Combat

A battle

Each battle has an attacking side and a defending side. If the location does not have a fort, the first unit present before a battle will be the defender. If the location has a fort, the fort's controller will always be the defender.

An army or navy that runs out of morale, loses a battle without all soldiers being killed, or is manually ordered by is country to retreat, will not fight another battle or receive new orders until it has reached its retreat destination.

Winning a battle gives a prestige bonus to the victor, and in wars between countries it also gives warscore.

Terrain

Base terrain modifiers

The attacking and in the case of frontage; defending armies can be affected by both topography and vegetation during battle. This can be in the form of penalties to dice rolls, frontage as well as some units having their own unique penalties and/or buffs in certain terrain types. For example, a mountainous woods province would give the attacker a -3 to their dice rolls (-2 from mountains, -1 from woods) and give both sides -6 possible frontage (-4 from mountains, -2 from woods).

Rivers and straits also provide dice roll penalties to the attacking army, so long as they cross over or into a location with a river or cross into a location through a strait. Rivers provide a penalty of −1, and straits a penalty of −2.

Unit specific modifiers

Unit types can sometimes get benefits or penalties from fighting in certain topography and vegetation types.

This modifier is represented as a percentile increase to your damage, such as +50% for galleys in narrows or -10% for cavalry in wetlands, mountains or jungles.

Unique units can have their own unique modifiers in terrain. For example, the Irish Hobelars (A cavalry unit) gets +50% damage in woods and hills and +25% damage in forests.

Combat

Phases

Combat is made up of multiple phases, which last 5 hours each. During each phase, both sides will roll a 6 sided die, which determines how much damage each side will deal until the next phase.

In land battles, if either army has an Artillery regiment, combat will begin with the Bombard Phase. This Phase lasts 5 hours and each hour Artillery regiments have a chance, equal to their bombardment efficiency, to deal damage to an enemy regiment on the same section. Afterwards, the combat phases will proceed as normal.

For regiments, the amount of damage they deal is calculated as  Combat Power multiplied by Strength. For ships, the amount of damage they deal depends on  Cannons and the amount of damage they receive depends on  Hull Size.

Sections and Engagement

Combat has four sections, center, left flank, right flank, and reserves. Each unit is assigned to one of the sections from the army screen. Units start the combat disengaged, incapable of dealing damage. Each hour, units that are placed in the center, left flank or right flank sections have a chance to become engaged, choose an enemy target to attack, and start dealing damage to it. The chance for a unit to become engaged depends on its  Initiative and is 0.1 + (Initiative*0.02)+(Hours*0.01). Hours reset after reaching a maximum of 5 hours to go back to 1 and revolve again. The maximum number of units that can be engaged at once in each section depends on the location's  Possible Frontage and each unit's  Frontage.

Units from reserve have a chance each hour to move to any of the flanks which depends on  Combat Speed. The chance to engage is 0.05* Combat Speed*Combat speed modifier. The most common combat speed modifiers are from general ability and from defensive values.

Units that join combat late by moving from an adjacent province are assigned either to the reserve or to their assigned section, with the chance of joining their section being the  Correct Section Chance

Target selection

When a unit engages in combat, they choose a target to attack, and will keep attacking it until either of the units is eliminated. Units will choose one of the engaged units in the opposite section to attack, seemingly at random. However, if there are no opposing engaged units, a unit may target a disengaged unit. It will continue to attack it even if there are valid engaged targets to attack later. A disengaged unit will take additional damage (see below). If the enemy army or navy does not have units in the same section, the nearest adjacent section will be targeted and the attacking unit may deal additional damage depending on its  Flanking Ability.

Damage

Army Damage Calculation

Base strength damage, measured in number of men killed in the opposing regiment, is $dice\_impact=10+(dice\_roll-1+terrain\_dice+crossing\_dice)\times 2$

Base morale damage is 1/200 of that, or $dice\_impact=0.05+(dice\_roll-1+terrain\_dice+crossing\_dice)\times 0.01$

In addition to damage from units, every regiment that is in combat, included not engaged units and reserves, takes 0.01 morale damage per hour.

Most of the calculation of strength and morale damage is the same, but there are a few modifiers that apply differently. Each of the modifiers listed here is applied multiplicatively on top of the others.

