## Combat Calculations

Formulas for calculating Damage, Attack Speed, and more in Fire Emblem 8 (The Sacred Stones).

# Guide Contents

This guide contains the following calculations/formulas.

# Weapon Triangle Bonuses

The weapon triangle returns again in FE8 in classic fashion. Swords beat Axes, Axes beat Lances, Lances beat Swords. For tomes: Anima beats Light, Light beats Dark, Dark beats Anima.

The bonuses in FE8 are the same as they were in FE7. The winning side will gain +1 Atk and +15 Hit, and the losing side will lose -1 Atk and -15 Hit. The hit bonus/detriment is doubled when a Reaver weapon is involved, unless both weapons are Reaver weapons. These values will be referred to in the rest of this guide as as follows.

\(T_{atk} = \begin{cases} +1, & \text{if winning} \\ -1, & \text{if losing} \\ 0, & \text{otherwise} \end{cases}\)\(T_{hit} = \begin{cases} +15, & \text{if winning} \\ -15, & \text{if losing} \\ 0, & \text{otherwise} \end{cases}\)# Attack

Attack (Atk) represents the maximum amount of damage a unit can do, assuming an enemy has no Def or Res. It depends on the unit's Str/Mag and the weapon's might. Weapon effectiveness, weapon triangle, and support bonuses also factor in. Weapon effectiveness was unnerfed from FE7 to be a factor of 3 again. The formula for Atk is the following.

\(Atk_{sp} = \text{Atk bonuses from supports}\)\(E = \begin{cases} 3, & \text{if using effective weapon} \\ 1, & \text{otherwise} \end{cases}\)\(Atk = (Str \parallel Mag) + E * (Mt_{wp} + T_{atk}) + Atk_{sp}\)The Light Brand and the Wind Sword from 2 range and the Runesword from 1 and 2 range use a modified version of the formula above, effectively halving your unit's strength. The formula for 2 range Light Brand and the Runesword is below.

\(Atk = \frac{Str}{2} + E * (Mt_{wp} + T_{atk}) + Atk_{sp}\)# Defense and Resistance

Defense (Def) and Resistance (Res) represent how well a unit can withstand physical and magic attacks respectively. Physical weapons target Def, whereas tomes target Res. The Light Brand and Wind Sword will target Def from 1 range, and Res from 2 range. The Runesword will always target Res. These values come from the unit's Def and Res stats, but can be increased by support bonuses and terrain. The Def and Res on the right side of the formula refer to the unit's stats. The formulas for Def and Res are the following.

\(Def_{ter} = \text{Def bonuses from terrain}\)\(Res_{ter} = \text{Res bonuses from terrain}\)\(Def_{sp} = \text{Def bonuses from supports}\)\(Res_{sp} = \text{Res bonuses from supports}\)\(Def = Def + Def_{sp} + Def_{ter}\)\(Res = Res + Res_{sp} + Res_{ter}\)# Damage

Damage (Dmg) is the total amount of damage inflicted per strike. A critical hit will multiple this value by 3. The formula for Dmg is the following.

\(Dmg = Atk_{attacker} - (Def_{target} \parallel Res_{target})\)# Attack Speed

Attack Speed (AS) represents how fast a unit can attack. If a unit has 4 or more AS than the unit they are attacking/countering, they will double hit. (quadruple hit for brave weapons). The base value for AS is the unit's speed stat. Weapon weight will decrease this value, but each point of Con will cancel out one point of weapon weight. The formula for AS is the following.

\(AS = Spd - (Wt_{wp} - Con)\)Note: Having extra leftover Con will not increase Attack Speed, if the unit has more Con than their weapon's weight then that part of the formula will be set to 0. Similarly, Attack Speed in general cannot go below 0.

# Hit

The hit rate (Hit) is calculated based on the weapon's hit, as well as the attacker's Skl and Lck. Weapon triangle and support bonuses also factor in. The formula for Hit is the following.

\(Hit_{sp} = \text{Hit bonuses from supports}\)\(Hit = Hit_{wp} + 2 * Skl + \frac{Lck}{2} + T_{hit} + Hit_{sp}\)Like in FE7, if a unit in FE8 has an S rank in the weapon type that they are currently wielding they will gain 5 extra Hit.

# Avoid

Avoid (Avo) represents how well a unit can dodge an attack. It depends on Attack Speed and Lck. Support bonuses and terrain also factor in. The formula for Avo is the following.

\(Avo_{sp} = \text{Avo bonuses from supports}\)\(Avo_{ter} = \text{Avo bonuses from terrain}\)\(Avo = 2 * AS + Lck + Avo_{sp} + Avo_{ter}\)# Displayed Hit

Displayed hit is what the game tells you the hit rate is when a unit attacks a target. This value depends on the attacker's Hit and the defender's Avo. This is not a percentage chance. FE8 uses true hit, meaning that it will roll 2 RNs to see whether or not an attack will hit. In general, this means that hit rates above 50 will hit more often than the number would suggest, and hit rates below 50 will hit less often.

\(Hit_{displayed} = Hit_{attacker} - Avo_{target}\)There are three staves that target enemies and inflict various status conditions: Berserk, Silence, and Sleep. The displayed hit of these staves is calculated through the following formula. Note that status staves use 1RN, so this is an actual percentage.

\(p = \text{Casting unit}\)\(e = \text{Target unit}\)\(D = \text{Tiles to target}\)\(Hit_{displayed} = 30 + 5 * (Mag_{p} - Res_{e}) + Skl_{p} - 2 * D\)# Crit

Crit represents how likely it is for a unit to land a critical hit, which does triple damage. Crit depends on the Crit value for the weapon/tome and Dex, as well as support bonuses.

\(Crit_{sp} = \text{Crit bonuses from supports}\)\(Crit = Crit_{wp} + \frac{Skl}{2} + Crit_{sp}\)The above value is increased by 15 for Berserkers, Swordmasters, Super Journeymen, and Super Recruits. Units wielding a weapon type that they have an S rank in will gain 5 extra Crit. Light Brands and Wind Swords cannot crit from 2 range, Runeswords cannot crit at all.

# Crit Avoid

Crit Avoid (Crit Avo) represents how well a unit can avoid enemy critical hits. The initial value is equal to defending unit's Lck, but can be increased by supports.

\(CritAvo_{sp} = \text{Crit Avo bonuses from supports}\)\(CritAvo = Lck + CritAvo_{sp}\)# Displayed Crit

Similar to Displayed Hit, Displayed Crit is calculated by subtracting the attacker's Crit by the defender's Crit Avo. Unlike Displayed Hit, Displayed Crit is rolled with 1 RN. However, this is still not a percentage chance because Crit rolls after Hit. Hence the formulas for Displayed Crit and actual Crit percentage are the following.

\(Crit_{displayed} = Crit_{attacker} - CritAvo_{target}\)\(Crit\% = \frac{Hit_{true}}{100} * Crit_{displayed}\)