Mathcraft: Cooldown becomes exponentally better the more you get.
Cooldown reduction is one of the only stats that actually gets better the more points you put into it.
Everything else tends to have a constant effect that appears to diminish over time relative to your new baseline.
For example, Attack Damage.
If you have 50 AD and farm up a BF Sword, this is a huge DPS increase of 100%. The next one you get is the same +50 damage, but is only a 50% increase from 100 to 150. Same exact effect but that first one sure seemed like it had a much bigger impact, didn't it?
Cooldown reduction is actually quite the opposite.
Say you have 10% CDR. Lets assume a 100 second cooldown ability.
10% CDR reduces it to 90 seconds.
In the span of 900 seconds, you could get 10 uses in, instead of the 9 you would normally have.
10% CDR means you get to use your ability 10/9 = 11% more often.
What happens when you get to 20% CDR?
80 second cooldown means 10 uses in 800 seconds, vs just 8 uses at 100 second cooldown.
20% CDR means you get to use your ability 10/8 = 25% more often
Notice the percentage gain you get from 10 to 20% CDR is MORE than what you got for the first 10%!
Using similar calculations we get...
30% CDR means 10/7 = 42.9% more uses
40% CDR means 10/6 = 66.7% more uses.
This makes sence when you think about it. Imagine 90% CDR which would give you 900% more uses (or 10 times more).
If you added just 10% more CDR to 100% you'd have NO cooldown whatsoever. 100% CDR and Karthus = just like WTF mode in DOTA with Zeus! What fun.
So when you have a champ that is highly dependent on his/her/its cooldowns, be sure to consider this when figuring out when to get their CDR item(s).
Yes this is true from a mathcraft point of view and for the most part in game.
Of course LoL gameplay consist of discrete events not 1 continuous teamfight that lasts the entire game, so there are thresholds and breakpoints. For example Lux's laser with max CDR can get to I think 22 seconds which actually makes it for poking standoffs. However, getting someone's ultimate to 45 seconds to 55 seconds might not be a big deal compared to making it hit harder, because either way you can use it 1 time in every fight if it's 45 or 55 seconds CD (for example Rammus ult).
QWE skills are what I assume you are talking about more, although the same thing applies with them too. Max CDR on Ryze Q is absolutely mandatory but on the other hand you get 15-25% on Pantheon but its not really worth finishing it due to priority on AD.
Isn't CDR calculated multiplicatively instead of additively though?
There's a fatal flaw in your comparison scheme.
In your AD example, you provide continuous increases (you go from 50 AD to 100, then 100 AD to 150).
In your CDR example, you constantly reset your base (0 CDR to 10%, 0 CDR to 20%).
Comparison flaws aside, as someone pointed out, just because you get to use your abilities more often doesn't make them more useful. Take Karthus for example. CDR makes his ult timer lower and lower, which is good, right? How often in the game is Karth's ult still just barely on CD when it would be useful, versus how often he's going to be using Lay Waste and Defile on everything in sight (abilities with virtually no cooldown) and want those to pack more punch through huge AP? A ton less often.
Maxing CDR reduction is great on some characters. I always tried to do it on Morg when I played her, because when her abilities are on CD, she's useless. When I play Mundo, I don't care much about CDR, but a bit is useful. It's all about the character.
(And to answer your questions, Peas, it's additively. If you have 10% CDR, and get an item with 10% CDR, you now have 20% CDR).
There is no flaw in the comparison. Just use your head a little.
The increase in ability spam from 10%CDR to 20%CDR would just be 25% - 11% which is 14%.
30%CDR to 40%CDR is 66.7% - 42.9% which is 23.8%.
Also, no one suggested taking CDR for Karthus.
CDR is a cool stat... yay
What purpose does this serve?
Bottom line: get blue buff whenever you can. Daamage.
CDR has a cap of 40% though, so once you hit that point getting any more is a waste of stats.
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.
The percent increase relative to baseline is not as important as it is relative to the enemy. If I farm up and get a bf sword, and the enemy has 1000 hp, I do 5% more dmg a hit. If I get my second one and he has 1500, I do 7% more a hit. The goal is to farm damage faster than the enemy squishies get health.
Now on some characters, cd does that. Not all characters, though. If I get 20% mundo vs 40%, does it make a difference to cleaver? I don't think so. If you're in a position where you're hitting so many cleavers the extra quarter or half a second or w/e on cooldown is going to show you a significant damage increase, I kind of feel like the other team has lost already. The only thing else that uses cdr is his ult, which is super helpful, but I wouldn't build around being able to pop it more often rather than building around its rate of regen.
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