1. We have added a Gift Upgrades feature that allows you to gift an account upgrade to another member, just in time for the holiday season. You can see the gift option when going to the Account Upgrades screen, or on any user profile screen.
    Dismiss Notice

The Mechanics of Combat (vanilla)

The Mechanics of Combat

Tags:
  1. vexing
    Combat
    How attacking and defending work

    Introduction

    Highly promoted spearman attacking highly penalized tank

    "Writing an anti-war book is like writing an anti-glacier book" - Kurt Vonnegut, Jr.
    "Knowing is half the battle" - G.I. Joe

    Given the inevitability of war in Civilization, it is prudent to be aware of the mechanics of combat. Whether engaged in an extensive entrenchment or a basic barbarian battle, primal fight or flight instincts need not be relied upon for guidance; expected and worse case scenarios can be determined prior to any combat.


    Definitions

    • CS - Combat Strength - The fully modified strength of units after all modifiers have been considered.
    • Modifiers - Percentages that are added to a unit's base strength to produce combat strength, such as terrain or promotions.
    • Melee - Unit vs unit combat that results in damage to both parties.

    Basics of Combat

    Melee combat occurs when a non ranged unit attacks any non civilian enemy unit. The units do an amount of damage to each other based upon their relative combat strengths. Both units engaged in the combat gain experience which can be used to earn promotions. At the end of combat, if a unit's hit points are reduced to 0 that unit is destroyed, though in melee combat one unit always survives (see Death). If the defender is destroyed, the attacker moves to occupy the defender's hex.

    Attacking typically expels all movement points for a unit. Some units, such as mounted, have the ability to move after attacking, and the blitz and logistics promotions also confer this ability. In this case, attacking expends as many movement points as moving into that hex would have were it unoccupied, for example attacking across a river expels all movement points just as moving across does.

    In determining the results of combat, the combat strength itself does not matter, just how it compares to the opponent: a 4 cs versus 8 cs battle will end the same as a 40 cs versus 80 cs battle. At even combat strength a melee unit will do 4-7 damage to an opponent, spread evenly across those values to average 5.5 damage. The damage dealt increases at a rate related to the combat strength ratios. A battle where the ratio is 1:2 will result in approximately 3 damage to the stronger party and 9.8 damage to the weaker. To find the final combat strength for the battle, each unit's base strength is modified by promotions, terrain and flanking. When a unit is damaged, the damage it deals is reduced by approximately 10% for each two whole points of damage the unit has suffered: odd amounts of damage do not reduce damage output.

    Combat Information Table


    The combat information table


    False numbers from a nonadjacent tile
    The combat information table gives an estimated prediction of the results of a battle, based on the current positions of the combatants. Note that if the units are not adjacent these numbers can change for actual combat (as pictured). It is comprised of these parts:
    • Approximate Damage
      This is the mean damage rounded to the nearest integer. Note that when it says 7, the real expected mean damage could be anywhere from 6.5 to 7.5, and the actual damage done can be from about 2/3rds this number (4 damage) to about 4/3rds (10 damage); the greater the possible damage the greater the spread.

    • Strength
      The combat strength with all modifiers applied. A 25 base strength unit with a single +20% modifier results in a listed 30 combat strength.

    • Modifiers
      A list of all the modifiers being applied to the unit's base strength, with positive modifiers in green and negative in red.

    • Health Bar
      A visual representation of the unit's current health and how much the expected damage will be.

    Damage Formula

    The game engine determines the result of combat as follows:
    • Calculates the ratio of the two combat strengths

    • Uses that ratio to create a modified ratio that is lessened at ratios close to 1:1 and strengthened at ratios beyond 3:1

    • Modifies the defined minimum damage (4 for melee) and spread (again 4 for melee) based on the modified ratio and other modifiers, such as a damaged unit loses 10% per 2 damage

    • Rolls a dice from 0 to the modified spread amount and adds that to the minimum damage