Damage Modifiers

The following modifiers are applied to both morale and strength damage based on the stats of the attacking regiment

•  Combat Power
•  Infantry Power, Cavalry Power, or  Artillery Power
•  Discipline
• When attacking a flank other than the opposing one,  Flanking Ability. 200% flanking ability is a 2x modifier, while 100% means no flanking bonus.
• When attacking  Regulars with Levies,  Levy Combat Efficiency. Levy combat efficiency starts at a base of 0.2 for age 1 levies, increases by 0.05 for each age's levies, and is then modified
• Terrain and vegetation modifiers. For example, most cavalry units face a 10% penalty in mountains, jungle, or wetlands.

The following defensive modifiers are based on the stats of the defender

• Damage is divided by  Military Tactics. Tactics of 2 would therefore be a 50% damage reduction
• Damage is reduced by Army Experience, divided by 2. At 100% experience, this is a 50% damage reduction.
• Damage Taken modifier of the unit type. This is currently 0.75 for cavalry for 1.5 for artillery.
•  Secure Flanks, multiplied by the number of adjacent flanks that are not empty. For infantry, this amounts to 50% damage reduction in the center and 25% on the flanks.
• Extra damage taken for levies defending against  Regulars, depending on the defending unit's age: Age of Traditions (100%), Age of Renaissance (50%), Age of Discovery (25%), Age of Reformation (12.5%)

Strength damage modifiers

Offensive Modifiers:

• Regiment Strength: 1 for naval units, or ${\frac {men\_in\_regiment}{1000}}$ for army units.
• Strength damage done modifier
• 1.1 if attacking a non-engaged regiment. This may happen during the bombard phase, or if there are no engaged units for the unit to target.

Defensive modifiers:

• Strength damage taken modifier

Morale damage

Offensive Modifiers:

• Proportion of maximum regiment strength (unlike strength damage, this is proportion rather than absolute numbers)
• Morale damage done modifier
• 1.2 if attacking a non-engaged regiment. This may happen during the bombard phase, or if there are no engaged units for the unit to target.

Defensive modifiers:

• Morale damage taken modifier

Navy Damage Calculation

Navy damage is split into both Strength Damage and Morale Damage.

Base strength damage, measured in percentage points, is $dice\_impact=0.25+(dice\_roll-1+terrain\_dice)\times 0.05$

Base morale damage is $dice\_impact=0.01+(dice\_roll-1+terrain\_dice)\times 0.002$

Navies attacking into Narrows locations should get a -1 on dice rolls but in version 1.0.10 this modifier does not currently apply.

Damage Modifiers

Naval damage is modified by the number of  Cannons vs  Hull Size. It calculates this by comparing the percentage increase required for the defending ship's hull value to meet the cannon value of the attacker. For example, a 9 cannon galley firing at a 6 hull light ship would have a +50% cannons vs hull size modifier because you need to increase 6 by 50% to get to 9. This can be represented as ((AttackerCannons - DefenderHull) / DefenderHull) to get the decimal value of the percentage.

The following modifiers are applied to both morale and strength damage based on the attacking regiment

• Current strength. A ship at 50% strength will have a -50% modifier applied to all it's outgoing damage
•  Galley Power, Heavy Ship Power,  Light Ship Power, or  Transport Power
•  Naval Damage Done. Up to 20% gained from Admiral Military ability and other sources from advances such as 10% from boarding parties.
• When attacking a flank other than the opposing one,  Flanking Ability is applied. Light ships get +20% when flanking.
• Terrain and vegetation modifiers. Galleys suffer a -100% damage dealt penalty in Deep Ocean, -50% in Ocean, while getting +25% in Inland Sea and +50% in Narrows
• If a ship is attacking another ship that is not engaged, the attacking ship deals +10% Strength damage, and +20% morale damage to that ship.

The following defensive modifiers are based on the stats of the defender

• Ship Experience, divided by 2. At 100% experience, this is a 50% damage reduction.
•  Naval Damage Taken which is a flat damage reduction based on the value.

Strength damage formula with modifiers

Below is a formula for all these damage modifiers alongside one another for strength damage. Any percentile values such as 50% are represented as a decimal such as 0.5 for the sake of the formula. This is purely for strength damage, not morale damage as they have different formulas.

Some values, such as NavalDamageTaken are negative values by default. For example, Norway's starting -5% for Naval Damage Taken will be represented as -0.05 here.

$(0.25+(DiceRoll-1+terrain\_dice)\times 0.05)\times (1+NavalDamage)\times \left(1+{\tfrac {{\text{AttackerCannons}}-{\text{DefenderHull}}}{\text{Defender Hull}}}\right)\times (1+(ShipStrength-100)\div 100)\times (1-(Exp\div 2))\times (1+ShipCombatAbility)$ $\times (1+FlankingAbility)\times (1+TopographyModifier)\times (1+NotEngagedModifier)\times (1+NavalDamageTaken)$

All modifiers, both negative and positive are multiplicative to one another in this formula, making all of them equally as important to consider for any aspiring admiral.

