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General Guide by Complexicate

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League of Legends Build Guide Author Complexicate

How the Math Works: Atk Spd, Crit, CDR, MR & Armor

Complexicate Last updated on May 11, 2012
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Introduction

This is a summary of some of the most important formulas that League of Legends uses, and the things that affect those formulas.

It was originally started because I kept playing with builds that focused on one stat or another. The rune calculations and the item numbers make it a quick and easy reference for that.


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Attack Speed

How it works
Cap = 2.500 attacks per second

Attack Speed = Base Attack Speed * (100% + Bonus Percent)

Base Attack Speed
Every champion's "base attack speed" is calculated using a hidden variable called "attack delay".
Base Attack Speed = 0.625 / (1 + attack_delay)

Attack Delay (Approximate Base Attack Speed)
-0.10 (0.69444):
-0.09 (0.68681):
-0.08 (0.67935):
-0.07 (0.67204):
-0.06 (0.66489):
-0.05 (0.65789):
-0.04 (0.65104):
-0.03 (0.64433):
-0.02 (0.63776):
+0.00 (0.62500):
+0.02 (0.61275):
+0.08 (0.57870):


Bonus Attack Speed Percent
Bonuses are additive
25 + 30 = 55% bonus

If a champion has about 0.665 base attack speed, 376% faster is 2.500
That means that 276% bonus would reach the 2.500 cap.


Bonus attack speed comes from 5 sources

  1. Runes
  2. 1 Mastery
  3. Items
  4. Every level, bonus attack speed is added (between 1% to 4% depending on the champion).
  5. Some champion abilities
    Camouflage, etc.



Runes (Alacrity)
10.2% = Greater Quintessence of Attack Speed x 3
15.3% = Greater Mark of Attack Speed x 9
6.84% = Greater Seal of Attack Speed x 9
5.76% = Greater Glyph of Attack Speed x 9

25.50% = x3 + x9
32.34% = x3 + x9 + x9
38.10% = x3 + x9 + x9 + x9


Masteries
+4% "Alacrity" Mastery


Items
15 , 40
20 , 40
20 , 20Zeke's Herald, 25 , 30 , 30 , 32 , 40 , 50 , 50 , 50 , 50 , 55

22 , 40 Classic
40 , 50 Dominion



See: Attack Speed on LoL Wiki


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Critical Strike Chance

How it works
Cap = 100%

Crit Percents are additive
25 + 30 + 30 = 85% chance


Critical Strike Chance comes from 3 sources

  1. Runes
  2. Items
  3. 3 champion abilities:
    Ashe's Focus
    Pantheon's Heartseeker Strike
    Tryndamere's Battle Fury



Runes (Malice)
5.58% = Greater Quintessence of Critical Chance x 3
8.37% = Greater Mark of Critical Chance x 9
3.78% = Greater Seal of Critical Chance x 9
2.52% = Greater Glyph of Critical Chance x 9

13.95% = x3 + x9
17.73% = x3 + x9 + x9
20.25% = x3 + x9 + x9 + x9


Items
8 , 18
10 , 12
15 , 15 , 15 , 18 , 20 , 25 , 30

8 Classic


See: Critical Strike on LoL Wiki


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Cooldown Reduction

How it works
Cap = 40%

CDR is additive
4% "Sorcery" Mastery + 6% "Intellegence" Mastery + 15 = 25% CDR


CDR comes from 4 sources

  1. Runes
  2. 3 Masteries
  3. Items
  4. 4 champion abilities:
    Heimerdinger's UPGRADE!!!
    Ryze's Overload
    Twisted Fate's Stacked Deck
    Viktor's Augment: Gravity



Runes
There are 2 Rune Sets, Focus and Celerity .

"Focus" is usually recommended because:
  1. "Focus" runes are more powerful than "Celerity" until level 13 and the first 12 levels often set the balance of the game.
  2. At level 18, Celerity x3 only gives 2.1% more CDR than Focus x3, and Celerity x9 only gives 2.77% more CDR than Focus x9. Most people do not think this late game CDR is worth giving up the early game CDR.

Some people like "Celerity" because, at level 18, you can hit the 40% cap from:
  • -15.64% from x3 + x9
  • -10% from Masteries (9/0/21)
  • -15% from just one item Shurelya's Reverie Zeke's Herald



Focus
-4.92% = Greater Quintessence of Cooldown Reduction x 3
-5.85% = Greater Glyph of Cooldown Reduction x 9
-2.61% = Greater Seal of Cooldown Reduction x 9
-1.44% = Greater Mark of Cooldown Reduction x 9

-10.77% = x3 + x9
-13.38% = x3 + x9 + x9
-14.82% = x3 + x9 + x9 + x9


Celerity runes only come as Quintessences or Glyphs .
Note: Testing on a rune page, I found that the Greater Glyph of Scaling Cooldown Reduction is actually closer to -0.9576% at 18 (-0.0532% per level). It has been rounded for the tooltip.

