User:Wethospu

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 loss in combat on daily basis. 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.

Key elements

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

List of modifiers

Lots of modifiers affect the damage formula. Land and naval combat focus on different modifiers which explains why some modifiers have an similar effect.

Modifiers mostly either increase outgoing damage or reduce incoming damage.

• Discipline: Multiplier for outgoing damage. Incoming damage is not reduced unlike what tooltip says in the game.
• Morale damage taken: Multiplier for incoming morale damage.
• Strength damage taken: Multiplier for incoming strength damage.
• Morale damage done: Multiplier for outgoing morale damage.
• Strength damage done: Multiplier for outgoing strength damage.
• Damage taken: Multiplier for incoming damage.
• Damage done: Multiplier for outgoing damage.
• Experience: Multiplier for incoming damage.
• Offense: Affects outgoing damage. Reduced by defense.
• Defense: Affects incoming damage. Reduces offense.
• Unit strength: Multiplier for outgoing damage.
• Unit morale: Multiplier for outgoing morale damage.
• Damage against unit type: Multiplier for outgoing damage.
• Daily morale multiplier: Multiplier for outgoing morale damage.
• Daily strength multiplier: Multiplier for outgoing strength damage.
• Base damage: Multiplier for all damage.

Base damage

The first step is to calculate outgoing damage for all units, before unit specific modifiers are applied.

• Dice roll: Random value between 1 and 6 is rolled every 5 days for each side.
• Terrain penalty: Terrain modifier causes up to -4 penalty for the attacker. #Terrain_modifiers
• Leader bonus: General causes up to 7 bonus to the side with a better general (skill difference / 2). #Leader_modifiers

 pips = dice_roll + terrain_penalty + leader_bonus
 base_damage = 0.08 + (0.02 × pips)

Total damage

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

Modifier	Type	Description	Multiplier
Strength	Source unit	Weakened units deal less damage.	0.0 - 1.0
Discipline	Source unit & type	Loyalty gives discipline. Main sources are military traditions and trade.	1.0 - ~1.4
Experience	Target unit	Experienced units take less damage.	0.625 - 1.0

Following modifiers apply to the source unit (often increasing the damage)

• Strength (unit): Multiplier. Weakened units deal less damage. From 0.0 to 1.0.
• Discipline: Multiplier. Main sources are military traditions, trade and loyalty. Usually from 0.0 to 1.4.
• Terrain bonus (unit type): Multiplier. Only applies when fighting in a specific terrain. Main source is military traditions. Usually from 0.0 to 1.15
• Versus (unit type): Multiplier. Unit types get damage bonus or penalty against other unit types. From 0.5 to 1.5.
• Offense (unit type):

Following modifier are based on the target unit (often reduing the damage)

• Experience: Multiplier. Experienced units take less damage. From 1.0 to 0.625.

• Discipline: Increases caused damage in all combat situations. Main sources are military traditions, trade and loyalty. Usually from 0% to +40%. (#Discipline)
• Terrain bonus: Unit type may cause increased damage in the current terrain. Main source is military traditions. Usually from 0% to +15%.
• Vs Defender: Unit type may cause increased or reduced damage against the opposing unit type. From -50% to +50%. (Unit Types)
• Tactic vs Tactic: Selected tactic may cause increased or reduced damage against opponent's tactics. Amount of the increased damage depends on unit types in the battlefield. From -10% to +25%. (#Combat_Tactics)
• Attacker Offense vs Defender Defense: Units may cause increased damage or receive reduced damage. Main sources are military traditions and trade. Usually from -15% to +30%.
• Defender Experience: Unit's experience reduces received damage. From 1.0 to 0.625. #Experience

 experience_reduction = 0.003 * VS_experience * (morale_damage_taken + strength_damage_taken) / 2

 total_damage = base_damage × (1 + discipline) × (1 + terrain_bonus) × (1 + VS_unit_type) × (1 + tactics_mod) × (1 + offense - defense) × (1 - experience_reduction)

Example damage tooltip. Note: "Morale: +26.00%" is incorrect and should read "x0.26"

The damage formula is mostly explained in-game on the damage tooltip. The tooltip is split to 5 sections.

Unit information

• Unit type: The tooltip uses the common name of the typ when the modifier is based on the unit's type.
• Unit name: The tooltip uses the unit's name when the modifier is based on the unit's attributes.
• Unit strength: Multiplier for all damage dealt.
• Unit morale: Multiplier for morale damage dealt.

Inflicted losses

This sections shows losses that this unit will cause to the target unit in the next round. The text is misleading indicating these losses were caused this round. However the values use the current strength and morale of the unit, not values in the previous round.

Strength and morale damage

Total damage gets multiplied by strength of the unit and then further modified by strength and morale specific multipliers.

• Damage from: Should show total damage from the attacker. Currently always shows 0.
• Casualties from Tactics: Some tactics increase or decrease strength damage for both attacker and defender. From -50% to +20%. (#Combat_Tactics)
• Daily Multiplier: Multiplier (0.2x) for strength damage.
• Defender: Some unit types receive increased or reduced strength damage. From -50% to 0%. (Unit Types)
• Morale: Attacker's own morale directly affects caused morale damage. Tooltip shows wrong value (should be reduced by 100%, for example +26.00% should be -74.00%). Usually from -75% to 200%.
• Daily Multiplier: Multiplier (1.5x) for morale damage.
• Defender: Some unit types receive increased or reduced morale damage. From -25% to +25%. (Unit Types)

 strength_damage = total_damage × current_strength × (1 + casualties_from_tactics) × 0.2 × (1 + VS_unit_type)

 morale_damage = total_damage × (current_strength ÷ 1000) × (current_morale ÷ 2) × 1.5 × (1 + VS_unit_type)

One notable difference from EU4 is that current, not maximum morale, is used to determine morale-damage; so worn down units inflict much less morale-damage on the enemy. Also units that are flanking or in reserve do not suffer any morale hits.

On average you can expect to roll (1+6)/2 = 3.5 and with equal generals and no terrain penalties have a base-damage of 0.8 + 0.2*3.5 = 0.15. In the absence of other modifiers this corresponds to 1000-man cohort with 3.0 morale killing 0.15*1000*0.2 = 30 men and inflicting 0.15*1*(3/2)*1.5 = 0.33 morale damage per day.

Each pip modifies base-damage by 13% of this expected average.
The worst possible base-damage is 0.02, having -4 from terrain and rolling a 1 with an equal or worse general. The best possible is 0.34, rolling a 6 with +7 from general (14-skill general vs no general) and no terrain penalty.