    • Rounds that result down to the nearest whole number to get the actual damage dealt, with a minimum of one damage always dealt.
    Precisely, the formula is as follows:

    r = max combatant's CS / min combatant's CS
    m = 0.5 + ( r+3 )^4 / 512
    min damage to weaker party = base min damage * m
    damage spread to weaker party = base spread * m
    min damage to stronger party = base min damage / m
    damage spread to stronger party = base spread / m
    mean damage = min damage + spread / 2 - 0.5
    max damage = floor( min + spread )
    actual damage = max( floor( min damage + random( 0, spread ) ), 1 )​

    The damage can have the following modifiers applied:
    • Damaged Unit: 1 - floor( damage / 2 ) / 10 (a 10% reduction per two points of damage)

    • City: 0.5
    As an example let us consider a 30 vs 22.5 CS melee battle with both units at full hp

    r = 30/22.5 = 4/3
    m = 0.5 + ( 4/3 + 3 )^4 / 512 = 1.19
    damage to the 22.5 cs unit:
    min: 4.75, mean: 6.63, max: 9, spread: 4: 5.2%, 5-8: 21.0% each, 9: 10.7%​
    damage to the 30 cs unit:
    min 3.37, mean 4.55, max: 6, spread: 3: 18.9%, 4-5: 29.7% each, 6: 21.7% ​

    The displayed expected results will be 7 damage (6.63 rounded) and 5 damage (4.55 rounded)​

    If the 22.5 CS unit was attacking a 30 strength city, the damage it deals remains the same, but the min damage the 30 CS city will deal the unit changes from 4.75 to 2.38, the mean from 6.63 to 3.07.


    Min, Mean and Max damage results from melee at full health.

    Modifiers


    An attacking crossbowman upgraded to rifleman falsely listing +65% open terrain ranged bonus.
    Note the listed modified strength is unaffected and still the appropriate 25

    The following modifiers can be applied:
    • Rough Terrain: +25% - applied to the defender if they are in a forest, jungle or hills tile. Some units (such as mounted) have a no defensive bonuses promotion which prevents this bonus.

    • Marsh/Fallout: -15% - applied to the defender if they are in a tile with these features.

    • Open Terrain: -10% - applied to the defender in all other terrain.

    • Attacking Over River: -20% - applied to the attacker when a river is immediately between the combatants.

    • Amphibious Attack: -50% - applied to a melee attacker if attacking from water.

    • Flanking Bonus: +10% (multiple) - a +10% bonus per friendly unit adjacent to the enemy.

    • Fortification: +25% first turn / +50% every turn after - applied to units who begin their turn by fortifying. Some units (such as mounted) have a no defensive bonuses promotion which makes them unable to fortify and gain this bonus.

    • Strategic Resource Penalty: -50% - a penalty applied to all units requiring a specific strategic resource when using more of that resource than available.

    • Very Unhappy Penalty: -33% - a penalty when happiness is at -10 or lower.

    • Promotions: Miscellaneous - most bonuses and penalties are encoded as promotions, which vary in strength and conditions in which they are applied.
    These modifiers are all added together then applied to the base strength of a unit, for example a very unhappy (-33%) unit in rough terrain (+25%) will only be at -8% when defending. Promotions are the main source of modifiers. There is no cap on how much strength can be gained via modifiers, however there is a maximum penalty of -90%. Note that a ranged strength bonus will have no impact if the unit is upgraded to a melee unit, although the promotions may be listed. For example, a crossbowman upgraded to a rifleman with open terrain ranged bonus will have the +65% bonus listed if the defender is in open terrain, however it does not alter their strength.

    Ranged Combat

    Units with a ranged combat strength such as archers and catapults engage in ranged combat when attacking. They can attack units in nonadjacent tiles, and do not take damage as a result of the combat. These units have two separate strength listings: Strength and Ranged Attack. Strength is the base strength at which they will defend against melee attacks, and is generally around 2/3rds of ranged strength for normal ranged units and 1/2 for siege units. Ranged attack strength is the strength at which they attack at. As with normal melee combat units, attacking with a ranged unit expels all its movement points unless it has the logistics promotion or the ability to move after attacking, in which case attacking expends one movement point.

