# Attack Speed

Attack Speed is a measure of how fast a hero is able to attack. The attack speed of a hero is set by their base cooldown time (BCD) and their increased attack speed (IAS).

IAS can be increased by using abilities, passives, auras, items, and agility. Each point of agility will increase IAS by 2 percentage points.

## Attack Speed Table

Description Attack Speed
Very Slow > 3.00
Slow 2.00 - 2.99
Normal 1.50 - 1.99
Fast 1.00 - 1.49
Very Fast 0.00 - 0.99

## Attack Speed Formula

Using a hero's BCD and IAS, their attack speed (length of time it takes to attack) is calculated using this formula:

Attack Speed = Base Cooldown Time ÷ (1 + Increased Attack Speed)

The BCD is a unique value for each hero, ranging from 1.64s for the Blood Mage to 2.5s for the Alchemist. The IAS is the combined effect of all attack speed bonuses (and debuffs) stacked additively. Thus, using that agility gives a 2% increase:

Increased Attack Speed = (0.02 * Agility) + Item Bonuses + Ability Bonuses

### Agility example The Blood Mage has the shortest base cooldown time

Knowing that a level 1 Blood Mage, with no items or buffs, has 14 agility, the IAS can be calculated as:

Increased Attack Speed = (0.02 * 14) = 0.28 = 28%

The resulting attack speed is found using the BCD

Attack Speed = 1.64s ÷ (1 + 0.28) = 1.281s

### Ability example

Should the same Blood Mage get a Bloodlust buff, this should increase the attack rate by 40%. The new IAS is:

Increased Attack Speed = (0.02 * 14) + 0.4 = 0.68 = 68%

The resulting attack speed is

Attack Speed = 1.64s ÷ (1 + 0.68) = 0.976s

Note: Since the attack rate bonuses stack additively, not multiplicatively, this buffed Blood Mage’s attack is not 40% faster than the unbuffed hero.

## Effect on DPS

Damage per Second (DPS) is why attack speed ultimately matters. A buff that increases the attack rate, will give the player a higher damage output, which could decide the fight in his or her favor. DPS is defined as follows:

Damage per Second= Damage per Hit ÷ Attack Speed

Using the formulas above, this could be rewritten as

Damage per Second = Damage per Hit ÷ Base Cooldown Time * [1 + (0.02 * Agility) + Item Bonuses + Ability Bonuses]

From this formula it’s easy to see that:

• DPS increases linearly with agility
• The absolute DPS increase of Agility, Bloodlust or Gloves of Haste is constant (as long as the damage is unchanged) and independent of each other
• The relative DPS increase of these buffs diminishes with more agility or if there are multiple buffs

### Calculating DPS Example

Continuing with the level 1 Blood Mage from the examples above, this hero does an average of 24 damage per hit. With no items or buffs, the DPS is therefore given by:

Damage per Second = 24 ÷ 1.64s * [1 + (0.02 * 14) ] = 18.73

If the hero then picked up a Gloves of Haste, increasing the attack rate by 15%, the DPS added by this could be calculated independently as:

Damage per Second = 24 ÷ 1.64s * [ 0.15 ] = 2.20

The total DPS is 18.73 + 2.20 = 20.93.

Note: Again, since the attack rate bonuses stack additively, not multiplicatively, this buffed Blood Mage’s DPS is not 15% higher than the unbuffed hero, rather, it's approximately 12%.