Guild Wars 2

As stated in the Chronomancer release, Alacrity is supposed to function as the inverse of chill; with both chill and alacrity on you, skills will recharge at a normal rate. So, lets do some math.

A skill normally recharges at 1 second of skill time per 1 second of real time.

Under the chill condition, a skill will recharge at .66, or 2/3 of a second of skill time per 1 second of real time. This produces the -66% rate shown on the chill tooltip.

The alacrity buff is supposed to be the inverse of chill. Therefore:

Under the alacrity buff, a skill should recharge at 3/2, or 1.5 seconds of skill time per 1 second of real time. This is a +50% rate of recharge, and is the exact inverse of chill.

/endmath

As we’ve all seen, the alacrity tooltip shows +66% rate of recharge. This was obviously generated by someone assuming ‘well, chill is -66%, so the opposite of that must be +66%’. Unfortunately, rates and percents introduce a bit of complexity to the equation, and so that line of logic is incorrect.

The alacrity tooltip should read ‘Increases the rate of skill cooldowns by 50%’.

This leads me to another, potentially more impactful point: Alacrity might be coded wrong. If the person that coded alacrity didn’t understand the math I just went through, they may have simply coded in a 1.66 modifier, thinking that was the proper inverse of chill. If this is the case, alacrity will actually be performing better than they have conceived it to perform.

I think you may be getting confused by the wording, or possibly the wording is mixed up. It isn’t clear whether things are coded multiplicatively as you have assumed.

First, the wiki pages says that “for every 3 seconds chilled, only 1 second of cooldown will have expired” (https://wiki.guildwars2.com/wiki/Chilled). If this is wrong then everything that follows is irrelevant.

If the above is true, this implies skill recharge modifiers are applied additively, for example according to something like the following:

The base rate of recharge is 1 (1 second per 1 second). The actual rate of recharge is given by (1+M), where M is the modifier. Now assuming no chill or alacrity, M=0. Based on the above, I think it’s safe to assume that chill applies -.66 additively to M as follows, if we let MC be the modifier under the effects of chill:

(1+MC)=1-.66=.33, or 1/3. This would match the information on the wiki, giving us 3 seconds under chill to achieve 1 second of recharge.

If the above is true, then the “+66%” language simply means MA, the modifier for alacrity, is .66 and is applied additively as above:

(1+MA)=1+.66=1.66 or 5/3. This means that for every 3 seconds of real time you get 5 seconds of recharge. Moreover if things are coded additively like this, then the chill and alacrity modifiers would be the “opposite” of each other: Under the effects of both your recharge would look like

(1+MC+MA)=1-.66+.66=1.

So, I don’t think it’s clear that there is an error unless you can see exactly how these modifiers are coded and applied (multiplicatively as you have assumed, or additively as above). English is going to be imprecise, and really the only precise statement possible is to just show the equations in the code (would be neat if they would just do that).

MSFone.3026:

First, the wiki pages says that “for every 3 seconds chilled, only 1 second of cooldown will have expired” (https://wiki.guildwars2.com/wiki/Chilled). If this is wrong then everything that follows is irrelevant.

This is wrong, I tested it myself last night.

For 9 seconds real time, a chilled skill recharged for 6 seconds of time.

I’ll just go ahead and update the wiki actually.

Edit: You’re still right about multiplicative vs additive calculations though. However, additive is NOT a % rate, it’s flat. If they want to use % on tooltips, then they need to use it properly.

Even if they calculated it as -.33 seconds per second, and +.33 seconds per second, which would be the additive way of doing it…alacrity is not the rate reversal of chill, it’s simply a flat counter rate.

Fay.2357:

MSFone.3026:

First, the wiki pages says that “for every 3 seconds chilled, only 1 second of cooldown will have expired” (https://wiki.guildwars2.com/wiki/Chilled). If this is wrong then everything that follows is irrelevant.

This is wrong, I tested it myself last night.

For 9 seconds real time, a chilled skill recharged for 6 seconds of time.