Unit stats

Units have the following stats:

• Initiative is the chance that a unit will engage during the combat phase if placed in the center, left flank or right flank.
• Frontage determines how many units can fight at the same time. It is also affected by the topography or vegetation of a location.
• Food storage is the amount of food that a unit can carry. It is reduced by 50% if the unit retreats.
• Movement speed determines how fast a unit moves across the map.
• Combat speed determines how fast the unit moves from reserves to another section during battle. For ships, it also impacts how quickly a damaged ship can leave the current section to retreat.
• Flanking ability is how much damage the unit can inflict on units in a different section.
• Attrition loss is how much damage attrition does each month.

Regiments have the following additional stats:

• Combat power is the direct damage dealing attribute of a regiment. It is multiplied with the manpower of the regiment to determine how much damage the regiment does.
• Maximum strength increases how many more men the regiment has, thus increasing its manpower cost. A regiment with a higher amount of manpower but with the same frontage is more effective in combat.
• Unit weight is compared against the army location's supply limit to determine whether the regiment will suffer attrition.
• Food consumption is the amount of food that a regiment will consume each month.
• Secure flanks provides a defensive bonus when there are friendly troops in a neighboring section. The bonus is doubled if both flanks are secure.
• Experience reducing the damage taken by 0.5% per point up to 50% at max experience.

Ships have the following additional stats:

• Cannons determine how much damage the ship does.
• Hull size reduces the damage the ship takes.
• Crew size determines how many sailors are requires for the ship to be operational.
• Transport capacity is how many regiments can embark on the ship.
• Anti-piracy impact is the effect the ship will have on privateers in their area.
• Blockade capacity determines how effective the ship is at blockading.

Base Unit Stats

	category	buildable	max_strength	combat_power	impact			combat			bombard_efficiency	artillery_barrage
					jungle	wetlands	mountains	jungle	wetlands	mountains
a_age_1_traditions_infantry	army_infantry	no	0.1	1
a_age_2_renaissance_infantry	army_infantry	no	0.2	1
a_age_3_discovery_infantry	army_infantry	no	0.4	1
a_age_4_reformation_infantry	army_infantry	no	0.8	1.5
a_age_5_absolutism_infantry	army_infantry	no	1.6	2.25
a_age_6_revolutions_infantry	army_infantry	no	3.2	3
a_age_1_traditions_cavalry	army_cavalry	no	0.05	4	0.1	0.1	0.1	-0.1	-0.1	-0.1
a_age_2_renaissance_cavalry	army_cavalry	no	0.1	4	0.1	0.1	0.1	-0.1	-0.1	-0.1
a_age_3_discovery_cavalry	army_cavalry	no	0.2	4	0.1	0.1	0.1	-0.1	-0.1	-0.1
a_age_4_reformation_cavalry	army_cavalry	no	0.3	4	0.1	0.1	0.1	-0.1	-0.1	-0.1
a_age_5_absolutism_cavalry	army_cavalry	no	0.6	4	0.1	0.1	0.1	-0.1	-0.1	-0.1
a_age_6_revolutions_cavalry	army_cavalry	no	1.2	4	0.1	0.1	0.1	-0.1	-0.1	-0.1
a_age_1_traditions_auxiliary	army_auxiliary	no	0.05	0.25
a_age_2_renaissance_auxiliary	army_auxiliary	no	0.1	0.25
a_age_3_discovery_auxiliary	army_auxiliary	no	0.2	0.25
a_age_4_reformation_auxiliary	army_auxiliary	no	0.3	0.25
a_age_5_absolutism_auxiliary	army_auxiliary	no	0.6	0.25
a_age_6_revolutions_auxiliary	army_auxiliary	no	1.2	0.25
a_age_1_traditions_artillery	army_artillery	no	0.01	2							0.1	1
a_age_2_renaissance_artillery	army_artillery	no	0.05	3							0.125	3
a_age_3_discovery_artillery	army_artillery	no	0.1	4							0.15	4
a_age_4_reformation_auxiliary	army_artillery	no	0.3	5							0.2	5
a_age_5_absolutism_artillery	army_artillery	no	0.6	6							0.25	7
a_age_6_revolutions_artillery	army_artillery	no	1.2	8							0.25	9

