Damage Formula

The damage system in the Wars series is not based on formulas; rather, the formulas merely alter the base damage for the unit matchup. In the case of an attack that ends in decimal figures, the final damage is rounded down. This base damage is documented in the game in question's damage chart (shown below). The formulas are as follow:

Super Famicom Wars

$TotalDamage=\left(Base\cdot \left({\frac {LevelAttackModifier}{100}}\right)\cdot \left({\frac {LevelDefenseModifier}{100}}\right)\cdot \left({\frac {Attacker'sHP}{10}}\right)+Luck+CarolineModifier\right)\cdot frac{100-TerrainCover}{100}$

• Level Attack Modifier is 100 at base, and increased by 20 for every Level Up the attacking unit has gained (maximizing at 180)
• Level Defense Modifier is 100 at base, and decreased by 20 for every Level Up past the first 2 that the defending unit has gained (minimizing at 60)
• Luck is a random number choosing from 0 to 9
• Caroline Modifier is 0 at base, with 5 added when Caroline is the attacking unit's CO, and 5 subtracted when she is the defending unit's CO; note that both can cancel out with each other if Caroline is used on both sides

Game Boy Wars 3

$TotalATK=UsedATK\cdot \left(\left(100+LevelValue+FlankValue+SupportValue\right)\cdot {\frac {HP}{100}}\right)$

$TotalDEF=UsedDEF\cdot \left(\left(200+LandValue+LevelValue+FlankValue\right)\cdot {\frac {HP}{100}}\right)$

$Defender'sNewHP=\min(Defender'sOldHP,\lceil {\frac {Attacker'sTotalATK-Defender'sTotalDef}{2\cdot Defender'sUsedDef}}\rceil )$

Used ATK is the unit type's ATK value against the defending unit's unit family. Used DEF is similarly the unit type's DEF value against the attacking unit's unit family.

Land Value is the terrain's Cover value. This is automatically set to 0 for air units.

Level Value is based on the unit's Rank. At the base of D-Rank, this is 0; this is modified by +10 per level up, to a maximum of +40 at S-Rank.

Flank Value, always set as 0 or a negative number (absolute values will be stated below), is the reduction incurred to the unit based on how strongly the unit is flanked if direct attack is involved:

• If there are no other enemy units adjacent to the unit or if the attack is at range regardless of range, the value will be 0.
• The penalty is determined by how many adjacent spaces are not subject to enemy Zone of Control (adjacent to an enemy unit) or outright occupied to an adjacent unit. 4 spaces will have this penalty at 20, increasing by an additional 15 for each additional space, to a maximum penalty of 50.

Support Value is the boost from ally units in the enemy unit's Zone of Control, increased by 12.5% of each unit's own Used ATK.

PALBal Patch differences

The initiator now receives doubled Support Value and halved Flank Value, and the defender also has halved Support Value.

Range attacks now receive a penalty for the initiator except when firing both at 2 spaces away and without moving. When not moving, the penalty is at 5 for each space beyond the first 2 spaces, capping at 20 when at 6 or more spaces away. Moving instead increases the penalty to a minimum of 30 at 2 spaces, increasing by 10 for each additional space, to a maximum of 70 at 6 or more spaces away. Both show up as the Flank Value.

Flank Value's contribution to the Total DEF value now caps at the sum of the DEF boosts (the Level and Support Values), but is also added to the multiplier part of the enemy's Total ATK. The nonzero Flank Values were also reduced by 10, resulting in a range of 10 to 40. This is naturally irrelevant with range attacks.

Controlled Communication Towers now each grant +5, capping at 200, to the Level Value. This is not displayed visibly on the Battle Forecast.

Planes now get 40 Land Value, but this is reduced by 20 against range attacks, and 20 against planes, both stacking where applicable.

Helicopters now benefit from terrain but have a minimum Land Value of 20. They also get a further bonus of 30 Land Value against range attacks.

Advance Wars

$AttackValue=\left(Base\cdot {\frac {IndividualATK}{100}}\cdot {\frac {UniversalATK}{100}}\right)+Luck$

$DefenseValue={\frac {100-TerrainStars\cdot HP}{100}}\cdot {\frac {200-IndividualDef}{100}}\cdot {\frac {200-Target'sUniversalDef}{100}}$

$TotalDamage={\frac {Attacker'sHP}{10}}\cdot Attacker'sAttackValue\cdot Defender'sDefenseValue$

• Individual ATK and DEF refers to the corresponding CO's ATK and DEF values to specific units. Both default to 100 but may be modified based on given factors.
• Universal ATK and DEF refers to the corresponding CO's ATK and DEF values to all units. Both default to 100 when not having CO Power active, and 110 when having CO Power active, but may be different such as Eagle under Lightning Strike having 80 for ATK and 70 for DEF.
• Values for DEF with both actually use the subtraction result in the game's data
• Luck is a random number, choosing from 0 to 9 with any CO with the exceptions of Nell (0 to 19 daily, or 0 to 59 under Lucky Star) and Sonja (-15 to 9)

Advance Wars 2: Black Hole Rising / Advance Wars: Dual Strike

The damage inflicted to the defending unit when the attacking unit attacks is described by the formula below. Note: When attacking, Black bomb inflicts 5 HP and Oozium inflicts 10 HP (ignoring the formula and all stats).

Overview: The default damage is 10. Multiply that by the matchup multiplier (between .05 and 1.5). Increase it by your atk boost (default 0%, often ~10%) plus 0% to 9% (assuming default luck). Then, reduce the damage by defender's defense boost (default 0%, often ~10%) plus 0%-40% based on their terrain (scaling with their HP). Finally, multiply it by your HP/10.

