Average auto attack damage per second formula for League of Legends:

The purpose of this thread is to provide the reader with a formula he can use to determine the average auto attack damage per second

The following terms are multiplied together.

• ( ATTACK_DAMAGE *(1 + (CRITICAL_STRIKE_CHANCE/100)*(1 + CRITICAL_STRIKE_DAMAGE/100 )*(0.9*ENEMY_REINFORCED_ARMOR_MASTERY) ) + ON_HIT_PHYSICAL_DAMAGE ) * 100/(100 + (ENEMY_ARMOR - FLAT_ARMOR_SHRED) * PERCENT_ARMOR_PENETRATION_FACTOR * PERCENT_ARMOR_SHRED_FACTOR - FLAT_ARMOR_PENETRATION )
• ON_HIT_MAGIC_DAMAGE + 100/(100 + (ENEMY_MAGIC_RESIST - FLAT_MAGIC_RESIST_SHRED) * PERCENT_MAGIC_RESIST_PENETRATION_FACTOR * PERCENT_MAGIC_RESIST_SHRED_FACTOR - FLAT_MAGIC_RESIST_PENETRATION )
• 0.9*ENEMY_NINJA_TABI
• 0.97*ENEMY_OPPRESSION
• 1.02*MELEE_DOUBLE_EDGED_SWORD
• 1.01*ENEMY_MELEE_DOUBLE_EDGED_SWORD
• 1.015*RANGED_DOUBLE_EDGED_SWORD
• 1.015*ENEMY_RANGED_DOUBLE_EDGED_SWORD
• 1.01*ALLIED_EXPOSE_WEAKNESS
• 1.03*BLADE_WEAVING
• 1.05*EXECUTIONER
• BASE_ATTACK_SPEED*(1 + BONUS_ATTACK_SPEED/100)*ATTACK_SPEED_SLOW_FACTOR

Now add the following:

ON_HIT_TRUE_DAMAGE * BASE_ATTACK_SPEED*(1 + BONUS_ATTACK_SPEED/100)*ATTACK_SPEED_SLOW_FACTOR

The values in the formula are as follows:

BASE_ATTACK_SPEED is equal to the blue number stated in the tooltip as you hover above your attack speed in your stats panel, and can be found here http://leagueoflegends.wikia.com/wiki/List_of_champions%27_attack_speed

BONUS_ATTACK_SPEED is equal to the sum of all bonus attack speed from any source

ATTACK_SPEED_SLOW_FACTOR is equal to the following terms multiplied together:

• (1 - ONE_ATTACK_SPEED_SLOW*0.9*SWIFTNESS*0.75*SLOW_RESIST/100)
• (1 - ANOTHER_ATTACK_SPEED_SLOW*0.9*SWIFTNESS*0.75*SLOW_RESIST/100)
• (1 - YET_ANOTHER_ATTACK_SPEED_SLOW*0.9*SWIFTNESS*0.75*SLOW_RESIST/100)

CRITICAL_STRIKE_CHANCE is equal to the sum of all critical strike chance from any source

CRITICAL_STRIKE_DAMAGE is equal to the sum of all critical strike damage from any source

ENEMY_ARMOR is equal to the number stated in the stats panel of the enemy unit

FLAT ARMOR_SHRED = ONE_FLAT_ARMOR_SHRED + ANOTHER_FLAT_ARMOR_SHRED + YET_ANOTHER_FLAT_ARMOR_SHRED ...

PERCENT_ARMOR_PENETRATION_FACTOR is equal to the following terms multiplied together:

• (1 - ONE_PERCENTAGE_ARMOR_PENETRATION/100)
• (1 - ANOTHER_PERCENTAGE_ARMOR_PENETRATION/100)
• (1 - YET_ANOTHER_PERCENTAGE_ARMOR_PENETRATION/100)

PERCENT_ARMOR_SHRED_FACTOR is equal to the following terms multiplied together:

• (1 - ONE_PERCENTAGE_ARMOR_SHRED/100)
• (1 - ANOTHER_PERCENTAGE_ARMOR_SHRED/100)
• (1 - YET_ANOTHER_PERCENTAGE_ARMOR_SHRED/100)

FLAT_ARMOR_PENETRATION = ONE_FLAT_ARMOR_PENETRATION + ANOTHER_FLAT_ARMOR_PENETRATION + YET_ANOTHER_FLAT_ARMOR_PENETRATION ...

PERCENT_MAGIC_RESIST_PENETRATION, PERCENT_MAGIC_RESIST_SHRED, FLAT_MAGIC_RESIST_SHRED, FLAT_MAGIC_RESIST_PENETRATION operates analogously to the factors for armor

The following values are either 1 if the item is a factor, or 0 if the item is not a factor

ENEMY_NINJA_TABI

SLOW_RESIST ( boots of swiftness)

The following values are either 1 if the mastery is a factor or 0 if the mastery is not a factor. In order to make the damage equation simpler, when the mastery value is 1, it is assumed that the mastery is completely ranked as far as possible.

SWIFTNESS

ENEMY_REINFORCED_ARMOR_MASTERY

ENEMY_OPPRESSION

MELEE_DOUBLE_EDGED_SWORD

ENEMY_MELEE_DOUBLE_EDGED_SWORD

RANGED_DOUBLE_EDGED_SWORD

ENEMY_RANGED_DOUBLE_EDGED_SWORD

ALLIED_EXPOSE_WEAKNESS

BLADE_WEAVING

EXECUTIONER