VainGlory was the first game I played that used a statistic called *Cooldown Acceleration*. I have played ~~hundreds~~ thousands of hours of League of Legends which uses a different statistic called *Cooldown Reduction*, so to understand it better I did a short write-up.

*Cooldown Reduction* is a flat, percentage reduction of the ability cooldown as a whole. This mean that an ability with a 100 second cooldown would be reduced by 1 second for each 1% of cooldown reduction a character had. In League of Legends it needed a cap because any character with more then 40% cooldown reduction would start doing magical things. See URF.

*Cooldown Acceleration* behaves quite differently. Because of the nature of accelerating cooldowns it has drastically lower rate of returns based on the amount that you have. Imagine that your abilities are coming off cooldown at a current rate of 100%. This makes the math the easiest. As you gain percentage points of cooldown acceleration that 100% increases. With each percentage point of cooldown acceleration, you add a point to that 100%, then the ability is divided by the whole number.

If you had an ability with a 100 second cooldown and you had 50% cooldown acceleration (summing up to 150% normal cooldown speed) you would divide the 100 second full cooldown by 1.5 (150%) resulting in 66.6 seconds of cooldown. 50% cooldown acceleration is therefore equal to 33.3% cooldown reduction. However, 100% cooldown acceleration only results in 50% cooldown reduction. The rate of return has already halved. The first 50% gave you 33.3% cooldown reduction, the second 50% only gave you 16.6% cooldown reduction. These diminishing returns are outlined further below:

Base Cooldown | Cooldown Acceleration | Equivalent Cooldown Reduction | Difference | Cooldown |

10 sec | 0% | 0% | 0 sec | 10 sec |

10 sec | 25% | 20% | 2 sec | 8 sec |

10 sec | 50% | 33% | 1.33 sec | 6.66 sec |

10 sec | 75% | 42.8% | 0.95 | 5.71 sec |

10 sec | 100% | 50% | 0.71 | 5 sec |

10 sec | 125% | 55.5% | 0.56 | 4.44 sec |

10 sec | 150% | 60% | 0.44 | 4 sec |

While this is probably information that people already knew, I was hoping someone would find it useful or educational. Thanks for reading!

For funsies, the most cooldown acceleration you can have would be six Clockworks, which would be 300%, giving you 75% reduction on your cooldowns. You’d be able to use Glaive‘s Afterburn every three seconds, which would be helpful because you wouldn’t have boots. It would also be doing 610 damage. You would run out of energy. Probably.

Great post! I love it when players nerd out on math like this!

The formula works out such that CDA is exactly the same as attack speed: 100% means you can use abilities 2x as often, just like how 100% attack speed means you can attack 2x as fast! In that sense, both stats provide linear returns, not really diminishing returns.

In LoL, Cooldown Reduction is problematic because it provides INCREASING returns. Meaning if you already have 20% CDR, the next 20% is EVEN BETTER. This causes builds to either have NO CDR, or have LOTS CDR, but rarely in between. Note the double-morello build from Bjergson this weekend at IEM, the frequent Athenes + Deathfire Grasp builds you see on AP mids. We believe having linear returns allows the entire spectrum from none to max CDA to be strategically viable.

Cheers!

SupriseBirthday

Hi SurpriseBirthday! I’ve been nerding out on math for far too long!

I like the examples of Bjergsen this weekend, despite the fact I missed most of IEM because of a double Glory weekend coupled with a pre-release of GvG in Hearthstone!

I should have correlated it to the math behind armor. Armor appears to have diminishing returns when you buy more of it, but that’s not the case. You’re still extending your health by the same amount the more armor you buy, despite the division equation to determine effectiveness of armor.

Cool stuff! Thanks for reading!

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The formula works out such that CDA is exactly the same as attack speed: 100% means you can use abilities 2x as often, just like how 100% attack speed means you can attack 2x as fast! In that sense, both stats provide linear returns, not really diminishing returns.

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