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Math! About Haste!

December 3, 2009

First, I couldn’t have done this without the post on Planet of the Hats regarding Crit vs Haste.  All my math assumes numbers posted in that article.

So, the overall goal was to figure out what was the initial point at which haste becomes less of a priority in terms of gearing.  Now, I went ahead and made the assumption that you’d be dropping Wrath of Air for an added 5% spell haste.  In raw haste, that gives you:

5 = Amount of Haste / 32.78998947

Do your math:

5 * 32.78998947 = Amount of Haste

And you get 163.9499 additional spell haste.  That’s not an insubstantial amount, but remember that these numbers assume that buff is present.

Edit: While the section above here is good… my understanding at the time this was initially authored was limited.  It has since changed… so the number above is kind of useless.  Please, just ignore it.

The overall goal is to fit 5 lightning bolts into a single cooldown of Lava Burst, which is 8 seconds.  Alternatively, I also wanted to know if I could throw in a couple of Chain Lightnings… but that may actually be a DPS loss.  I’m going to figure out the numbers on that in a little while.

So, the first step was to figure out the cast times of the different spells once haste was factored in.  Thankfully, these numbers and formulae exist in the post I referenced above.

Hasted Casting Time = Base Cast Time [inc. talents] /( (1+ Haste % /100) * (1+ Haste Effect % / 100) )

There you go.  Now, since I added in haste a different way, we need to alter his formula a bit.  Edit: This formula is wrong.  Wrongy wrong wrong.

Hasted Casting Time = Base Cast Time [inc. talents] /[ (1+ ({Raw Haste + 164} / 32.78998947) /100) ]

Or (with some numbers) if we assume our haste value is 500.

1.663222 = 2 / ( 1 + (663.9499474 / 32.79) / 100)

Edit: Based on comments from Charles @ Planet of the Hats left (you can see them below!), I need to add in my Percentage buffs multiplicatively.

1.6527 = 2 / ( 1 + [ (500 / 32.7989) / 100 ] * ( 1 + 5 / 100 ) )

That would be your Lightning Bolt cast time with haste accounted for.  So, we want to know how many LB’s we can fit into a LvB cooldown of 8 seconds.  We do:

8 = X * 1.663222 1.6527

With our math:

X = 8 / 1.663222 1.6527

Which is 4.809941 4.84.  So, roughly 4 casts, which is 6.652887 6.61 seconds.  If we go ahead and cast that 5th, we’ll spend 8.316109 8.2637 seconds casting.  Now, this isn’t bad, because it will go ahead and allow you to queue the LvB with the server at the end of the cast of the last LB.  Alternatively, you could throw out a Chain Lightning, but then you’d still be waiting a fraction of a second for LvB to come off CD (In the event you want to know, the cast time of CL/LvB @ 500 Haste with Wrath of Air is 1.247416 1.2396 seconds.  That means that if you do a rotation with 4 LBs and 1 CL, you’d be casting a sum total of 7.900303 7.8505 seconds.).

I hope this helps anyone that needs it…

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6 Comments
  1. Glad you found my post helpful, but I must admit that I nabbed all the maths-y stuff from WoWwiki and Elitist Jerks threads. I’m not really a maths person myself. Writing the spreadsheet is what really helped me get a grasp of it all.

    So just to totally rain on your parade (sorry 😦 ), haste effects stack multiplicatively with haste from gear. So you can’t really simplify a haste effect into the amount of equivalent rating it provides and then simply add it onto your existing rating. If you have haste rating giving A% haste and external haste %age buffs B and C, the total haste is:
    (1+A)*(1+B)*(1+C) = total haste %age

    So rather than adding together the equivalent ratings, you’d work out your haste total in two steps. First, find your haste percentage from haste rating as Rating / 32.79, then divide that by 100 to give you a decimal percentage and add one to it (because you’re casting 100% of normal spells plus the extra percentage from haste). Then multiply the resulting number by one plus your first haste buff (e.g. Wrath of Air). Then multiply that by one plus your second haste buff, and so forth. For your numbers above this gives (1+500/32.79/100)*(1+0.05)=1.21, which is 21% haste.