I’ll just go ahead and update the wiki actually.

Edit: You’re still right about multiplicative vs additive calculations though. However, additive is NOT a % rate, it’s flat. If they want to use % on tooltips, then they need to use it properly.

Even if they calculated it as -.33 seconds per second, and +.33 seconds per second, which would be the additive way of doing it…alacrity is not the rate reversal of chill, it’s simply a flat counter rate.

They just need to publish what the equations are. Trying to parse English descriptions of mathematical equations, which almost by necessity are always cumbersome and confusing, is a waste of time.

MSFone.3026:

Fay.2357:

MSFone.3026:

First, the wiki pages says that “for every 3 seconds chilled, only 1 second of cooldown will have expired” (https://wiki.guildwars2.com/wiki/Chilled). If this is wrong then everything that follows is irrelevant.

This is wrong, I tested it myself last night.

For 9 seconds real time, a chilled skill recharged for 6 seconds of time.

I’ll just go ahead and update the wiki actually.

Edit: You’re still right about multiplicative vs additive calculations though. However, additive is NOT a % rate, it’s flat. If they want to use % on tooltips, then they need to use it properly.

Even if they calculated it as -.33 seconds per second, and +.33 seconds per second, which would be the additive way of doing it…alacrity is not the rate reversal of chill, it’s simply a flat counter rate.

They just need to publish what the equations are. Trying to parse English descriptions of mathematical equations, which almost by necessity are always cumbersome and confusing, is a waste of time.

Agreed. You can describe mathematical equations in a precise and clear manner with english syntax, but I don’t expect video game developers to have the knowledge and understanding to be able to do that. Publishing the equations would be the best way.

I tested it now with a guildie. But let’s first look again at the wording of chill:

Movement speed decreased by 66%; skill cooldown increased by 66%; stacks duration.

What they mean is (CD always refers to skill cool down):
The time required to recharge the CD under chill is increased by 66%.
This results in 1.66…s (166% of 1s ) that is required to recharge CD by 1s.

I tested it. First I confirmed that the unchilled CD of Chaos Storm is in synch with the timer of my video editing program (adobe premiere 2.0). Then I measured the time it took to recharge one second of chilled Chaos Storm CD with the time indicator of the editing program. And it varied between 1.66 and 1.67 seconds. So I am fairly sure it was actually 5/3s or 1.66…s (166% of 1s ).

That means in return that within 1s of ingame time a chilled CD is recharged only by 0.6s (1/[1+1*2/3]).

EDIT:
So under alacrity, if I understand it right (and that chill and alacrity neutralize each other), the time to recharge CD by 1s would be only 1/3s of ingame time. In turn this means that after 1s of ingame time a CD had been recharged by 3s (1/[1-1*2/3]).

If both effects (chill + alacrity) are applied, the time to recharge the CD would be the same as if none of the effects would apply (t/[t+t*2/3-t*2/3]).

This would explain the “balance” of Well of Recall, which applies 1s of Alacrity (friendly) and 5s of Chill (hostile). Because in 1s of Alacrity you recharge 3s of CD, and under 5s of Chill you also recharge only 3s CD. However, if the enemy manages to transfer that Chill back on you, the Chill would be stronger for it’s longer duration. Because for 1s (both effects applied) they would neutralize each other (t/[t+t*2/3-t*2/3]). The rest of the time (4s) you would suffer only from chill.

IMO the tooltips are correct, you can do the recount of this using the growth formula http://pages.uoregon.edu/rgp/PPPM613/class8a.htm

so for instance 8 seconds of chill increases skill cooldowns the same amount as alacrity decreases it.

Here’s why:

Alacrity for 8 seconds: 8 x (-0.66%) = 2.72s (or rather 8 × 0.34)

recount using growth rate formula:
[present - past/past x 100 = growth/degrowth rate]
2.72-8/ 8 x 100 = -66(%)
This means that alacrity reduced the skill cooldown by (8-2.72) = 5.28 seconds

Now 8 seconds of chill:
8 × 1.66 = 13.28

recount
13.28-8 /8 x100 = +66 (%)
This means that chill increased the skill cooldown by (13.28-8) = 5.28 seconds

the result is 5.28 decrease and increase in both cases so alacrity and chill do in fact cancel each other out.

