Attack

The attack of a unit or building indicates the maximum (kind of) damage it can inflict upon opposing units or buildings. These attacks are blocked by the corresponding armor of the unit. Units and buildings may deal additional damage to the target based on the attack bonuses due to armor classification system which varies from game to game, and in some rare cases due to negative armor values. As opposed to the main attack, this bonus attack does not interact with the target's visible armor values, but with the corresponding specialized armor of the target, which is often hidden.

Examples of such bonuses include the Halberdier and Camel Rider lines' bonus against cavalry in Age of Empires II, as well as the Cataphract's bonus against infantry in Age of Empires and Age of Empires II.

The attack of almost all military units can be improved by researching certain technologies at various buildings. If the attack of a unit or structure is improved with technologies, the added value is separately shown in the infobox (see image).

Attack system

Age of Empires, Age of Empires II, and Age of Empires IV use an additive attack and armor system. This means that values of armors and attack bonuses are numbers. Attacks are subtracted by armors and then added with attack bonuses to calculate damage.

Age of Mythology and Age of Empires III use a multiplicative attack system. This means that values of armors and attack bonuses are fractions. Attacks are multiplied by $1 - Armor$ and then multiplied with attack bonuses to calculate damage. In Age of Empires III, they are accurately called resists and multipliers respectively.

The attack system is differs from game to game and is very complex, but it can be presented in a simple manner for basic understanding. Even for the same type of attack logically, the nomenclature is different between games.

If a unit has multiple base attacks, the UI shows only the largest value.

Base attack

Attacks which are advertised on a unit's statistics are called base attacks. These usually come in four forms:

Attack	Description	Corresponding armor	Name in AoE	Name in AoE2	Name in AoM	Name in AoE3	Name in AoE4
Hack/Melee	attack done by non-ranged* units	Hack/Melee	Melee	Melee	Hack	Melee	Melee
Pierce/Ranged	attack done by buildings, ships, siege and ranged units	Pierce/Ranged	Pierce	Pierce	Pierce	Ranged	Ranged
Crush/Siege/Torch	attack done by melee units (against siege units, buildings and ships), siege units, and ships	Crush/Siege/Fire	-	-	Crush	Siege	Torch
Unresisted/Siege	attack done by siege units and ships	-	Unresisted		-	Siege	Siege

- means that the entry is not applicable
Non-ranged units are also called melee units. Ranged units are also called archers.

Siege attack

Siege attack in Age of Empires III appears twice because how different units attack. Like Torch damage in Age of Empires IV, infantry and cavalry units use this attack only against buildings and ships. Coincidentally, both use torches to attack. Crush attack in Age of Mythology is used against all units and buildings, but units other than siege and ships have 99% resistance against crush attack, making it effective only against these units.

Siege attack cannot be blocked by any kind of armor. Units which do this damage are:

• Catapult Trireme and Juggernaut in Age of Empires
• Secondary projectiles of Hussite Wagons in Age of Empires II
• Cannons, including those mounted on ships, in Age of Empires III
• Incendiary Ships, Warships and siege engines (except Springald, Culverin and Ribauldequin) in Age of Empires IV

Anomalies

In Age of Empires, the Stone Thrower line and the Fire Galley deals melee attack instead of pierce attack. The Catapult Trireme and Juggernaut deal an unresisted attack instead of pierce attack.

In Age of Empires II, the Throwing Axeman, the Mameluke, the Gbeto, and the Chakram Thrower deal melee attack instead of pierce attack. The Turtle Ship, the Dromon, and the Mangonel, Bombard Cannon, and Cannon Galleon lines deal melee attack instead of pierce attack too. Non-ranged siege units and ships also have melee attack instead of pierce attack. The Scorpion and Fire Galley lines, Chu Ko Nu and Kipchaks have an additional melee attack along with their pierce attack. Secondary projectiles of Hussite Wagons deal an unresisted attack type.

In Age of Mythology, the Throwing Axeman deal hack attack instead of pierce attack. Myth units deal either hack or pierce damage, sometimes combined with crush damage. Hero units likewise deal either hack or pierce damage, depending on their attack range. Even most damaging god powers deal one or more of these damage types, influencing their effectiveness against different targets. Among ships, hammer ships deal hack attack, archer ships deal pierce attack, and siege ships deal crush attack.

In Age of Empires III, buildings may deal siege attack instead of ranged attack. Ranged infantry and cavalry units initially attack at range but switch to melee damage if their target closes up on them, while keeping a siege attack for buildings and ships (torches for most units, grenades for Grenadiers).

Damage formula

Additive systems

The basic damage formula in Age of Empires - I, II, and IV is: $Damage = \max(1, k_{elev} \times \sum_i \max(0, Attack_i - Armor_i))$

The exact formula for Age of Empires II is mentioned below.

As a special case, for buildings in Age of Empires, the damage becomes: $Damage = \max(0.1, k_{elev} \times 0.2 \times \sum_i \max(0, Attack_i - Armor_i))$

In these formulae, k_elev is the elevation multiplier (hill/cliff bonuses) in Age of Empires I and II, i is the armor class (of which melee, pierce, torch and siege are part of). The formula basically says that for every type of attack, its corresponding armor value is subtracted, and if it is greater than 0, they are added to damage. The minimum damage is set to 1 (0.1 for buildings in Age of Empires), if the damage dealt is less than that value.

