League of Legends Formulas

Last Updated: December 30th 2019

The following formulas were also used to create "LoL Item Optimizer" program in this website.

Basic League of Legends Formulas

Intermediate League of Legends Formulas

% Damage Increase Formulas

% Durability Increase Formulas

- GO Armor against physical damage only (Or Magic Resist against magic damage)

Advanced Derivation of League of Legends Formulas

% Damage Increase Formulas

- GO Critical Strikes

- GO Armor, Magic Resist, Damage Reduction, Attack Speed Slow

Armor

100 + Armor

Example:

If you have 50 armor,

50

100 + 50

= 0.3333

You take 33.3% less damage from physical attacks.

Magic Resist works the same way as this against magic attacks.

Base_Attack_Speed * (1 + Bonus _Attack_Speed)

Example:

Ashe has 0.658 base attack speed and gets 4% bonus attack speed per level after level 1. At level 10, Ashe will have

0.658 * (1 + 0.04 * 9levelups)

= 0.658 * (1 + 0.36)

= 0.895

Therefore, Ashe will autoattack 0.895 times per second.

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Enemy's_Total_Attack_Speed * (1 - Attack_Speed_Slow)

(It literally takes away a percentage of enemy's total attack speed.)

Example:

When you buy , enemies with 1.00 attack speed will now have 0.85 attack speed

Note: This can be considered as reducing enemy's autoattack DPS by 15%.

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100
+ Old Armor

100 + New Armor

Example:

If an enemy has 100 armor and you have 35% armor pen and 15 armor pen,

100 + 100

100 + 100* (1-0.35) - 15

= 1.33333

Therefore, you do 33.33% more damage with the armor penetration stats

Concept

You can confirm the above example with this very simple logic. If you have 100 Attack Damage and autoattack the enemy,

Previously the enemy had 100 armor so he would take only 50 damage

With Armor Pen the enemy now effectively has only 50 armor so he takes 66.66 damage

Therefore, the relative difference is 66.66/50 = 1.3333

100 + New Armor

Example:

If an enemy has 100 armor and you have 35% armor pen and 15 armor pen,

100 + 100

100 + 100* (1-0.35) - 15

= 1.33333

Therefore, you do 33.33% more damage with the armor penetration stats

Concept

You can confirm the above example with this very simple logic. If you have 100 Attack Damage and autoattack the enemy,

Previously the enemy had 100 armor so he would take only 50 damage

With Armor Pen the enemy now effectively has only 50 armor so he takes 66.66 damage

Therefore, the relative difference is 66.66/50 = 1.3333

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1 - Old CDR

1 - New CDR

Example:

If you have 0% CDR and you get 40% CDR

1 - 0

1 - 0.40

= 1.66666

Therefore, your casting DPS goes up by 66.66% with 40% CDR.

Concept:

You can confirm the above example with this very simple logic.

Say there is a spell with 10s cooldown. In 60 seconds, you can cast it 6 times.

Now with 40% cooldown reduction, the new cooldown of the spell becomes 6s which means you can cast it 10 times in 60 seconds.

Hence, the casting DPS is 10/6 = 1.6666

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100
+ New Armor

100 + Old Armor

Example:

If you have 50 armor and you purchase (100 armor), you now have 150 armor.

100 + 150

100 + 50

= 1.66666

Therefore, you are now 1.6666 times more durable against physical attacks (66.7% tankier against physical attacks)

Or take the reciprocal of that (1/answer) and you are left with 0.60 which means you take 40% less damage relative to when you didn't have

Concept

You can confirm the above example with this very simple logic. When an enemy champion with 100 Attack Damage autoattacks you,

With 50 armor, you take 66.66 damage

With 150 armor, you take 40 damage

Therefore, the relative difference is 66.66/40 = 1.6666

100 + Old Armor

Example:

If you have 50 armor and you purchase (100 armor), you now have 150 armor.

100 + 150

100 + 50

= 1.66666

Therefore, you are now 1.6666 times more durable against physical attacks (66.7% tankier against physical attacks)

Or take the reciprocal of that (1/answer) and you are left with 0.60 which means you take 40% less damage relative to when you didn't have

Concept

You can confirm the above example with this very simple logic. When an enemy champion with 100 Attack Damage autoattacks you,

With 50 armor, you take 66.66 damage

With 150 armor, you take 40 damage

Therefore, the relative difference is 66.66/40 = 1.6666

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1 + NewCritChance * (1 or 1.5)

1 + OldCritChance * (1 or 1.5)

*1.5 with only

Example:

When you have 0% critical chance, the critical strike and damage portion of will increase your DPS by,

1 + 0.20 * (1.5)

1 + 0 * (1)

= 1.3

Therefore, your DPS has increased by 30% relative to before with only the critical strike stat portion of

Concept:

You can confirm the above example with this very simple logic. When you auto-attack 5 times, you deal

Before: 100, 100, 100, 100, 100 = 500 damage

After: 100, 250, 100, 100, 100 = 650 damage (since 20% chance of critical striking)

Therefore, the relative difference is 650/500 = 1.3

Additional Notes:

receives 10% damage penalty on his critical strikes, which means the formula now changes to

1 + NewCritChance * (0.8 or 1.25)

1 + OldCritChance * (0.8 or 1.25)

's receives a flat 50% critical damage penalty.

Convert critical strike stats into bonus damage by multiplying the respective AD ratio with the modified critical strike bonus

(70/80/90/100/110% AD) * CritChance * (0.5 or 1)

= Bonus Average Damage for

's benefits only 60% from critical strikes.

Convert critical strike stats into bonus damage by multiplying the AD ratio with the modified critical strike bonus

(100% AD) * CritChance * (0.6 or 0.9)

= Bonus Average Damage for

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Old: (AA*P.Red * AA.Red. ) + (P*P.Red.) + (M*M.Red.) + T

New: (AA*P.Red * AA.Red. ) + (P*P.Red.) + (M*M.Red.) + T

Variable Meanings:

AA = Autoattack damage you receive before armor and other modifiers are taken into account

P = Non-autoattack physical damage you receive before armor is taken into account

M = Magic damage you receive before magic resist is taken into account

T = True damage

AA.Red. = (1 - [0 or 0.10] ) * (1 - %AttackSpeedSlow)

P.Red. = 100 / (100+Armor)

M.Red. = 100 / (100+Magic Resist)

Example:

You used to have 100 Armor and 100 Magic Resist and now you buy and which give you additional 100 armor, 40 magic resist and 15% attack speed slow.

- You are autoattacked by a champion with 300 AD 5 times (AA = 1500)
- You are hit by an ability which does 1000 raw physical damage (P = 1000)
- You are hit by magic attacks which do 1500 raw magic damage (M = 1500)
- You are hit by Ignite spell which deals 500 true
damage (T = 500)

- AA.Red. = (1 - 0) * (1 - 0.15) = 0.85
- P.Red. = 100 / (100 + 200) = 0.33333
- M.Red. = 100 / (100 + 140) = 0.41666

- AA.Red. = (1 - 0) * (1 - 0) = 1
- P.Red. = 100 / (100 + 100) = 0.5
- M.Red. = 100 / (100 + 100) = 0.5

(1500 * 0.333 * 0.85) + (1000 * 0.333) + (1500 * 0.416666) + 500

= 1.328

Therefore, you are now 32.8% tankier with for the above conditions

(or take the reciprocal of that which is 0.753 so you take 24.7% less damage relative to before)

Concept:

Given the damage type you can reduce the amount with armor, magic resist, and attack speed slow when applicable.

Then you can compare the difference of the actual damage you receive.