@Smirgel:
At least for chill I can tell you that you are wrong. According to my measurements, under chill, a skill recharged 0,6 time the normal rate. This is caused by the effect, that chill increases the time, a skill will be recharged by 66%. So instead of a rate of ‘1s skill recharge per 1s game time’ it is under chill ‘1s of skill recharge per 1.67s of game time’.

Under chill a skill would recharge only 3s within 5s of game time. In your example with 8s game time under chill, a skill would actually only recharge only 4.8s.

Assuming that Alacrity will neutralize chill, there are 2 ways that could happen:

• Either Alacrity works exactly the opposite to chill, meaning it would lower the interval, in which 1s of skill cool down is recharged to only 1/3 of a second.
  In this case 1s under Alacrity will already recharge 3s of skill cool down. Within 8s it would recharge 24s of skill cool down.
• Or the effect works at the recharge rate level. This would mean that instead of a recharge rate of 1s skill cool down per second, Alacrity would speed it up to 1.67s skill cool down per second. In this case a skill under alacrity would recharge within 1s 1.67s within 8s 13,33s. (this method works in the case of chill-alacrity-neutralization only for a single second and would require iterative calculations each second)

Given that Well of Recall applies 1s of alacrity and 5s of chill, I guess it will work like the 1st variation. Because this would in both cases result in a 3s skill cool down:

• Chill: Within 5s of chill a skill would only recharge 3s of cool down.
• Alacrity: Within 1s of Alacrity a skill would already recharge 3s of cool down.

If the 2nd variation is applied it would look like this:

• Chill: Within 5s of chill a skill would only recharge 3s of cool down.
• Alacrity: Within 1s of Alacrity a skill would already recharge 1.67s of cool down.

TyPin.9860:

I tested it now with a guildie. But let’s first look again at the wording of chill:

Movement speed decreased by 66%; skill cooldown increased by 66%; stacks duration.

What they mean is (CD always refers to skill cool down):
The time required to recharge the CD under chill is increased by 66%.
This results in 1.66…s (166% of 1s ) that is required to recharge CD by 1s.

I tested it. First I confirmed that the unchilled CD of Chaos Storm is in synch with the timer of my video editing program (adobe premiere 2.0). Then I measured the time it took to recharge one second of chilled Chaos Storm CD with the time indicator of the editing program. And it varied between 1.66 and 1.67 seconds. So I am fairly sure it was actually 5/3s or 1.66…s (166% of 1s ).

That means in return that within 1s of ingame time a chilled CD is recharged only by 0.6s (1/[1+1*2/3]).

Interesting. My test was not done using video capture, but just with a stopwatch, so your results fall well within my margin of error. So the 66% comes from the increase of real time units necessary to recharge a unit of skill time.

TyPin.9860:

EDIT:
So under alacrity, if I understand it right (and that chill and alacrity neutralize each other), the time to recharge CD by 1s would be only 1/3s of ingame time. In turn this means that after 1s of ingame time a CD had been recharged by 3s (1/[1-1*2/3]).

If both effects (chill + alacrity) are applied, the time to recharge the CD would be the same as if none of the effects would apply (t/[t+t*2/3-t*2/3]).

No, this definitely isn’t right. Using that formula, alacrity would be causing skills to recharge at 3 times the normal rate. Watch the video, that’s obviously not the case. So the formula of (t/[t+t*2/3-t*2/3]) is definitely the wrong way to do the comparison.

So lets just straighten a couple things out, that way we can do some sanity checks on this math. Roughly speaking, chill increases how long it’ll take for a skill to recharge by about a third. Also roughly speaking, alacrity decreases how long it’ll take a skill to recharge by about a third. If your math isn’t sticking to those general bounds, then it’s wrong.

