Attack animation

Every unit in Dota 2 has an attack animation. In mechanical terms, this is a delay between when an attack command is issued, and damage is dealt (in the case of melee units) or a projectile is launched (in the case of ranged units).

Units also possess an animation backswing, which is a delay between the damage point of an attack and when another queued command will be performed. The backswing of an attack may be canceled by issuing another command, such as stop or move, to allow further commands to be followed more quickly.

Both attack point and backswing are reduced by the increased attack speed (IAS) attribute following the attack speed formula: 
 * attack point = (base attack point) / (1 + IAS)
 * attack backswing = (base backswing) / (1 + IAS)

 Where IAS is a percentage between -0.8 and 5.00.

With being the only exception (increasing attack projectile speed by 500), the speed of ranged attack projectiles cannot be altered. They can neither be hastened up, nor slowed down.

A unit's attack speed is completely independent of its attack animation. Attack animation strictly refers to the delay between when an attack order is issued and when the attack is launched. For example, if a unit has an attack time of one second, an attack point of 0.3 seconds, and an attack backswing of 0.5 seconds, they will be idle for 0.2 seconds during every attack cycle. Even if the backswing is canceled after 0.2 seconds, the idle period is extended to 0.5 seconds. However, during that idle period, other commands can be issued such as moving or casting spells.

In other words, canceling your animation does not allow you to attack faster.