    The damage a ranged attack does is slightly less than 2/3rds of what an equivalent strength melee combatant would do. The combat formula uses the same modified ratio as above, but the base minimum damage that gets modified is 2 instead of 4, though the base spread remains 4. At even combat strength a ranged attack will do 2-5 damage to an opponent, spread evenly across those values to average 3.5 damage.

    Land based ranged vs ranged combat follows a modified set of rules for determining damage. The defender uses its ranged strength instead of normal strength, regular combat promotions like drill or barrage do not help (although they are incorrectly listed in the combat information table), and the defender gains a 1.25x strength multiplier which is applied after all other modifiers are applied. For example, an archer with the cover promotion (+25% strength vs ranged attacks) in rough terrain (+25%) defending against another archer will be fighting at a ratio of 1.875:1, a result of the total 1.50x combat strength from modifiers gaining the 1.25x ranged defense multiplier. The effective result of this is it's generally inefficient to attack ranged units with ranged attacks, including city bombardment, while melee units should tear through through a ranged defender's lower base strength easily.


    Two upgraded destroyers in battle; the attacker's 22 ranged strength * 1.6 modifiers
    outguns the defender's 35 base strength * 1.6 modifiers * 0.4 naval defense penalty

    Naval Combat

    Naval military units with the exception of the carrier all engage in ranged combat. They typically have a ranged strength equal to 2/3rds their base strength. In addition to being able to engage in ranged combat, all naval military units can kill an embarked unit outright by moving onto its tile. While doing this does not expel all movement points as a normal ranged attack would, it does count as an attack for the round.

    Although naval units engage in ranged attacks, they do not follow the same ranged vs ranged rules: they use their normal combat strength when defending. For naval vs naval combat there is a 0.4x defense strength multiplier penalty, applied after all modifiers. Gaining targeting 3 promotion (+60% strength vs naval units) provides only an additional 24% defense (60% * 0.4). The effective result of this attacking naval units with other naval units results in significantly more damage than an equivalent strength ranged unit.

    Death

    When two low-hit-point melee units engage in combat, only one of them can die. The winner always survives with one hit point. In this situation the total damage is calculated as normal, and if the attacker ends up with what would be more hit points than the defender, the attacker survives. If the combat would result in an equal amount of hit points, the defender will survive, which tips the scales in favor of the defender. In combat between two equal strength units both at 2 hit points, the attacker will die about 2/3rds of the time.

    The same rules are not applied when capturing cities; if a city is brought to 0 hp, the unit is guaranteed to survive and capture the city. This can result in low hp units successfully capturing low hp cities without dying in many situations, and a city at 1 hp is guaranteed to fall to any attack.

    With a high enough combat ratio, units become unkillable via melee (though any ranged attack will kill them). A defender with about 3.6x the strength of an attacker (such as infantry vs pikeman) will always do at least 10 damage and and take at most 1, resulting in the defender always surviving.

    Rules of Thumb

    Given that plugging the combat formula into a calculator whenever engaged in combat may be a bit much, the following general rules can be learned and relied upon
    1. The real result can range from about 2/3rds to 4/3rds what the combat information table predicts.

      • A predicted 6 damage can result in from 4 to 9 damage.

      • A predicted 1 damage can result in at most 2 damage.

      • A predicted 10 damage can potentially result in 6 minimum.

    2. Units gain damage at odd amounts of health; a 9 hp unit fights as though it were full strength.

    3. The guaranteed kill ratio is at about 2.7x strength; the unit will do 10 damage and generally take at most two.

    4. Attack melee units with ranged, and ranged units with melee.

    5. Attack and destroy naval units with naval units; do not receive counterattacks from naval units.

    6. If both combatants are predicted to die, the attacker must end up with more hit points to survive.

    Patch version of this article: 1.0.1.383

    Images

    1. damage.png
    2. combatwindow.jpg
    3. badnumbers.jpg
    4. rangedtomelee.png
    5. spearmanvstank.jpg
    6. navalcombat.png