Attack Speed is the rate at which a hero attacks per second. Often, this term is referred to as IAS, which is short for Increased Attack Speed. Increasing a hero's attack speed reduces the time it takes to kill an enemy hero and increases the amount of damage your hero deals per second. See DPS for more information on Damage Per Second.
The Attack Speed per game second of a unit can be calculated by (1+IAS)/(BAT), where BAT is the hero's Base Attack Time. Also, less often used is Game Seconds per Attack, which is calculated by (BAT)/(1+IAS).

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