Turn rate

Turn rate is the speed at which a unit can turn. When moving to a location, a unit first turns to face that location, then begins walking. Similarly, when targeting another unit with an attack or spell, a unit first turns until it is facing the target, and then continues with the action. A unit only starts moving, or only starts casting a spell on a targeted area or point when the target is within 11.5° angle in front of the ordered unit. This can make kiting more difficult, as the hero has to spend time turning towards and away from the target with each attack.

Every unit has a base turn rate, which can be lowered by some abilities. The vast majority of heroes have a turn rate between 0.6 and 0.5, meaning it takes between 0.15 and 0.19 seconds for the hero to make a 180° turn.

There are currently no talents that improve turn rate.

Mechanics
Turn rate is expressed in radians per 0.03 seconds. A 180° turn is the same as $$\pi$$ (3.1416) radians, therefore 0.03$$\pi$$ divided by the turn rate of the unit equals the time it takes to turn 180°.

Turn rate is defined as



With  being the time it takes to turn around and   the turn rate sources.

Turn rate slow directly affects the base turn rate, and all sources of turn rate slow stack multiplicatively.


 * $$\sum T =

\begin{cases} T_{Set} & \text{if} \;\; T_{Set} = \top \\ T_{b} \times \displaystyle\prod_{i=1}^n (1-r_i)(1+a_i) & \text{otherwise} \end{cases}$$

With  being the Set Turn Rate Value,   the Base Turn Rate,   the Turn Rate Slow Value and   the Turn Rate Improve Value.

A unit does not immediately start turning at the highest rate it can turn. The turn rate ramps as the unit starts turning, reaching the unit's max turn rate after a certain amount of time. The rate at which the turn rate ramps up is unknown.

If a unit starts turning due to an ability or item cast order (by targeting a point, area or unit which is not within the required 11.5° facing angle), the turning cannot be canceled by a move, attack or a new spell cast order. Because the 11.5° angle can be in either direction, this creates a 23° angle directly in front of the hero allowing instant actions on any target within 23°. For any target beyond this angle, the hero must wait until they turn before the action occurs. The above formula is used to find the maximum time, so the time until the action takes place is actually ≤ 168.5°.

Any command ordered while turning due to a spell cast order gets queued up and executed once the spell is cast. In order to cancel the spell or ability cast, the player must issue a stop or halt command, in the same way how to cancel spell during its cast animation. This is to prevent accidental canceling of casts due to fast clicking. Issuing a stop or halt command (with S) does not stop the unit from turning if it has already started to turn, but stops the order which initiated the turning. For example, this allows to turn during  without canceling the ability, as long as the move command is stopped before the targeted point is within the required angle.

Stacking

 * Example 1


 * is affected by a turn rate slow of 70%. What is his current actual turn rate? How long would it take for him to turn 180°?






 * affected by a turn rate slow of 70% has a lowered turn rate of and it takes him roughly s to turn 180° in this example.


 * Example 2


 * is affected by two turn rate slows of 70% and 50%. What is his current actual turn rate? How long would it take for him to turn 180°?






 * affected by two turn rate slow of 70% and 50% has a lowered turn rate of and it takes him roughly s to turn 180° in this example.

Turn Rate Comparison
Below is a comparison of the turn rates of all heroes:
 * does not need to turn to take any actions.
 * However, Pangolier still turns and uses his turn rate for all actions which require facing (except for targeted items), despite not needing it. This is important for abilities which rely on facing direction, like and.
 * During, , , and , the caster does not require to turn to take actions.
 * ,, , , , , , , , and do not require their caster to face towards the target.
 * During, the caster does not require to turn to cast.
 * During, the caster does not require to turn to cast or.
 * When is toggled on, Mars cannot and does not need to turn to take any actions.

Modifying Turn Rate
Several abilities and items have abilities that slows or improve turn rate. For better readability, some of the turn rates in pages are given as degrees per second, instead of radians per 0.03 seconds.

Turn Rate Slowing Abilities
The following abilities slows turn rate:

Turn Rate Improving Abilities
The following abilities improves turn rate:

Turn Rate Setting Abilities
Set Turn Rate ( $$T_{Set}$$ ) sets a unit's turn rate to a fixed value for the duration, so it cannot be altered by other effects.

The following abilities sets turn rate to the given value for the duration.

Abilities Preventing Turning
The following abilities completely prevent the affected unit from turning: