Wednesday, May 20, 2009

The GCD

Patch: 3.1.2

Building upon my previous post regarding the 3.1 Nature's Grace, I wanted to look into the 1-second GCD limit and figure out at what spell-haste rating it would come into effect for caster druids.

EDIT 3/21/10: 3.3 Resto druid GotEM changes are in a new post, found here. All moonkin stuff in this post should still be current.


Base Hasted GCD limit:

Ignoring both Nature's Grace and Gift of the Earth Mother (as well as any other raid buffs or potions), it will take 1639.5 haste rating at level 80 to reach the 1-second GCD limit (which is 50% spell haste). The conversion from haste rating to % at level 80 is 32.79 %/rating.

Base Formula:
HastedCastTime = BaseCastTime /(1 + (% SpellHaste / 100))

1639 haste rating / 32.79 = 49.98% Spell haste at level 80
HastedGCD = 1.5s /(1 + (49.98 / 100)) = 1.00013 seconds


Going from 1639 to 1640 haste rating will push you to a 0.9999 second GCD (at level 80), just below the hard-set 1-second limit; thus, 1639 haste rating is as close as you can get to a 50% spell haste unbuffed by procs/talents/potions/abilities/etc. You are extremely unlikely to see this raw amount of haste rating on your gear in the current game, and if you do, you are probably severely gimped in all other stats. Do not try to get that much haste rating.

I repeat: do not try to stack haste on your gear to reach that 1639/40 limit. There are many raid buffs and talents in the game that will boost your haste for you, instead.



Other Haste-effecting Procs, Buffs, and Talents:
Raid-wide buff spells do not stack with each other if they provide the same buff. Thus, the haste from imp. moonkin aura will not stack with the haste from imp. ret auras (the other parts of the moonkin/ret auras still work, like the spell crit), and Bloodlust/Heroism does not stack with Power Infusion. There are 3 distinct raid-buff categories here, in which the buffs do not stack within their category:
  • Bloodlust/Heroism and Power Infusion
  • Imp Moonkin Aura and Imp Ret Aura
  • Wrath of Air totem
The distinction for Wrath of Air is that it is a generic haste increase, while Imp Moonkin and Imp Ret specifically say "spell haste." Why they decided to do this, I don't know, but if it's stacking the aura with the totem, should we really argue? ;)



Notes on Haste Math:

My assumption is that each of these buffs will also reduce the GCD, proportionally. Note that when it comes to calculating hasted cast times, whether you apply a 3% haste bonus or a 20% bonus first does not alter the outcome of your cooldown time. Haste will also stack multiplicatively (crit, on the other hand, stacks additively).

3% first:
1) 1.5s -(1.5*0.03) = 1.455 seconds
2) 1.455s - (1.455*0.2) = 1.164 seconds
20% first:
1) 1.5s -(1.5*0.2) = 1.2 seconds
2) 1.2s - (1.2*0.03) = 1.164 seconds

HOWEVER, if you have any talent that reduces a cooldown/cast-time by a set amount rather than a percentage (ie -0.5 seconds), it MUST be taken into account first before applying any percent reductions, including haste from gear.



Moonkin vs Resto GCDs:

The following charts assume that:
  • Celestial Focus and GotEM will stack with raid buffs.
  • Moonkin will have both Celestial Focus and Imp Moonkin Aura.
  • Resto druids will either have 0 points in GotEM, or 4 points, or 5 points.
  • GotEM will only reduce the GCD of Lifebloom, Rejuv, and Wild Growth.
  • Raids may or may not have a WoA totem
  • Resto druids' raids may or may not have a moonkin or ret pally.
  • Wrath of Air totem (edit) stacks with Moonkin or Ret pally talented auras.
  • Moonkin and Ret haste auras will not stack.
  • Bloodlust will stack with all other raid buffs (excluding Power Infusion).
  • All haste buffs and talents will affect the GCD.


NOTE: The GotEM haste variable in these resto tables is no longer accurate.
For updated resto druid tables, go here.



So what does all of this mean?

Any time a line in the graphs above dips below 1 second (the heavy red line), the GCD is at its 1-second limit. The GCD can never be less than 1 second, no matter what kind of spell haste or buffs you have! This is a hard limit put in place by the game's developers and designers.

The haste that you have on your gear, as well as buffs and talents, will push the 1.5 second baseline GCD closer and closer to this 1 second limit, as shown above. What buffs and talents you have will impact how much haste is needed to reach this 1-second GCD limit, and may impact your choices in what talents you take (such as how many points in Gift of the Earth Mother) and how much haste you put on your gear as a insta-casting-fiend of a resto druid.

Bloodlust:
In most all cases, getting Bloodlusted will reduce your GCD to its 1-second minimum. The few cases that it does not are when you have low haste rating on your gear, have no moonkin/ret pally/WoA totem, and are not using a spell that has been reduced by GotEM.

GotEM:
Remember that this talent will only reduce the GCD of lifebloom, rejuv, and Wild Growth. Spells such as remove curse, abolish poison, and Nature's Grasp will not be affected by GotEM. However, in regards to GotEM: the higher your haste rating, the fewer points in it you will need to reach the base of a 1-second GCD.

To reach a GCD of 1.0 seconds with GotEM (rough estimate):
  • On average with only a WoA totem, each 150 points of haste rating beyond 500 will reduce the number of points you need to spend in GotEM by 1.
  • On average with only a ret pally or moonkin aura, each 150 points of haste rating beyond 550 will reduce the number of points you need to spend in GotEM by 1.
For a more accurate assessment, I am reminded to link over to Phaelia's calculator at resto4life!