At level 1
-0.39% = Greater Quintessence of Scaling Cooldown Reduction x 3
-0.48% = Greater Glyph of Scaling Cooldown Reduction x 9
-0.87% = x3 + x9

At level 7
-2.73% = Greater Quintessence of Scaling Cooldown Reduction x 3
-3.35% = Greater Glyph of Scaling Cooldown Reduction x 9
-6.08% = x3 + x9

At level 13
-5.07% = Greater Quintessence of Scaling Cooldown Reduction x 3
-6.22% = Greater Glyph of Scaling Cooldown Reduction x 9
-11.29% = x3 + x9

At level 18
-7.02% = Greater Quintessence of Scaling Cooldown Reduction x 3
-8.62% = Greater Glyph of Scaling Cooldown Reduction x 9
-15.64% = x3 + x9


Masteries
+ 4% "Scorcery" Mastery (offense tree)
+ 8.1% at level 18 "Enlightenment" Mastery (+0.45% per level) (defense tree)
+ 6% "Intelligence" Mastery (support tree)

Items
10 , 10 , 10 , 10 , 15
10 , 10 , 15 , 15 , 15Shurelya's Reverie, 15 , 15Zeke's Herald, 20 , 20 , 25

10 Classic
10Hextech Sweeper Dominion

See: Cooldown Reduction on LoL Wiki


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Armor and Magic Resistance

How they work
Armor lets only a fraction of physical damage through.
Magic Resistance lets only a fraction of magic damage through.

That fraction is calculated the same way for both Armor and Magic resistance.
Physical Damage is multiplied by the fraction: 100 / (100 + Armor)
Magic Damage is multiplied by the fraction: 100 / (100 + MR)

If you are hit by 600 magic damage and have 50 MR, it will only hurt for 400 damage.
600 * 100/(100 + 50) = 600 * 2/3 = 400


Fractions of damage
Your protection -> Damage you take
50 -> 2/3 damage
100 -> 1/2 damage
200 -> 1/3 damage
300 -> 1/4 damage

Adding more and more protection gets less and less cost effective.
The first 50 points (from 0 to 50) block 1/3 (33%) of incoming damage.
The next 50 points (from 50 to 100) block 1/6 (17%) of incoming damage.
The next 50 points (from 100 to 150) block 1/10 (10%) of incoming damage.
The next 50 points (from 150 to 200) block 1/15 (6%) of incoming damage.




See:
Magic Resistance on LoL Wiki
Armor on LoL Wiki


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Resistance Reduction

The Armor and MR from the chapter above can be lowered 2 different ways.

  1. Reduction: can put resistances below 0, granting extra damage.
  2. Penetration: does nothing when resistance is below 0.


Resistances are calculated in this order:
  1. Percentage Reduction
  2. Flat Reduction
  3. Flat Penetration
  4. Percentage Penetration


Reduction comes from 2 sources
  1. Items
  2. Champion Abilities
Penetration comes from 3 sources
  1. Runes
  2. Masteries
  3. Items


Runes
Armor Penetration
9.99 = Greater Quintessence of Desolation x 3
14.94 = Greater Mark of Desolation x 9
24.93 = Greater Quintessence of Desolationx3 + Greater Mark of Desolationx9

Magic Penetration
6.54 = Greater Quintessence of Magic Penetration x 3
8.55 = Greater Mark of Magic Penetration x 9
6.12 = Greater Glyph of Magic Penetration x 9
15.09 = x3 + x9
21.21 = x3 + x9 + x9

Armor & Magic Penetration
6, 3.9 = Greater Quintessence of Precision x 3
9, 5.13 = Greater Mark of Precision x 9
15, 9.03 = x3 + x9


Masteries
"Sunder" = 6 Armor Penetration
"Weapon Expertise" = 10% Armor Penetration
"Arcane Knowledge" = 10% Magic Penetration



Items
Armor
Flat Reduction: 45
Flat Penetration: 15 , 20
Percentage Penetration: 40%

MR
Flat Reduction: 20 , 24
Flat Penetration: 20 , 20
Percentage Penetration: 40%




See:
Armor Penetration on LoL Wiki
Magic Penetration on LoL Wiki


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