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### Mathcraft: Cooldown becomes exponentally better the more you get.

Craixis

Senior Member

... Can you explain to me how your formula is working, I keep trying to do the numbers and I can't wrap my head around what you're doing. I mean, wouldn't it be (number of uses)/(current time) = (number of uses)/(new time), so 1/10 = 1/9, which is cross multiplication... which is 90/100, which is .9 (or 10% increase). Why are we dividing 9 into 10 again? 9 is the new time, I get that, and 10 is the old time, but don't you need to include the number of uses above each? 9 and 10 are the times, yes, but we're not doing the times alone, its number of uses over the amount of time it takes to use.

I look at Fearful's equation and think "shouldn't he have the base use in the equation" so something like
1/(10-(10*CDR%)) = 1/10?
1/(10-(10*40%{4}))= 1/10
1/(10-4{6})=1/10
60/100 = .6
1-.6 = .4, or 40%...

Like what am I doing wrong here?

Edit: Nvm, I'm talking the decrease to CDR instead of increase to usage... Yeah, 25% increase, I'm gonna find my dunce cap now...

gallantgreg

Senior Member

Quote:
Craixis:
... Can you explain to me how your formula is working, I keep trying to do the numbers and I can't wrap my head around what you're doing. I mean, wouldn't it be (number of uses)/(current time) = (number of uses)/(new time), so 1/10 = 1/9, which is cross multiplication... which is 90/100, which is .9 (or 10% increase). Why are we dividing 9 into 10 again? 9 is the new time, I get that, and 10 is the old time, but don't you need to include the number of uses above each? 9 and 10 are the times, yes, but we're not doing the times alone, its number of uses over the amount of time it takes to use.

I look at Fearful's equation and think "shouldn't he have the base use in the equation" so something like
1/(10-(10*CDR%)) = 1/10?
1/(10-(10*40%{4}))= 1/10
1/(10-4{6})=1/10
60/100 = .6
1-.6 = .4, or 40%...

Like what am I doing wrong here?

The way I think about it is the amount of abilities you can use with CDR in the same timeframe of the ability without cooldown.

So if there is a parrrley with a 6 second cooldown and we have 40% CDR.
Then we get a 3.6 cooldown parrrley and you can shoot 6 / 3.6 = 1.66 times in 6 seconds.
That extra .66 is the 66% bonus spell spam or damage you get.

If that doesn't make sense how about shooting it as much as you can in 18 seconds.
Without CDR you get 3 hits. With CDR you get 5 hits.
5 / 3 = 1.66 more hits or more damage

Which is the same as 66% crit chance or 186 AD lol

Craixis

Senior Member

Yeah, was talking with some friends about it on LoL...

I wasn't thinking the increase to uses, I was thinking total decrease (which is 20%)
20% of 100 is 80, 100/80 = 1.25, which is the increase to how many skills we use in a set time frame.

So for a 5 base cooldown on a skill, 20% is 4 base cooldown, how many times can you use both in 20 seconds?

20/5 = 4
20/4= 5
5/4 = 1.25, or 25% more uses for 20%CDR...

I get it now -.-'

Sackrace

Senior Member

That's simply because CDR reduces the variable in question, while AD,AS,AP etc all increase the variable they govern. Each time you buy CDR you're taking a constant time of your CD, but the time you're taking it off is diminished withe ach CDR applied.
It's like how a 5% loss on the stockmarket is more in absolute terms than 5% gain.

Warrrrax

Senior Member

Quote:
Fearful Ferret:
I hate to be a math minor and all (actually not, but whatever), but it's not exponential, and people need to stop throwing that word around.

It's an inverse relationship. With a normalized cooldown of 1 unit of time (say, 10 seconds), the number of times you can use that skill within that unit of time goes inversely with the value (100%-CDR). The number of times you can use a 10-second cooldown skill within a 10-second time span is equal to 1/(100%-CDR). At 50% CDR (ignoring the maximum), this value is 2. At 75% CDR, it is 4. At 99% CDR, it is 100. As CDR approaches 100%, it becomes infinite, mathematically speaking.

All of which is totally different from k*(a^CDR). It's not linear. It's not exponential. It's inversely proportional. That nitpick aside, yes, CDR does scale better the more you get of it, when taken by itself and out of all in-game context.

I KNEW someone would mention this. :-)

Still, if you graph out % increase in spamming vs CDR on the x axis, it looks exponential. It is not precisely e to some power, but it does look like a second order polynomial. This is what most people think of when you say exponential growth, so I went with it.

Anyways, the point was I found this interesting and tells me that If I DO happen to max CDR on a particular champ that it would behoove me to consider maxing the CDR sooner rather than later. I was not saying that one should always max CDR on every champ or that it is always useful.

Rrbhaunoch

Recruiter

Love the explanation and discussion... +1 OP

EatsBlood

Senior Member

Quote:
Fearful Ferret:
I hate to be a math minor and all (actually not, but whatever), but it's not exponential, and people need to stop throwing that word around.

It's an inverse relationship. With a normalized cooldown of 1 unit of time (say, 10 seconds), the number of times you can use that skill within that unit of time goes inversely with the value (100%-CDR). The number of times you can use a 10-second cooldown skill within a 10-second time span is equal to 1/(100%-CDR). At 50% CDR (ignoring the maximum), this value is 2. At 75% CDR, it is 4. At 99% CDR, it is 100. As CDR approaches 100%, it becomes infinite, mathematically speaking.

All of which is totally different from k*(a^CDR). It's not linear. It's not exponential. It's inversely proportional. That nitpick aside, yes, CDR does scale better the more you get of it, when taken by itself and out of all in-game context.

y=x^(-1). An inverse function IS an exponential function. Unless you've got a periodic function like a sine wave, almost any time you've got curves instead of straight lines, you've got an exponential function of some type. The graph of this is asymptotic, as the percentage increase approaches infinity and the CDR approaches 100%.

This is also why LoL caps CDR at 40%. Because they can't increase the itemization cost for additional CDR since it spans across multiple items and abilities and runes.

And as others stated, sometimes the utility of CDR is worthless. And sometimes CDR will just hit a soft floor as your mana regen fails to keep up with the increased demand.

And sometimes the priority of other stats is so high that even their linear nature still exceeds the utility of CDR.

Tyroie

Senior Member

Don't forget that Cooldown Reduction actually has a hidden downside to it.

If you actually take advantage of your CDR and cast your abilities as often as you can, you spend your mana / resource faster than normal. It takes much less time to run out.

If you're fighting opponents who bought Ability Power instead of CDR, then you need to spend much more mana than normal just to match their effectiveness.

Of course, this doesn't mean CDR is bad, not at all. Especially for champions which don't use resources when using ability. Or if you're playing Soraka, where you gain mana regen when you take CDR. But I think it does play a role in how Riot balanced it.

EatsBlood

Senior Member

CDR is meant for burst abilities. It doesn't matter if they have more mana than you if they're dead.