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→Calculation: change calculation to dynamically pull frmo itemdata like the pages for range / duration. also changed the items around because Diviner's Kevlar no longer gives cooldown reduction
 
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'''Ability Cooldown''' is the time it takes for an [[Ability]] to be usable again.  
'''Ability Cooldown''' is the time it takes for an [[Ability]] to be usable again.


==Overview==
==Overview==
Cooldowns range from a few seconds, as in [[Lady Geist|Lady Geist's]] Malice, to a few minutes, as [[Dynamo|Dynamo's]] Singularity. Ability cooldowns can be reduced by acquiring the Cooldown Reduction stat, which reduces the cooldown by a percentage of base [[ability]] time.
Cooldowns range from a few seconds, as in {{HeroIcon|Lady Geist}}'s {{AbilityIcon|Malice}}, to a few minutes, as in {{HeroIcon|Dynamo}}'s {{AbilityIcon|Singularity}}. Ability cooldowns can be reduced by acquiring the Cooldown Reduction stat, which reduces the cooldown by a percentage of base [[ability]] time.
 
In the in-game HUD, ability cooldowns only show decimal values below 2s.
 
Unlike [[Ability Range]] and [[Ability Duration]], ability cooldown does not affect items. Items are only affected by a separate stat called [[Ability Cooldown#Item Cooldown|Item Cooldown Reduction]] which is granted by {{ItemIcon|Transcendent Cooldown}}.


===Charged Abilities===
===Charged Abilities===
Some abilities can acquire multiple charges. In those cases, the ability cooldown represents the time for a charge to become available again after being used. This should not be confused with the time between charges, which describes the delay after using a charge that a different charge can be used.
Some abilities can acquire multiple charges. In those cases, the ability cooldown represents the time for a charge to become available again after being used. This should not be confused with the time between charges, which describes the delay after using a charge that a different charge can be used.


===Stacking===
== Calculation ==
Despite being presented in-game as +X% Cooldown Reduction, different sources of cooldown reduction stack multiplicatively, not additively. With <math>n</math> different sources of cooldown reduction, total cooldown reduction is given by:


<math>CR_{Total} = 1 - \prod_{i=1}^n (1 - CR_i)</math>
=== Calculating Cooldown Reduction ===
Despite being presented in-game as +X% Cooldown Reduction, multiple sources stack '''multiplicatively''', not additively:


For example, with 12% Cooldown Reduction from [[Diviner's Kevlar]] and 16% Cooldown Reduction from [[Improved Cooldown]], total cooldown reduction is:
<math>\text{Total Cooldown Reduction} = 1 - (1 - CR_1) \times (1 - CR_2) \dots</math>


<math>CR_{Total} = 1 - (1 - 0.12) \times (1 - 0.16) \approx 26%</math>
'''Example:'''
With '''{{ItemData|{{#vardefineecho: Item1|Superior Cooldown}}|CooldownReduction}}''' from {{ItemIcon|{{#var: Item1}}}} and '''{{ItemData|{{#vardefineecho: Item2|Spellslinger}}|CooldownReduction}}''' from {{ItemIcon|{{#var: Item2}}}}:
# Convert percentages to decimals: {{ItemData|{{#var: Item1}}|CooldownReduction}} to {{#vardefineecho: Item1Duration|{{#expr: {{#replace: {{ItemData|{{#var: Item1}}|CooldownReduction}}|%|}} / 100}}}} and {{ItemData|{{#var: Item2}}|CooldownReduction}} to {{#vardefineecho: Item2Duration|{{#expr: {{#replace: {{ItemData|{{#var: Item2}}|CooldownReduction}}|%|}} / 100}}}}.
# Subtract from 1: (1 - {{#var: Item1Duration}}) = '''{{#expr: 1 - {{#var: Item1Duration}}}}''' and (1 - {{#var: Item2Duration}}) = '''{{#expr: 1 - {{#var: Item2Duration}}}}'''.
# Multiply the remainders: {{#expr: 1 - {{#var: Item1Duration}}}} × {{#expr: 1 - {{#var: Item2Duration}}}} = '''{{#vardefineecho: CombinedItemDuration|{{#expr: (1 - {{#var: Item1Duration}}) * (1 - {{#var: Item2Duration}}) round 4}}}}'''.
# Subtract from 1: 1 - {{#var: CombinedItemDuration}} = '''{{#expr: 1 - {{#var: CombinedItemDuration}} round 4}}'''.
# Total Cooldown Reduction is '''{{#expr: (1 - {{#var: CombinedItemDuration}}) * 100 round 1}}%''', not {{#expr: ({{#var: Item1Duration}} + {{#var: Item2Duration}}) * 100 round 1}}%.


== Sources of Ability Cooldown Reduction ==
== Sources of Ability Cooldown Reduction ==
Items that reduce the cooldown of all abilities:
{{Item stat table|Ability Cooldown Reduction}}
{{Item stat table|Ability Cooldown Reduction}}
* {{ItemIcon|Witchmail}} has a passive that reduces the cooldown of a random ability as the player takes [[Spirit Damage]].
* {{ItemIcon|Golden Goose Egg}} grants random [[Permanent Buffs]], including Cooldown Reduction.


===Map Spawns===
===Map Spawns===
* [[Golden Statue|Golden Statues]] have a chance to drop a permanent Cooldown Reduction buff.
* [[Golden Statue|Golden Statues]] have a chance to drop a permanent Cooldown Reduction buff.
* [[Powerup]] runes can provide a temporary Casting buff that provides +'''12'''% to +'''25'''% Cooldown Reduction for 160 seconds (scaling with game time from 5 to 40 minutes).
* [[Powerup]] runes can provide a temporary Casting buff that provides +'''12'''% to +'''20'''% Cooldown Reduction for 160 seconds (scaling with game time from 5 to 40 minutes).
 
== Item Cooldown ==
Item Cooldown is the time it takes for an [[Item]] to be usable again. This includes both [[Active]] and Passive items.
 
[[Charge-Up]] items such as {{ItemIcon|Tankbuster}} and {{ItemIcon|Mercurial Magnum}} are not affected by Item Cooldown Reduction.
 
=== Sources of Item Cooldown Reduction ===
{{Item stat table|Item Cooldown Reduction}}


{{Stats}}
{{Stats}}
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