My math cannot be wrong. I don’t make mistakes^^

Well, I’ll check the video then more closely and will come back to you

EDIT: I am downloading the video now to check in my editing program. But looking at the video, the alacrity effect is pretty huge. Just by looking at it, it could well be 3s recharge in 1s… but I will measure it more closely.

Why are we assuming that it was programmed with an equation in the first place?

There are only 4 possible cases (chill + alacrity, chill, alacrity, none) and 3 distinct results.

The 66% must refer to something. We are only trying to figure out to what.

EDIT: Ofc the neutreulization could be coded without an actual equation. It could just say:
if chill + alacrity applied —> CD normal

However, I still wanna know, how alacrity actually works^^

TyPin.9860:

The 66% must refer to something. We are only trying to figure out to what.

EDIT: Ofc the neutreulization could be coded without an actual equation. It could just say:
if chill + alacrity applied —> CD normal

However, I still wanna know, how alacrity actually works^^

Regarding what Robert stated on the livestream https://youtu.be/71Ls5bjLFBk?t=5m , which paraphrased was, “if you have chill for 3s you gain 1s of recharge; if you have alacrity for 3s you lose 1s of recharge (my math may not be 100% correct)”
(According to your earlier calculations, the extra 1s of recharge is closer to 1.2s)

I find it a little misleading to refer to alacrity as “inverse chill” rather than “negative chill” when you compare it to Robert’s statements.

It seems the general forumla should be:
Boolean IsChilled // (1 or 0)
Boolean IsAlacrity

Recharge = BaseRecharge + (ChillFactor * BaseRecharge* IsChilled) – (ChillFactor * BaseRecharge * IsAlacrity)

Hmm you might be right math-wise. Those percentages seem to convert weirdly in practice though.

What kind of data do you have on chill? From my super-quick, non scientific observations, I’d imagined it was like this:
Chill: .66s recharge per 1s “real life” time.
I’d assumed Alacrity would be:
Alacrity: 1.33s recharge per 1s “real life” time.

When you have both- normal. I think you describe this above as “additive”.

Though mathematically correct, as 1.50 recharge per 1s “real life” time feels crazy large. You could be right though! I’m definitely hoping to see some more info/data.

The things I’m hoping we find out during testing are:
- What’s the ‘true’ recharge time reduction of Alacrity?
- What percentage Alacrity up-time can the various mesmer builds expect (50%? 25%? 100%?)
- What percentage up-time to allies can the various mesmer builds provide (10% up-time? 25%? 50%?)

Assuming a 50% up-time on Alacrity, which may be on the high end, and assuming a “1.33s recharged per 1s real time”… it’s still a pretty impressive buff, working out to something like 16-17% cooldown reduction on all our skills. For those worrying that the OH weapon would mean we’d have “fewer buttons to push”… a reduction like that will bring a LOT more activity to the profession, not even counting Continuum Split.

Okay, I had some issues with my software.

But it seems that recharging one second of CD under alacrity takes 0.6s game time (it was actually 0.611…s, but I think there was an issue with some frames; A confirmation of those numbers wouldn’t hurt). This results in a 1.67s CD recharge per 1s game time.

So let’s summarize, based on my measurements:

Chill:
“Movement speed decreased by 66%; skill cooldown increased by 66%; stacks duration.”
Increases skill cool down by 66%. It takes 1.67s game time to recharge 1s of skill cool down. Within 1s of game time a skill cool down recharges 0.6s. The tool tip would be correct here.

After 3s under chill a skill cool down will have recharged only 1.8s (1.2s recharge loss).

Alacrity:
“66% skill recharge rate”
Increases the recharge rate ([skill recharge]/[game time]) by 66%. Within 1s of game time a skill cool down recharges 1,67s. It takes 0.6s game time to recharge 1s of skill cool down. The tool tip would not be correct in this case.

After 3s under Alacrity a skill cool down will have already recharged 5s (2.0s recharge win).

However, they could simply change the system a bit in GW2. In this case all my measurements were for nothing^^
If those numbers are correct though, both effects are not mirrored. While chill changes skill cool down by 66%, Alacrity changes the recharge rate rate by 66%, resulting in different win/loss numbers.

To achieve same win/loss numbers and to simply:
Chill: reduce recharge rate ([skill recharge]/[game time]) by 40% (same effect as CD increase of 66%) —> skill recharges 0.6s per 1s game time
Alacrity: increase recharge rate rate([skill recharge]/[game time]) by 40% (different effect as explained above. It equals approx a 28.6% CD decrease) —> skill recharges 1.4s per 1s game time.

With this change the win loss would be the same for the same time of applied effect (for 3s effect 1.2s).

TyPin.9860:

To achieve same win/loss numbers and to simply:
Chill: reduce recharge rate ([skill recharge]/[game time]) by 40% (same effect as CD increase of 66%) —> skill recharges 0.6s per 1s game time
Alacrity: increase recharge rate rate([skill recharge]/[game time]) by 40% (different effect as explained above. It equals approx a 28.6% CD decrease) --> skill recharges 1.4s per 1s game time.

With this change the win loss would be the same for the same time of applied effect (for 3s effect 1.2s).

I think this is probably what the devs are envisioning as how they want the skills to act. Were you able to figure out what alacrity does by counting frames on the blog post?

Fay.2357:

Were you able to figure out what alacrity does by counting frames on the blog post?

Yes, a bit like that. I actually downloaded the video from the PoI. So I could use video editing to figure it out.

TyPin.9860:

Chill: Increases skill cool down by 66%

Alacrity: Increases the recharge rate ([skill recharge]/[game time]) by 66%.

I arrived at the same conclusions while trying to visualize this (I’m bad at math but visualizing problems helps me understand).

Doesn’t chill make your skills recharge at 33% of the normal rate? So like 100% – 66%? Isnt the opposite of that 100% + 66% = 166%?

Eodwen.2613:

Doesn’t chill make your skills recharge at 33% of the normal rate? So like 100% – 66%? Isnt the opposite of that 100% + 66% = 166%?

No, it doesn’t. Take a look at some of the other posts in this thread for how it actually works.

So CD is counted backwards as you need to deplete the time to use it again. So lets say you have 30 sec cd. Lets take the first second under the effect of chill 30 -1+(1*66/100)=29.66 s . Isolating the chill effect would be -1s +(1s *66/100)= -0.34 s. So in fact instead of reducing cd for one second it only depletes it by 0.34s thus recharging at 33% rate or 66% slower.

Alarcity would be 30s-1s-(1s*66/100)= 28.34 isolating this would be -1s-(1s*66/100)= -1.66s sp 166% rate or 66% faster. I don’t see any problems with this tbh.

@Eodwen
Your calculation is only correct for alacrity. Because the 66% of the alacrity effect directly refers to the recharge rate (even if the wording is insufficient). However, the 66% of chill refer to the actual cool down. As I have measured and explained above. After 1s under chill, the skill would have recharged exactly 0.6s (1s recharges within 1,67s of game time), leaving a cool down of 29.4s, not 29.66s.

I see so the wording hints for 0.34s increase. But in actual testing is the increase 0.34s or 0.66s ? If its the later then chill is the opposite of alarcity and the tooltip should be updated.

In testing under chill it takes 1,67s to recharge 1s of skill cool down. So the cool down, not the recharge rate, increases by 66%. If for the whole time of skill recharge chill was effective, it would take for the skill 66% more time to recharge. Chill, so to speak, stretches the ‘way to go’, while alacrity makes you ‘go the way’ faster.

Just realizing, depending on the implementation of alacrity, it might be more profitable to not counter a chill with alacrity (if such a situation occurs), but to wait until chill is over. When both effects are active, most like they will be ‘added’ together multiplicative. That would neutralize both effects. If that happens, it would be best to trigger alacrity later, because if just one effect is active, it may be that the alacrity bonus is more, than the loss through chill.

I will do some close testing once HoT hits^^