$a=10\cdot matchupMultiplier\cdot (1+atkBoost)+10\cdot Rand(0,goodLuck-0.01)-10\cdot Rand(0,badLuck-0.01)$

$b=1-defBoost-terrainStars\cdot defenderHP$

$damage=Round(attackerHP/10\cdot a\cdot b)$

• matchupMultiplier is determined by the types of the attacking and defending units. Use the table in the attacking unit's page to determine which weapons can be used and their multipliers (if this table exists*). Primary is used if available. If the default weapon has ammo, the "Advance Wars: Dual Strike" table in Damage can be convenient. (An "x" indicates the attacking unit cannot attack the defending unit.) Example: If a Tank attacks infantry, matchupMultiplier = 75% = 0.75.
• atkBoost is that of the attacker, normally 0. Example: When Jake attacks with a unit on plains, atkBoost = 10% = 0.10.
• goodLuck is that of the attacker, normally 0.10 = 10%. Example: Rachel's CO power sets goodLuck = 40 for the turn.
• badLuck is that of the attacker, normally 0. Example: By default, Sonja has badLuck = 5% = 0.05.
• Rand(a,b) is a function that gives a random float (uniformly) between a (inclusive) and b (inclusive).
• defBoost is that of defender. Example: Rachel's CO power sets defBoost = 0.1 for the turn.
• terrainStars is determined by the terrain of the defending unit per the "Effects" table in Terrain. Example: If the defending unit is on plains, terrainStars = 1.
• defenderHP is the defending unit's HP. Example: A new unit has 10 HP.
• attackerHP is the attacking unit's HP.
• Round(a) is a function that rounds a to the nearest integer and rounds a=0.5 to 1.

*A matchup table with both primary and secondary weapons should be created.

Advance Wars: Days of Ruin

$ATKStats=100+COZoneATKBonus+LevelBonus+CommTower-Sandstorm$

$DEFStats=100+COZoneDEFBonus+VeteranBonus+TerrainStars\cdot HP+CommTower$

Display Damage

$DisplayDamage=\lfloor \lfloor \lfloor BaseDamage\cdot {\frac {ATKStats}{100}}\rfloor \cdot {\frac {HP}{10}}\rfloor \cdot {\frac {100}{TargetDEFStats}}\rfloor$

$\lfloor x \rfloor$ means the number is rounded down

"Display damage" is the damage in the preview when trying to attack an enemy.

True Damage

$TrueDamage=Round{\Biggl (}\lfloor (\lfloor BaseDamage\cdot {\frac {ATKStats}{100}}\rfloor +Luck)\cdot {\frac {HP}{10}}\rfloor \cdot {\frac {100}{TargetDEFStats}}{\Biggr )}$

$Luck=RandomNumber(0,10)$

Round() means the number is rounded to the nearest integer

The main difference with the display damage is the final number is Rounded instead of rounded down. Intermediate operations are still rounded down. Luck is affected by Attacker's HP then by the Target's Defense, but is not affected by Attack Stats. The random number varries between 0 and 10 included unlike previous entries of Advance Wars.

Simplified without including rounding or Luck

$Damage=BaseDamage\cdot {\frac {AttackerHP}{10}}\cdot {\frac {AttackStats}{TargetDefenseStats}}$

Attack Stat

• The default value for attack is 100%.
• If the unit is at Level 1, add another 5%.
• If the unit is at Level 2, add another 10%.
• If the unit is at Level Ace/Vet, add another 20%
• If the unit is in the Command (CO) Zone, add another 10%.
• If the unit is in the CO Zone and meets the COs criteria, add another 10% for each star.
• If the team has any Communication Tower in their possession, add another 5% for each one.
• If there is a Sandstorm in effect (and the CO is not Penny), subtract 30%.

Defense Stat

• The default value for defense is 100%.
• If the unit has Ace/Veteran status, add another 20%.
• If the unit is in the CO Zone, add another 10%.
• If the unit is in the CO Zone and fills the COs criteria, add another 10% for each star.
• If the team has any Communication Tower in their possession, add another 5% for each one.
• If the unit is lying on defensive cover, add another 1% for each star, multiplied by the units HP.
• If Waylon's CO Power (Bad Company) is in effect, add another 270%.

Luck damage

During any attack, there is a chance that a deviation in Damage dealt will occur, based on the Luck factor. In the first 3 Advance Wars game, luck can change the damage dealt based on whether the CO of the attacking unit has good or bad luck - good luck will result in more damage dealt, and bad luck will result in reduced damage. Almost all COs have a luck factor of between ±0% to +9%, changing the damage dealt by the same amount, while others have higher or lower levels of luck. In Days of Ruin, luck damage now includes +10%. In all games, luck damage is affected by the attacker's firepower as well as the defender's terrain defense bonus. Luck is multiplied by the unit HP to give up to an additional 10% damage. This means that weaker units cannot unexpectedly deal another 1 HP of damage, and weaker units will generally deal less luck damage than healthy units.

Counter Attack Damage

A counter-attack only occurs under the following conditions:

1. The attacking unit was a direct unit.
2. The defending unit survives (dead units do not fire back).
3. The defending unit can attack the attacking unit.

The counter-attack damage follows the same formula as above but the defender and attacker are swapped and the original defender can only attack with the reduced HP.

A special case for counter-attacks exists when a unit gets attacked during Sonja's SCOP.