Mechanics: Attack Speed

Attack Speed is an intuitive concept governed by unintuitive, arcane calculations and mechanisms. Everyone can understand that more attack speed means attacking faster, but the exact nature of the math can induce headaches.

To make this easier, we'll start with an oversimplified formula.

Attack Speed = Base Attack Speed * (1 + Attack Speed Bonuses)

Every champion has their own Base Attack Speed. These range from 0.579 to 0.694 attacks per second depending on the champion. Because of how the formula works this value is very important to a champion's ability to scale with Attack Speed. To reach 2.0 attacks per second a champion with 0.694 Base Attack Speed only needs 188% Attack Speed, whereas a champion with 0.579 Base Attack Speed needs 245%, a 57% gap worth roughly 1500 gold. A higher Base Attack Speed clearly results in substantially greater benefits from Attack Speed bonuses.

Champions also gain Attack Speed as they level, similar to how they gain AD. These range from 0.98% per level to 3.84% per level, including level 1. This Attack Speed functions the same as any other Attack Speed Bonuses.

So a level 18 Shaco with Madred's Bloodrazor and Berserker's Greaves has 65% Attack Speed from items, 54% from levels and a Base Attack Speed of 0.694 attacks per second. Attack Speed Bonuses are added together, so filling out the the formula we get:

Attack Speed = 0.694 * (1 + 119%)
Attack Speed = 0.694 * 2.19
Attack Speed = 1.520

If we replace Shaco with Nautilus, we only have 17.6% Attack Speed from levels, and a Base Attack Speed of 0.613, giving us:

Attack Speed = 0.613 * (1 + 82.6%)
Attack Speed = 0.613 * 1.826
Attack Speed = 1.119

As you can see, both Base Attack Speed and a champion's innate Attack Speed per level can have a huge influence on their scaling.

However, there's more to Attack Speed than that. The oversimplified formula ignores the effect of Attack Speed Debuffs, such as Frozen Heart or Malphite's Ground Slam. Factoring those in the equation changes.

Attack Speed = (Base Attack Speed * (1 + Sum of Attack Speed Bonuses)) * (Product of Attack Speed Debuffs)

Because of how this formula works Attack Speed Debuffs are incredibly powerful. Consider what happens to our Shaco when fighting an opponent with Frozen Heart's 20% Attack Speed Debuff.

Attack Speed = (0.694 * (1 + 119%)) * (1 - 20%)
Attack Speed = (0.694 * 2.19) * (0.8)
Attack Speed = 1.520 * 0.8
Attack Speed = 1.216

Shaco's final Attack Speed is reduced to a level equivalent to having only a 75.2% total Attack Speed Bonus. Because the 20% Debuff affects all attack speed as a multiplier it's as if Shaco lost 43.8% Attack Speed. The more Attack Speed a champion has, the greater this effective loss becomes.

Multiple Attack Speed Debuffs are multiplied together, so if our Shaco was affected by both Frozen Heart and Ground Slam the calculations are as follows:

Attack Speed = (0.694 * (1 + 119%)) * ((1 - 0.2) * (1 - 0.5))
Attack Speed = (0.694 * 2.19) * (0.8 * 0.5)
Attack Speed = 1.520 * 0.4
Attack Speed = 0.608

In this case our unfortunate Shaco is actually attacking slower than his Base Attack Speed. He effectively has -12.4% Attack Speed, making such an auto-attack heavy champion essentially worthless. This crippling combination is a key part of why Malphite has been a top ban.

As a matter of trivia, Attack Speed has both a cap and a minimum. You can't exceed 2.5 attacks per second, or go below 0.2 attacks per second. The circumstances for approaching either number are extremely rare, but not entirely improbable. There is also one confusing exception to the rules for debuffs, the passive effect of Randuin's Omen. For whatever reason, Randuin's Omen's passive is treated as a negative Attack Speed Bonus rather than as an Attack Speed Debuff. You won't often encounter situations where these tidbits are practicable, but they're interesting nonetheless.

What is useful is applying the understanding of Attack Speed mechanics to champion theory. Not too long ago AD Kennen was used in tournaments in place of traditional AD carries, and a large part of his success came from his excellent Base Attack Speed and Attack Speed per level. Combining his 0.690 attacks per second with his 3.4% Attack Speed per level, Kennen has the highest innate Attack Speed in the game. Despite only having a nominal AD steroid, Kennen's superior base stats and scaling allowed him to be a serious contender at the tournament level.

Similarly, Twitch is currently flying under the radar. Of the traditional AD carries Twitch has the highest Base Attack Speed and Attack Speed per level. That he also has an extremely strong Attack Speed steroid only adds to his hidden strength. It's only a matter of time before someone figures out an appropriate team composition and Twitch rises from the depths of obscurity.

Understanding Attack Speed isn't quite as critical as other mechanics, but for the teams that want to be on the bleeding edge of composition and champion theory it's another important piece of the puzzle.