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/summons an AlphaTheWhite
Working with Chronomancer well-support has made me curious about the exact effects each burst of alacrity I’m granting to allies. Specifically, I’d like to figure out how much I’m reducing their cooldowns.
But that involves numbers. I’m woefully allergic to numbers.
So instead I’ll present this question off to the mathematically-inclined Mesmers out there: Around how much (rounded to the nearest .5) am I reducing the cool down of my allies when I hit them with.
If you could use what a 20s CD would be reduced to as an example, would be much appreciated
Well each second of alacrity you give is 0.66s of CD reduction. That’s as simple as that. For example 1 well reduces your allies CD by 1.3s. Recall (7s) is 4.6s CD reduction. etc…
So during 1s, their CD recharges of 1.66s, hence the number Alpha gave:
1-1/1.66 = 40% CD reduction under perma alacrity.
Alacrity increases your CD recharge by 66%; so, for every second of alacrity, you actually recharge 1.66 seconds worth of cooldown. (I’m going to let you do the rounding yourself, a science background means I get twitchy if I eliminate significant figures.)
1 Well / iAvenger (2s Alacrity)
With 2 seconds of alacrity, you will recharge 3.32 seconds of cooldown, instead of 2.
1.66 * 2 = 3.33
3.32 – 2 = 1.33
“Gained” Cooldown = 1.33 seconds
New Cooldown Time = 20 – 1.33 = 18.67 seconds
2 Wells (4s Alacrity)
0.66 * 4 = 2.67
“Gained” Cooldown = 2.67 seconds
New Cooldown Time = 20 – 2.67 = 17.33 seconds
3 Wells (6s Alacrity)
0.66 * 6 = ~4
“Gained” Cooldown = ~4 seconds
New Cooldown Time = 20 – 3.96 = ~16 seconds
Well of Recall (5s Alacrity)
0.66 * 5 = 3.33
“Gained” Cooldown = 3.33 seconds
New Cooldown Time = 20 – 3.3 = 16.67 seconds
Well of Recall traited (7s Alacrity)
0.66 * 7 = 4.67
“Gained” Cooldown = 4.67 seconds
New Cooldown Time = 20 – 4.62 = 15.33 seconds
4 Wells Without Recall (8s Alacrity)
0.66 * 8 = 5.33
“Gained” Cooldown = 5.33 seconds
New Cooldown Time = 20 – 5.28 = 14.67 seconds
4 Wells With Recall (11-13s Alacrity)
Untraited: 0.66 * 11 = 7.333
Traited: 0.66 * 13 = 8.667
Untraited “Gained” Cooldown = 7.33 seconds
Traited “Gained” Cooldown = 8.67 seconds
New Untraited Cooldown Time = 20 – 7.33 = 12.67 seconds
New Traited Cooldown Time = 20 – 8.67 = 11.33 seconds = 12 seconds, due to Alacrity’s built-in limits
EDIT: Edited for my stupid formatting errors.
EDIT 2: Adjusted my numbers to more closely match in-game testing, rather than the tooltip.
EDIT 3: Changed my final example, to account for Alacrity’s 60% limit.
(edited by AtomsOrSystems.9420)
Gained cool downs below all rounded to the hundredths place.
1. Gained Cooldown = 1.33
2. Gained Cooldown = 2.67
…
…
…
7. Gained Cool down = 7.33 to 8.67 seconds
instead of 7.26 to 8.58
AtomsOrSystems has a rounding error.
You have to use 1 and two thirds (5/3) (or 1.6666666….) instead of 1.66 because they actually use a fraction instead of just the number 1.66
AlphaTheWhite taught me this in another thread.
The results are similar. However, when dealing with large numbers of alacrity, it may drive the results off a bit. The equations used by AtomsOrSystems are the same.
Gained Cooldown = ((5/3) X (Seconds of Alacrity you are under)) – (Seconds of Alacrity you are under)
I made this mistake before. When calculating cool down reduction, if you use 1.66 instead of (5/3), you will calculate a cool down reduction of 39.759% instead of the actual value of 40%
(edited by Xstein.2187)
AtomsOrSystems’ numbers seem to be correct
Gained cool downs below all rounded to the hundredths place.
1. Gained Cooldown = 1.33
2. Gained Cooldown = 2.67
…
…
…
7. Gained Cool down = 7.33 to 8.67 seconds
instead of 7.26 to 8.58
AtomsOrSystems has a rounding error.
You have to use 1 and two thirds (5/3) (or 1.6666666….) instead of 1.66 because they actually use a fraction instead of just the number 1.66
AlphaTheWhite taught me this in another thread.
The results are similar. However, when dealing with large numbers of alacrity, it may drive the results off a bit. The equations used by AtomsOrSystems are the same.Gained Cooldown = ((5/3) X (Seconds of Alacrity you are under)) – (Seconds of Alacrity you are under)
I made this mistake before. When calculating cool down reduction, if you use 1.66 instead of (5/3), you will calculate a cool down reduction of 39.759% instead of the actual value of 40%
I’ll stand corrected, if this is the case.
I was following the tooltip, which says 66%. That comes to 0.66, not 0.66 repeating. However, if some dev clarification or in-game testing shows that it’s actually 0.66 repeating, well… there you go.
Gained cool downs below all rounded to the hundredths place.
1. Gained Cooldown = 1.33
2. Gained Cooldown = 2.67
…
…
…
7. Gained Cool down = 7.33 to 8.67 seconds
instead of 7.26 to 8.58
AtomsOrSystems has a rounding error.
You have to use 1 and two thirds (5/3) (or 1.6666666….) instead of 1.66 because they actually use a fraction instead of just the number 1.66
AlphaTheWhite taught me this in another thread.
The results are similar. However, when dealing with large numbers of alacrity, it may drive the results off a bit. The equations used by AtomsOrSystems are the same.Gained Cooldown = ((5/3) X (Seconds of Alacrity you are under)) – (Seconds of Alacrity you are under)
I made this mistake before. When calculating cool down reduction, if you use 1.66 instead of (5/3), you will calculate a cool down reduction of 39.759% instead of the actual value of 40%
I’ll stand corrected, if this is the case.
I was following the tooltip, which says 66%. That comes to 0.66, not 0.66 repeating. However, if some dev clarification or in-game testing shows that it’s actually 0.66 repeating, well… there you go.
Yeah, the tooltips have a tendency to cut off the whole thing.
The real key is that they designed it based not around the number in the tooltip, but around the concept that 3 seconds of alacrity will get you 2 seconds of recharge. The same thing happens with chill.
And in testing, that appears to be the case (there’s certainly some room for some more precision testing to verify, if you can design a better test).
I usually round to 1.667, as I find that past that, the sig figs don’t have much effect usually (I take more care with ratios).
So.. If I’m understanding this properly:
If I drop 2 wells on a Warrior who just spammed Hundred blades…
…His hundred blades (normally 8s CD) will recharge in… essentially 5 seconds?
Stupid stereotypical writer-brain. This is really not processing in my head for some reason. >_<
Yeah, the tooltips have a tendency to cut off the whole thing.
The real key is that they designed it based not around the number in the tooltip, but around the concept that 3 seconds of alacrity will get you 2 seconds of recharge. The same thing happens with chill.
And in testing, that appears to be the case (there’s certainly some room for some more precision testing to verify, if you can design a better test).
Fair enough, I’m more than happy to take your word on it. That makes sense, I was just adhering a bit too closely to the tooltips.
And in-game testing isn’t usually my wheelhouse, but if I come up with something, I’ll be sure to let you know.
So.. If I’m understanding this properly:
If I drop 2 wells on a Warrior who just spammed Hundred blades…
…His hundred blades (normally 8s CD) will recharge in… essentially 5 seconds?
Stupid stereotypical writer-brain. This is really not processing in my head for some reason. >_<
In about ~5.3 seconds, yeah. Assuming he’s on CD the whole time he has the alacrity.
Basically, for any skill, you can take what I wrote as the “Gained” Cooldown. Subtract that from the normal skill cooldown, and there’s your answer.
Assuming that they’re in CD the whole time they have alacrity, and that the Normal CD is longer than the time they’re in alacrity.
(edited by AtomsOrSystems.9420)
It’s also worth noting the maximum reduction obtainable. With permanent alacrity, your new cd is 60% of the original one.
Fair enough, I’m more than happy to take your word on it. That makes sense, I was just adhering a bit too closely to the tooltips.
Well, at this point I’ve just started assuming that when they say .33 or .66 on anything, they mean 1/3 or 2/3, because that’s the only reason to pick those particular numbers, and the programmers seem fond of exact numbers.
My belief that that’s what they did with alacrity comes from some testing I did right at the start of BWE1, b/c that’s one of the questions I had.
So.. If I’m understanding this properly:
If I drop 2 wells on a Warrior who just spammed Hundred blades…
…His hundred blades (normally 8s CD) will recharge in… essentially 5 seconds?
Stupid stereotypical writer-brain. This is really not processing in my head for some reason. >_<
In about ~5.3 seconds, yeah. Assuming he’s on CD the whole time he has the alacrity.
Basically, for any skill, you can take what I wrote as the “Gained” Cooldown. Subtract that from the normal skill cooldown, and there’s your answer.
^
The generalized formula is::
BaseCooldown – (1 x FinalCooldown) – [(.66 x FinalCooldown) x max(AlacrityTime/FinalCooldown, 1)] = 0
Seems complicated, but intuitively, you’re just taking the original cooldown, subtracting the time that is going to pass (FinalCooldown), and then also subtracting the amount of recharge that alacrity will contribute, and setting that equal to zero.
max(AlacrityTime/FinalCooldown, 1)] means that if you have less alacrity uptime than the final cooldown will be, you need to multiply the alacrity recharge by the uptime percentage.
But if you have enough alacrity to cover the whole period, you just set that ratio to 1, and you get:
BaseCooldown – (1 x FinalCooldown) – (.66 x FinalCooldown) = 0
or
BaseCooldown = 1.66 x FinalCooldown
or
FinalCooldown = BaseCooldown/1.66 = .4 x BaseCooldown
or
1. FinalCooldown = .6 x BaseCooldown
If you already know you do not have enough alacrity to cover the whole cooldown, you can skip the general formula above, and cheat:
2. FinalCooldown = BaseCooldown – AlacrityTime x .66
For example, if you have an 8 second cooldown and only 2s of alacrity, there’s no way you’re going to have enough, so you can just subtract the Alacrity recharge directly.
The simplest way to doublecheck if you have enough alacrity time for 100% alacrity is to remember that with 100% alacrity, you have 40% cdr. So if your alacrity duration isn’t at least 60% of the Base Cooldown, you won’t have 100% alacrity, and you can use the second formula.
(edited by AlphatheWhite.9351)
It’s also worth noting the maximum reduction obtainable. With permanent alacrity, your new cd is 60% of the original one.
This is probably the simplest way to express Alacrity’s benefit, even if it doesn’t perfectly match all real-world situations.
If I have a big hitter skill on a 30s cooldown, then I can potentially reduce that skill’s cooldown to 18s with permanent Alacirty.
4 Wells With Recall (11-13s Alacrity)
Untraited: 0.66 * 11 = 7.333
Traited: 0.66 * 13 = 8.667
Untraited “Gained” Cooldown = 7.33 seconds
Traited “Gained” Cooldown = 8.67 seconds
New Untraited Cooldown Time = 20 – 7.33 = 12.67 seconds
New Traited Cooldown Time = 20 – 8.67 = 11.33 seconds
if u need to wait 13s to get the cd to 11,33s then the actual cd is in between 13s and 11,33s. or do i get that math wrong ?
edit: with alphas math its 8s coz 20×0,4 ..so one of u guys is wrong ?
(edited by MUDse.7623)
4 Wells With Recall (11-13s Alacrity)
Untraited: 0.66 * 11 = 7.333
Traited: 0.66 * 13 = 8.667
Untraited “Gained” Cooldown = 7.33 seconds
Traited “Gained” Cooldown = 8.67 seconds
New Untraited Cooldown Time = 20 – 7.33 = 12.67 seconds
New Traited Cooldown Time = 20 – 8.67 = 11.33 secondsif u need to wait 13s to get the cd to 11,33s then the actual cd is in between 13s and 11,33s. or do i get that math wrong ?
That is exactly why a few people mentioned that you gain 0.66s CD reduction for each second of alacrity BUT you cannot reduce the cooldowns by more than 40%. So for the traited cooldown, the time is actually 12s cooldown, using 12s alacrity which indeed corresponds to 8s cooldown reduction (the extra second of alacrity is wasted on this skill).
oh well i found the mistake in alphas math he said base cd / 1,66 = 0,4 x base cd.
but 1/1.66 ~ 0,6
the extra second is only wasted if u dont use it instantly again
so with well of recall and improved alacrity u already got perm alacrity .. u just need to shatter at least 2 illusions / 12s
oh well i found the mistake in alphas math he said base cd / 1,66 = 0,4 x base cd.
but 1/1.66 ~ 0,6
Edited that, thanks.
(edited by Xyonon.3987)
So.. If I’m understanding this properly:
If I drop 2 wells on a Warrior who just spammed Hundred blades…
…His hundred blades (normally 8s CD) will recharge in… essentially 5 seconds?
Stupid stereotypical writer-brain. This is really not processing in my head for some reason. >_<
Not sure if I’m more intrigued by this discussion or that link. Thanks.
That is exactly why a few people mentioned that you gain 0.66s CD reduction for each second of alacrity BUT you cannot reduce the cooldowns by more than 40%. So for the traited cooldown, the time is actually 12s cooldown, using 12s alacrity which indeed corresponds to 8s cooldown reduction (the extra second of alacrity is wasted on this skill).
Edited to fix, wasn’t accounting for that.
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