# impact = { <topography> / <vegetation> / <climate> }    # Modifies the damage the unit takes when fighting in certain terrain

# combat = { <topography> / <vegetation> / <climate> }    # Modifies the damage the unit deals when fighting in certain terrain

Standard Units From Each Age

category

copy_from

strength_damage_done

morale_damage_done

morale_damage_taken

combat_speed

initiative

light

default

buildable

levy

food_consumption_per_strength

build_time_modifier

mercenaries_per_location

upgrades_to

maintenance_demand

construction_demand

country_potential

pop_type

multiply

Tradition

a_footmen

army_infantry

a_age_1_traditions_infantry

-0.05

yes

burghers

0.1

a_men_at_arms

early_heavy_infantry_maintenance

early_heavy_infantry_construction

government_type != government_type:steppe_horde

a_archers

army_infantry

a_age_1_traditions_infantry

-0.1

0.2

5

yes

yes

burghers

0.1

a_crossbowmen

archer_infantry_maintenance

archer_infantry_construction

government_type != government_type:steppe_horde

a_footmen_levy

army_infantry

a_footmen

no

yes

a_horsemen

army_cavalry

a_age_1_traditions_cavalry

-0.1

0.2

5

yes

nobles

0.3

a_cavalrymen

a_armored_horsemen

army_cavalry

a_age_1_traditions_cavalry

nobles

0.3

a_heavy_cavalrymen

heavy_cavalry_maintenance

heavy_cavalry_construction

a_camp_followers

army_auxiliary

a_age_1_traditions_auxiliary

peasants

0.001

a_supply_carts

exists = government_type government_type != government_type:steppe_horde

Renaissance

a_men_at_arms

army_infantry

a_age_2_renaissance_infantry

-0.1

1

a_halberdiers

early_heavy_infantry_maintenance

a_crossbowmen

army_infantry

a_age_2_renaissance_infantry

-0.1

0.2

5

yes

burghers

0.1

a_early_arquebusiers

early_heavy_infantry_construction

a_handgonners

army_infantry

a_age_2_renaissance_infantry

0.1

-0.5

5

0.25

0.25

burghers

0.1

a_early_arquebusiers

infantry_maintenance

a_men_at_arms_levy

army_infantry

a_age_2_renaissance_infantry

no

yes

burghers

0.1

infantry_construction

a_cavalrymen

army_cavalry

a_age_2_renaissance_cavalry

-0.1

0.2

5

yes

nobles

0.3

a_light_lancers

a_heavy_cavalrymen

army_cavalry

a_age_2_renaissance_cavalry

nobles

0.3

a_lancers

heavy_cavalry_maintenance

a_houfnice

army_artillery

a_age_2_renaissance_artillery

burghers

0.5

a_falconet

heavy_cavalry_construction

a_supply_carts

army_auxiliary

a_age_2_renaissance_auxiliary

peasants

0.005

a_supply_convoy

Discovery

a_halberdiers

army_infantry

a_age_3_discovery_infantry

burghers

0.1

a_halberdiers

early_heavy_infantry_maintenance

a_early_arquebusiers

army_infantry

a_age_3_discovery_infantry

-0.1

0.2

5

yes

burghers

0.1

a_arquebusiers

early_heavy_infantry_construction

a_matchlock_levy

army_infantry

a_age_3_discovery_infantry

no

yes

burghers

0.1

a_light_lancers

army_cavalry

a_age_3_discovery_cavalry

-0.1

0.2

5

yes

nobles

0.3

a_pistoleers

a_lancers

army_cavalry

a_age_3_discovery_cavalry

nobles

0.3

a_heavy_lancers

heavy_cavalry_maintenance

a_falconet

army_artillery

a_age_3_discovery_artillery

peasants

0.005

a_chambered_cannon

heavy_cavalry_construction

a_supply_convoy

army_auxiliary

a_age_3_discovery_auxiliary

peasants

0.005

a_baggage_train

Reformation

a_pikemen

army_infantry

a_age_4_reformation_infantry

burghers

0.1

a_musketeers

pikemen_maintenance

a_arquebusiers

army_infantry

a_age_4_reformation_infantry

-0.1

0.2

5

yes

burghers

0.1

a_hunters

pikemen_construction

a_flintlock_levy

army_infantry

a_age_4_reformation_infantry

yes

no

yes

a_pistoleers

army_cavalry

a_age_4_reformation_cavalry

-0.1

0.2

5

yes

nobles

0.3

a_hussars

a_heavy_lancers

army_cavalry

a_age_4_reformation_cavalry

nobles

0.3

a_gallop_cavalry

heavy_cavalry_maintenance

a_chambered_cannon

army_artillery

a_age_4_reformation_artillery

peasants

0.005

a_royal_mortar

heavy_cavalry_construction

a_baggage_train

army_auxiliary

a_age_4_reformation_auxiliary

peasants

0.005

a_wagon_train

Absolutism

a_musketeers