Note that the damage may not be an integer (and it may be less than 1), but the game works with the values just fine. It does subtract fractional hit points, but the UI shows only the integer part of the remaining hit points. The unit dies when the remaining hit points reach below 1 (does not have to be less than or equal to 0).

Example 1: A Bowman has 3 pierce attack and a Small Wall has 200 HP and 3 pierce armor. Since the wall's pierce armor cancels the Bowman's attack, the Bowman does 0.1 damage per arrow. The first arrow lowers the wall's HP to 199.9 (199 shown in-game), but for the HP to get below 199 (so that the game shows 198 HP) the Bowman has to fire ten more arrows (thus it looks the first arrow does 1 damage while the following nine do no damage).

Example 2: A Slinger has 2 pierce attack, which again is cancelled by the wall's pierce armor. However, the Slinger also has 3 attack against defensive structures, so the Slinger does 3/5 = 0.6 damage. The first five strikes lower the wall's HP to 199.4, 198.8, 198.2, 197.6, 197 (thus it looks like strikes 1, 2, and 4 do 1 damage while strikes 3 and 5 do no damage).

For more information about damage calculation, visit the respective Armor class page.

Age of Empires II

The existence of attack bonus resistance and armor-ignoring properties in Age of Empires II makes the damage calculation formula even more complex. The formula is mentioned below, and is discussed in detail with examples in the armor class page:

$Damage=\max \left(1,k_{elev}\times k_{miss}\times k_{taper}\times k_{cracked}\times \sum _{i}{\bigg (}(1-k_{resist})\times \max {\big (}\min(0,k_{mult_{i}}\times Attack_{i}),k_{mult_{i}}\times Attack_{i}-Armor_{i}{\big )}{\bigg )}\right)$

where,

$k_{elev}=$Elevation multiplier, generally 1.25 if attacker is on higher ground and 0.75 from lower ground, with special cases for the Tatars, Georgians, etc.

$k_{miss}=$0.5 if the projectile of the projectile-based attacker mishit another target than the intended one. Does not apply to units with Area of Effect damage, Chakram Throwers, Arambai, units with blast damage, or secondary projectiles of Hussite Wagons and Organ Guns.

$k_{taper}=$Only for attackers with Area of Effect damage, value depending on blast attack type.

$k_{cracked}=$1.2 if the target is a building on a desert cracked terrain, and 1 otherwise.

$k_{resist}=$Bonus damage resist multiplier. Used for cases where bonus attack received is decreased multiplicatively, for certain units of Bengalis and Sicilians, 0 in other cases.

$k_{mult_{i}}=$Attack multiplier against a particular armor class. Used for cases where bonus attack is increased multiplicatively, such as when Siege Engineers is researched (its value is then 1.2), and for bonuses of Bohemians, Burgundians, and Gurjaras.

$Attack_{i}=$Attack value of the attacker for a particular armor class.

$Armor_{i}=$Armor value of the target for a particular armor class (if the target does not have the armor class, this value is the base armor value, which is usually 1000, but is 0 for Ornlu the Wolf).

Age of Mythology

The basic damage formula is: $Damage = \max(1, k_{elev} \times t \times AttackBonus \times \sum_i Attack_i \times (1 - Armor_i))$

• AttackBonus is the bonus against the category the target belongs to. As a direct multiplier, it no longer ignores armor but scales with attack upgrades. If the value is lower than 1, it effectively acts as a damage penalty (such as myth units dealing half damage or less against heroes)
• k_elev is the elevation multiplier, equal to 5/4 if a unit attacks above its target, 3/4 if a unit attacks below its target or 1 otherwise
• t is the duration of the attack animation in seconds (longer animations result in higher damage)

Note: The Egyptian Siege Tower and Chinese Immortal actually switch between different attacks, instead of attacking with multiple attack types.

Age of Empires III

The basic damage formula is:

$Damage_{m/r/s}=Attack_{m/r/s}\times \left(1-Resist_{m/r/s}\right)\times \prod _{i}AttackBonus_{i}$

• All possible bonus multipliers against a unit are combined. For instance, the Crossbowman has a 2× multiplier against light cavalry but a 0.75× multiplier against cavalry; as light cavalry is a subset of cavalry, light cavalry units actually take 1.5× more damage.
• It is possible to inflict less than 1 damage per hit.

Age of Mythology

Compared to the predecessors, small and/or specific attack bonuses are comparatively less common, and some typical specialized unit types even work without specific damage bonuses (such as Hammer ships exploiting Siege Ships low hack armor, and many siege units are effective against buildings by default thanks to the new damage type). It is however still crucial to the additional layer of myth units and heroes and their interactions, though not in how they interact with regular units. Myth units are more effective against each other and weaker to heroes (dealing less damage and taking more), while their strength against soldiers is in their regular attributes, lack of weaknesses and their special attacks. Heroes are countered by normal soldiers by strength of numbers rather than attack bonus mechanics as well (though some are subject to regular attack bonuses due to a secondary unit typing, such as Norse Hersirs, which are also infantry).

In Age of Mythology, some units (such as Arkantos, and the General) have special abilities that can temporarily boost the damage output of themselves and/or other allied units around them. Some god powers also temporarily boost damage for certain units. In both cases, the increase is reflected in the unit info.

Gallery

A Knight attacking a donkey in Age of Empires II: Definitive Edition

An intense fight in Age of Empires IV.

The Scorpion's information panel shows an arrow instead of a sword to denote its pierce attack type