inflicted losses.
• Terrain & Leader Modifiers: +3 bonus to roll because of good general. This may change if a better general joins the battle.
• Base Damage: 0.26 base damage on the previous round (0.08 + 0.02 * 9, values from patch 1.2).

Damage modifiers

• Discipline: Total discipline gives a 14% damage bonus.
• Hills Bonus: Unit has a 15% damage bonus when fighting in hills.
• Vs Light Infantry: Unit has a 25% damage bonus against Light Infantry.
• Bottleneck vs Shock Action: Bottleneck tactic counters Shock Action which gives a 10% damage bonus (20% * 50% efficiency).
• Archers Offense vs Light Infantry Defense: Light Infantry has 10% more defense than Archers have offense which results in a 10% damage penalty.
• Kydonia's 1st Chiliostys Experience: Experience of the target gives a 2.26% damage penalty.

Strength and morale damage

• Damage from 985 Men: Currently always shows 0.
• damaged from Tactics: Shock Action gives a 10% strength damage bonus for both sides. (Land_warfare#Combat_Tactics)
• Daily Multiplier: Constant multiplier for strength damage.
• Kydonia's 1st Chiliostys: Target doesn't take increased or reduced strength damage.
• Morale: 3.05 morale gives a 1.525 morale damage multiplier for the next round (0.5 base multiplier is applied here). Slightly different value on the tooltip means that the unit actually has 3.0556 morale. The tooltip also shows a wrong value (should be +52.78%).
• Daily Multiplier: Constant multiplier for morale damage.
• Kydonia's 1st Chiliostys: Target takes 25% less morale damage.

Example tooltip (naval)

Example tooltip for naval combat

Example of a tooltip from naval combat. Most of the information is same as with the land combat. Some differences exist:

• Unit strength is shown as a percentage instead of as a manpower.
• Naval damage done and naval damage taken are shown instead of discipline. However discipline still applies to naval combat.
• Daily multipliers show wrong values from land combat.
• Strength damage done is not shown but still applies to naval combat.

Examples

All calculations use 5 precision with extra decimals dropped. For example 0.123456 becomes 0.12345.

Example: No modifiers

Source unit

• 100% strength, 3.00 morale

With roll 1

 Base damage = 0.096 + 0.024 = 0.12
 Total damage = 0.12 (Base damage)
 Strength damage = 0.12 (total damage) * 0.2 (daily multiplier) = 0.024 = 24 manpower
 Morale damage = 0.12 (total damage) * 3.0 (morale) * 1.5 (daily multiplier) / 2.0 = 0.27

With roll 6

 Base damage = 0.096 + 0.024 * 6 = 0.24
 Total damage = 0.24
 Strength damage = 0.048 = 48 manpower
 Morale damage = 0.54

Conclusion

• Units lose ~36 manpower and ~0.4 morale on the first day if there are no modifiers.

Example: Land combat (example tooltip)

Source unit

• General skill 6, Roll 6
• Bottleneck tactic (50% efficiency)
• Archer, 98.5% strength, 3.0556 morale
• +14% discipline (4% from Strategos, 10% from Military tradition)
• +15% hill bonus
• +25% versus bonus against Light Infantry

Target unit

• General skill 0
• Shock Action tactic (+10% casualties)
• Light Infantry, 100% strength, 1.08 morale
• +10% defense
• -25% morale damage taken
• 8.61% experience

Inflicted losses

 Base damage = 0.26 (value from patch 1.2)
 Tactics = 1.1 
 Experience = 0.02260
 Total damage = 0.26 (base damage) * 0.985 (strength) * 1.14 (discipline) * 1.15 (terrain) * 1.25 (versus) * 1.1 (tactics) * 0.9 (offense vs. defense) * 0.97740 (experience) = 0.40609
 Strength damage = 0.40609 (total damage) * 1.1 (tactics) * 0.2 (daily multiplier) = 0.08933
 Morale damage = 0.40609 (total damage) * 3.0556 (morale) * 1.5 (daily multiplier) * 0.75 (morale damage taken) *  0.5 (base multiplier) = 0.69797

Conclusion

• The tooltip shows that next round should kill 89 manpower and inflict 0.69 morale damage.
• These match the calculated values 0.08933 and 0.69797 as they are rounded down on the tooltip.
• Actual result may be off by one because partial damage carries over from previous rounds.

Example: Naval combat (example tooltip)

Source unit

• General skill 4, Roll 2
• Frontal Assault tactic
• Mega-Polyreme, 91% strength, 2.49 morale
• +3.5% discipline (Strategos)
• -10% damage done (Boarding Tactics)
• +40% strength damage done

Target unit

• General skill 8
• Close Ranks tactic
• Mega-Polyreme, 100% strength, 3.00 morale
• -50% strength damage taken
• -30% morale damage taken
• +10% damage taken (Ramming Tactics)

Inflicted losses

 Base damage = 0.08 + 0.02 * 2 = 0.12 (value from patch 1.2)
 Tactics = 0.9 (countered)
 Total damage = 0.12 (base damage) * 0.91 (strength) * 1.035 (discipline) * 0.9 (damage done) * 0.9 (damage done) * 0.9 (tactics) = 0.08239 (damage done is applied twice and damage taken is ignored in patch 1.2)
 Strength damage = 0.08239 (total damage) * 1.4 (strength damage done) * 0.5 (strength damage taken) * 0.5 (daily multiplier) = 0.02883
 Morale damage = 0.08239 (total damage) * 2.49 (morale) * 2.0 (daily multiplier) * 0.7 (morale damage taken) * 0.5 (base multiplier) = 0.14360

Conclusion

• The tooltip shows that next round should damage 2% strength and inflict 0.14 morale damage.
• These match the calculated values 0.02883 and 0.14360 as they are rounded down on the tooltip.
• Actual result may be off by one because partial damage carries over from previous rounds.

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