# Attack Speed

Attack Speed is a measure of how fast a hero or unit 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 and auras. Heroes can also use items and their attack speed is increased by agility. Each point of agility increases IAS by 2 percentage points.

The attack speed can be reduced, if the unit or hero is slowed. For heroes the attack speed reduction is substracted from the IAS.

## Attack Speed Table[edit]

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[edit]

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

*Attack Speed = BCD/1 + IAS*

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:

*IAS = (0.02 * Agility) + Item Bonuses + Ability Bonuses*

### Agility example[edit]

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

*IAS = (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[edit]

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

*IAS = (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[edit]

**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

*DPS = Damage per Hit * [1 + (0.02 * Agility) + Item Bonuses + Ability Bonuses]/BCD*

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[edit]

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:

*DPS = 24*[1 + (0.02 * 14)]/1.64s = 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:

*DPS = 24*[ 0.15 ]/1.64s = 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%.