    Then following your math with that figure it’d be:
    LB cast time = 2/1.21 = 1.65 seconds
    8/1.65 = 4.84
    The numbers don’t end up being that different really.

    I enjoy reading your blog, by the way 🙂

    • It’s not raining on a parade, I promise! 😉

      So, I have to ask, every single effect is added to every other effect? So if there’s a third percentage, you add it on top of your gear number and the percent that follows?

  2. Yep. All haste rating – which comes from normal gear, relics or trinket procs – adds up, like you would expect, into one big lump o’ rating which constitutes the first “haste effect”. So for example if you have 460 haste on your gear with Totem of Electrifying Wind and Scale of Fates proccing at once, then you just add up all the ratings (460+200+432) into that big lump. For the numbers I just gave that’d be about 33.3% haste.

    Then all subsequent buffs are included multiplicatively. So let’s say you have Wrath of Air Totem (5%), Improved Moonkin Form (3%), the troll Berserking racial (20%) and Bloodlust (30%) all at once. You’d figure out the total haste as:
    (1+ HasteFromRating) * (1+ WoA) * (1 + IMF) * (1 + Berserking) * (1 + Bloodlust)
    or
    (1.333) * (1.05) * (1.03) * (1.2) * (1.3) = 2.24 (that’s 124% haste!)
    And if the same player in patch 3.3 decided (foolishly, since we don’t benefit from haste beyond 100%) to use Elemental Mastery at the same time, it’d be
    (1.333) * (1.05) * (1.03) * (1.2) * (1.3) * (1.15) = 2.58 (158% haste!)

    And so on.

    (Incidentally by that point LB would be taking only 0.78 seconds to cast, but we’d be prevented from casting any more spells until the global cooldown’s hard-cap (which is 1 second) completed. That’s why people talk about 100% as being elemental’s “haste soft cap”.)

    • Ok, so I think I’m starting to get a handle on this. I’m going to update the post to reflect the changes to the math, but before I do, I want to make sure I understand.

      Anything that gives you a Haste Rating buff goes into the HasteFromRating part of the formula (like you said, the Electrifying Winds totem, etc.), and then anything that adds a X% Haste buff is added in after you’ve done your work with the Haste Rating? (Even if it increases it past 100%.)

      Doesn’t that make the effectiveness of some of the %age buffs decrease as more of them are present?

      • To the first question, yes – just make sure that all the Haste % buffs are added multiplicatively (A*B*C*D).

        As to the second – well, it depends. All things being equal, using haste effects together is the same as using them one after the other. So over a 55 second period, it’s just as much DPS to use Bloodlust for 40 seconds then 3.3’s EM for 15 seconds as it is to use Bloodlust+EM for 15 seconds, then just Bloodlust for the remaining 25 seconds, then have no haste effect active for the final 15 seconds.

        The benefit of using haste effects together is that you can use other temporary effects at the same time, and the extra haste boosts the benefit of those effects – such as DPS potions, on-use trinkets, and so on. Obviously the more spells you can cast during the limited period these effects are active the better!

        If, however, using haste effects together leaves you with over 100% haste, you start to lose some of the benefit of the extra haste till you reach a point where it’s better to stagger the haste effects one after the other than it is to use them together. This is because the extra benefit you get from the staggered haste effects (where during each effect your spells are not GCD-capped) exceeds the benefit of extra haste for the other buffs you were stacking with your haste effects.

        I hope that makes sense…

        (100% is just the haste “soft cap” for elementals because of our 2-second primary nuke and the 1-second GCD cap. Different classes/specs have different points at which haste reduces in usefulness.)

      • It makes sense. You were perfectly clear. I just wanted to make sure that I understood it correctly. This whole endeavor was just out of my curiosity regarding itemisation.

        I wanted to have a good grasp of the point to which I needed to prioritize haste to start with. My baseline was LB in the LvB cooldown. I was going to try to go for the scenario that was simplest (IE, just me), because I want to avoid using raid synergy as I can.

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