Take into account your trinket use, potion use, and Nature's Grace procs as applicable.

Nature's Grace:
This talent will reduce much more than just your GCD, but my focus in this study is looking only at its impact on the GCD (which has particular importance with instant-cast spells). Proccing it in combination with GotEM will assuredly reduce your GCD to the 1-second limit, even if you have but 4 points in it and low haste rating. For other insta-cast spells such as Abolish Poison, you cannot count on GotEM to contribute, but the cooldown will still be lowered significantly by the NG proc. NG itself has the same % GCD reduction as a fully-talented GotEM, and though it is proc-based, it will effect all of your spells.

For turkeys, this talent is pretty much a necessity, and should be factored in on any haste calculations. Graylo at Gray Matter has a great post about the "soft haste cap" for moonkin, assuming Nature's Grace.



TL:DR!

In summary, you have a 1.5 second base global cooldown (GCD), and it can be lowered down to a minimum of 1 second by haste rating and talents and raid buffs. Depending on your expected raid buffs and talents, you can determine what sort of haste rating is "overkill" for your GCD, since it would always push against the 1-second minimum cap.

Why is this important? For any spell that takes longer to cast than your GCD, it's not! (Such as Starfire, regrowth, etc). But, if you're casting lots of insta-casts or quick spells such as nourish, wrath, or talented+glyphed HTs, the GCD is a big deal, because it is often your true limit to your cast time. If you over-stack on haste without accounting for talents and raid buffs, then you're wasting stats on your gear.

The exact makeup of your raids, spec, and spell rotations will determine your "soft cap" for haste for your GCD. You can browse through the charts to see what best applies to you (where the heavy red line is the 1-second cap), and look at the haste rating on the x-axis from there.

  • Always remember that while haste may be worthless beyond a certain point for you for your GCD, it can still affect other spells you cast, if they take longer than a base of 1.5 seconds to cast. Your use of these longer-cast spells will in turn affect your overall soft haste cap, depending on your spec, class, raid makeup, and healing style/turkey tactics.



~ As always, I have an ear open for comments on the math and any buffs or druid caster talents I may have missed or misinterpreted!

As a random note, I myself run about 320 haste rating with 4 pts in GotEM and full Nature's Grace. This doesn't put me at the 1-second cap, but meh :) ~

12 comments:

Anonymous said...

Nice math. Unfortunately WoA totem and the minor haste auras stack multiplicatively

Kae said...

Most sites, blogs, and EJ forums have stated that Wrath of Air haste does not stack with the paladin/moonkin +haste auras. The haste from the moonkin and ret pally auras themselves do not stack, either.

It is in this same way that the +healing buff from tree form does not stack with the +healing buff from prot pallies' improved devo aura.

Aertimus said...

This is the most perfectly timed post for me (I've been needing to get my haste shit together) and one of the most helpful ones I have read in a very very long time. The math and the graphs are beautiful, well explained, and easy to follow.

Thank you, thank you, thank you, thank you!

Leslie said...

Sweet post. Great to read up on as a tree drood who didn't know the real deal about spell haste.

Thanks! :)

fallingleavesandwings said...

Great post Kae!

I have been toying around with changing up my spec a bit to put 14 points into balance, but I am still undecided on if I want to do it =)

Kae said...

Hehe, I installed Power Auras recently and have it popping up a flashy, glowy icon on my screen when NG procs, to help me know when I have faster GCDs/cast times. I really wish it lasted longer for restos, though I know that would make it waaaay OP for moonkin :D

Anonymous said...

To reiterate, WoA totem and minor haste auras stack.

http://www.resto4life.com/2009/02/06/gift-of-the-nerfmother/
http://elitistjerks.com/f73/t40221-resto_pve_healing_discussion/p11/#post1079687

This is why the haste softcap with 5/5 GotEM is 359, not 468

Kae said...

Hmm... well, learn something new every day :) By your original comment, though, you seemed to be argueing that ret aura and moonkin haste auras would stack as well, which I *know* to be false, as Blizz has grouped them in the same buff category.... and that threw me off.

I find it odd that Blizzard would be so specific about buffs not stacking, but would allow for something so small a difference as generic haste vs spell haste to stack. *shrug*

Will see about updating the moonkin graph later to account for WoA + the built-in aura. Thanks!


(There are others out there that have insisted that they do not stack, btw... it seems they have misguided me!)

Anonymous said...

NP, I do appreciate the math and look forward to reading the revisions.

wowenomics said...

Really nice calculation and graphing. Well done.

Anonymous said...

elitistjerk:
Wrath of Air and Improved Moonkin Aura/Swift Retribution Aura
0/5 GotE = ~38.7% Haste = ~1269 Haste Rating
1/5 GotE = ~30.8% Haste = ~1010 Haste Rating
2/5 GotE = ~23.8% Haste = ~781 Haste Rating
3/5 GotE = ~17.5% Haste = ~574 Haste Rating
4/5 GotE = ~11.9% Haste = ~391 Haste Rating
5/5 GotE = ~6.7% Haste = ~220 Haste Rating

Kae said...

Anonymous,

Those numbers you pasted are from before the mechanic change to GotEM, when the talent shaved off an exact amount of time from the GCD, rather than applying haste %. You can see those same numbers being "fixed" for the talent mechanic change here:

http://elitistjerks.com/f73/t40221-resto_pve_healing_discussion/p11/#post1079250