Turn rate

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°^[1] 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[edit]

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

t={\frac {0.03\pi }{T}}

With t being the time it takes to turn around and T 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 T_Set being the Set Turn Rate Value, T_b the Base Turn Rate, r the Turn Rate Slow Value and a 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 Templar Assassin to turn during Meld without canceling the ability, as long as the move command is stopped before the targeted point is within the required angle.

Stacking[edit]

Example 1

Earthshaker 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°?

T=0.9\times (1-0.7)=0.27

t={\frac {0.03\pi }{0.27}}=0.349

Earthshaker affected by a turn rate slow of 70% has a lowered turn rate of 0.27 and it takes him roughly 0.349s to turn 180° in this example.

Example 2

Earthshaker 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°?

T=0.9\times (1-0.7)\times (1-0.5)=0.135

t={\frac {0.03\pi }{0.135}}=0.698

Earthshaker affected by two turn rate slow of 70% and 50% has a lowered turn rate of 0.135 and it takes him roughly 0.698s to turn 180° in this example.

Turn Rate Comparison[edit]

Below is a comparison of the turn rates of all 121 heroes:

Heroes	Base turn rate	Time required to turn 180°/sec
Batrider, Bristleback, Earthshaker, Faceless Void, Hoodwink, Lifestealer, Pangolier, Phoenix, Shadow Fiend	0.9	0.105s
Death Prophet, Magnus, Mars, Puck, Storm Spirit, Windranger	0.8	0.118s
Arc Warden, Dark Willow, Dazzle, Drow Ranger, Io, Meepo, Oracle, Pudge, Rubick, Slark, Sniper, Templar Assassin, Tusk, Void Spirit	0.7	0.135s
Abaddon, Alchemist, Ancient Apparition, Anti-Mage, Axe, Bane, Beastmaster, Bloodseeker, Bounty Hunter, Brewmaster, Broodmother, Centaur Warrunner, Chaos Knight, Chen, Clinkz, Clockwerk, Crystal Maiden, Dark Seer, Dawnbreaker, Disruptor, Doom, Dragon Knight, Earth Spirit, Elder Titan, Ember Spirit, Enchantress, Enigma, Grimstroke, Gyrocopter, Huskar, Invoker, Jakiro, Juggernaut, Keeper of the Light, Kunkka, Legion Commander, Leshrac, Lich, Lina, Lion, Lone Druid, Luna, Lycan, Medusa, Mirana, Monkey King, Morphling, Naga Siren, Nature's Prophet, Necrophos, Night Stalker, Nyx Assassin, Ogre Magi, Omniknight, Outworld Destroyer, Phantom Assassin, Phantom Lancer, Pugna, Queen of Pain, Razor, Riki, Sand King, Shadow Demon, Shadow Shaman, Silencer, Skywrath Mage, Slardar, Snapfire, Spectre, Spirit Breaker, Sven, Techies, Terrorblade, Tidehunter, Timbersaw, Tinker, Tiny, Treant Protector, Troll Warlord, Underlord, Undying, Ursa, Vengeful Spirit, Venomancer, Viper, Visage, Warlock, Weaver, Winter Wyvern, Witch Doctor, Wraith King, Zeus	0.6	0.157s

Pangolier 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 Cloak and Dagger and Force Staff.
During Omnislash, Rolling Thunder, Icarus Dive, and Sun Ray, the caster does not require to turn to take actions.
Burning Army, Torrent, Sticky Napalm, Shadow Amulet, Glimmer Cape, Bottle, Clarity, Enchanted Mango, Healing Salve, and Repair Kit do not require their caster to face towards the target.
During Battle Trance, the caster does not require to turn to cast Whirling Axes (Ranged).
During Burrow, the caster does not require to turn to cast Impale or Mana Burn.
When Bulwark is toggled on, Mars cannot and does not need to turn to take any actions.

Modifying Turn Rate[edit]

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[edit]

The following abilities slows turn rate:

Turn Rate Slowing Abilities

Batrider - Sticky Napalm
Max Stacks: 10
Turn Rate Slow: 10%/30%/50%/70%
Stack Duration: 8
Medusa - Mystic Snake
Turn Rate Slow: 50%
Slow Duration: 3
Medusa - Stone Gaze
Radius: 1200
Facing Angle: 85°
Turn Rate Slow: 35%
Duration: 5/5.5/6 ( 7/7.5/8)
Affect units while facing the caster.

Turn Rate Improving Abilities[edit]

The following abilities improves turn rate:

Turn Rate Improving Abilities

Phase Boots - Phase
Turn Rate (Melee): 1
Duration: 3
For melee heroes, increases the base turn rate to the given value for the duration.
Spider Legs
Turn Rate Increase: 50%
Passive.

Turn Rate Setting Abilities[edit]

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.

Turn Rate Setting Abilities

Clockwerk - Jetpack
Turn Rate: 0.039
Duration: 6
Requires Aghanim's Shard. This equals to 75° per second.
Hoodwink - Sharpshooter
Turn Rate: 0.031
Max Aim Time: 5
This equals to 60° per second.
Phoenix - Sun Ray
Turn Rate: 0.013
Ray Duration: 6
This equals to 25° per second.
Pangolier - Rolling Thunder
Turn Rate: 0.063
Turn Rate After Start/Jump/Bounce: 0.149
Turn Rate Boost Duration: 0.25
Rolling Thunder Duration: 10 ( 13
Sets Pangolier's turn rate while ability is active to 120° per second.
When boosted, adds on an extra 165° per second, effectively increases the turn rate to 285 per second for that time.
Pangolier - Roll Up
Turn Rate: 0.092
Roll Duration on Attack: 0.75
Roll Up Duration: 4
Requires Aghanim's Shard.
Sets Pangolier's turn rate while ability is active to 175° per second. Pangolier does not roll during Roll Up, if an attack of an hero lands on him, he rolls for 0.75 seconds.
Snapfire - Mortimer Kisses
Turn Rate: 0.039
Launch Duration: 6
This equals to 75° per second.

Abilities Preventing Turning[edit]

The following abilities completely prevent the affected unit from turning:

Abilities Preventing Turning

Ember Spirit - Activate Fire Remnant
While traveling, Ember Spirit cannot turn, but he still requires to face his targets to attack, cast abilities and use items.
Mirana - Leap
During Leap, Mirana can only attack, cast abilities, and use items in the direction she is facing.
Juggernaut - Omnislash
During Omnislash, Juggernaut cannot turn and does not need to turn in order to cast targeted spells or items. However, Blade Fury is inactive for the duration and cannot be cast.
Juggernaut - Swiftslash
Requires Aghanim's Scepter.
Same values and notes from Omnislash applies.
Mars - Bulwark
Can be toggled, removing Mars's ability to attack, and locking the direction he is facing. When active, reduces movement speed and redirects attack projectiles aimed at Mars's allies towards Mars instead.
Phoenix - Icarus Dive
Phoenix can attack, cast abilities and use items while diving (including channeling abilities). However, Sun Ray is inactive for the duration and cannot be cast.