army_infantry

a_age_5_absolutism_infantry

burghers

0.1

a_fusiliers

heavy_infantry_maintenance

a_hunters

army_infantry

a_age_5_absolutism_infantry

-0.1

0.2

5

yes

burghers

0.1

a_sharpshooters

heavy_infantry_construction

a_militiamen

army_infantry

a_age_5_absolutism_infantry

yes

no

yes

a_hussars

army_cavalry

a_age_5_absolutism_cavalry

-0.1

0.2

5

yes

nobles

0.3

a_light_dragoons

a_gallop_cavalry

army_cavalry

a_age_5_absolutism_cavalry

nobles

0.3

a_cuirassiers

heavy_cavalry_maintenance

a_royal_mortar

army_artillery

a_age_5_absolutism_artillery

peasants

0.005

a_flying_battery

a_wagon_train

army_auxiliary

a_age_5_absolutism_auxiliary

peasants

0.005

a_logistics_corps

Revolutions

a_fusiliers

army_infantry

a_age_6_revolutions_infantry

burghers

0.1

heavy_infantry_maintenance

a_sharpshooters

army_infantry

a_age_6_revolutions_infantry

-0.1

0.2

5

yes

burghers

0.1

heavy_infantry_construction

a_conscripts

army_infantry

a_age_6_revolutions_infantry

yes

no

yes

a_light_dragoons

army_cavalry

a_age_6_revolutions_cavalry

-0.1

0.2

5

yes

nobles

0.3

a_cuirassiers

army_cavalry

a_age_6_revolutions_cavalry

nobles

0.3

heavy_cavalry_maintenance

a_flying_battery

army_artillery

a_age_6_revolutions_artillery

peasants

0.005

a_logistics_corps

army_auxiliary

a_age_5_absolutism_auxiliary

peasants

0.005

Sieges

A siege

When an army stops in an enemy location and said location is not protected by its own army, it will begin a siege. Each location has a Garrison number. When the garrison is killed or its morale is gone, the siege will be won by the attackers. If multiple allied armies are present in a siege, the country with the highest number of soldiers will always have the option to take control of the siege if not already.

For a siege to progress, there needs to be at least as many men besieging it as the number of men in the garrison. For a location without fortifications, there needs to be at least 100 men, who will occupy the location in 15 days, but this can be changed by various factors.

The attacker of a siege can always order an assault, which will add siege progress at a fast rate but also cause the army to lose soldiers. An assault cannot be cancelled once ordered. During a siege, up to 3 Breaches may occur, which will reduce the number of soldiers killed in the assault. Hovering over the button to order an assault will show an estimation of whether the assault will be successful or not.

Each siege will last multiple phases. A phase lasts 30 days, but the number can be increased or decreased by various factors. Each phase will roll a die with the value between 1 and 14. The result of each dice roll is decreased by 1 for each Fort Level of the besieged location, increased by 2 for every Breach, and can be increased if the attacker's army has artillery regiments. The maximum dice roll bonus from artillery is initially 5 but can be increased by various factors. If the location is coastal and not blockaded, it also reduces the dice roll by 1. Depending on the dice roll, the following will happen:

Dice result	Effect	Besieger dice bonus
1	Disease Outbreak
2-4	Status Quo
5-11	Supplies Shortage	1
12-13	Food Shortage	2
14-15	Water Shortage	3
16-19	Defenders Desert	2
20	Surrender	Victory

Constructions are paused in locations which are under siege.

Artillery bonus appears to work as follows: each artillery regiment's artillery barrage stat is taken as its base stat multiplied by strength ratio, so a houfnice with a base barrage stat of 3.00 and 160 of its 200 max manpower will have a barrage stat of 2.40. Each of these barrage stats has the fort level subtracted from it, then all the barrage stats are added together, and the result divided by 3 is the dice roll bonus from artillery. So the hypothetical 160/200 manpower houfnice siegeing a level 2 fort would only contribute 0.133 to the dice roll bonus while a full-strength houfnice would contribute 0.333, and a houfnice at 133 or less manpower would contribute nothing at all.

References

Mechanics