Friday, July 27, 2012

HoT/DoT Breakpoints and Haste Mechanics

Picture unrelated. Just pretend she's
a math angel, here to bring you math.
Time for some meaty math! With a new expansion looming, it's hard to write any theorycraft posts that will be of use to people by the time the expansion actually launches. So, I'm writing about something a little bit more abstract: haste breakpoints. What are they, how can we calculate them, and do they matter? I'll answer all of that in this post.

So, some of my readers may be wondering what a haste breakpoint even is. Simply put, it's the amount of haste at which a periodic effect gains an additional tick. Nearly every periodic effect in the game can gain additional ticks in this way, from simple HoTs and DoTs, to channeled spells like Divine Hymn. Notably, Mind Flay and Mind Sear do not gain ticks ever. Once upon a time, during the Cataclysm beta, both spells gained ticks, just like normal DoTs, but people complained that their Mind Flay felt like it took too long to cast. So Blizzard made an exception for them. This seems to be standard for all channeled DPS spells, but not channeled healing spells.

We can find the amount of haste needed to reach each breakpoint by taking the "base" number of ticks, and finding its inverse. So, for Vampiric Touch, with 5 base ticks, we need 1/5 = 0.2, or 20% haste for each "bonus" tick. However, the first bonus tick takes only half as much haste. So VT gains extra ticks at 10%, 30%, 50%, 70%, and so on. Similarly, if we're under a -haste debuff, like Curse of Tongues, we can lose ticks at -10%, -30%, and so on. Notably, at -90% haste, VT should not tick at all. If anyone can construct such a situation, I would be interested to know how the game handles that.

  • Vampiric Touch - 5 base ticks, +1 at 10%, +1 each 20% thereafter.
  • Shadow Word: Pain - 6 base ticks, +1 at 8.33%, +1 each 16.66% thereafter.
  • Devouring Plague - 8 base ticks, +1 at 6.25%, +1 each 12.5% thereafter.
  • Improved Devouring Plague - As the talent description, but uses only haste rating when determining the number of ticks to use for calculating damage, not buffs like Heroism.

A side note on haste buffs and debuffs: effects worded as "increases casting time by X%" actually grant -100(1-1/(1+X))% haste. So, Curse of Tongues is a -23% haste debuff, not -30%. Similarly, anything worded as "reduces casting time by X%" actually gives -100(1-1/(1-X))% haste. I can't think of an example though, nearly everything that worked that way was removed in Cataclysm.

New haste buffs tend to say "increases spell casting speed by X%". They're not simple either. They grant 100((X*bH)+X)% haste, where bH refers to your "base haste", meaning your haste without the buff. So Heroism gives 30% haste if you had 0% haste to begin with, and 39% haste if you had 30% haste to start with, and so on. You can think of this as Heroism acting as a multiplier for your existing haste rating on top of its obvious effects. Darkness, Mind Quickening, and Power Infusion all work this way too. If you look the buff up on Wowhead, it will say "Mod Haste %" instead of "Mod Rating (917504)" if it works as a multiplier.

So does any of this matter? I mean, you add 1 haste rating, changing to 30% haste up from 29.9%, your VT still ticks at almost exactly the same rate, and as long as you never let it fall off either way (you don't, right?) it doesn't contribute noticeably more damage.

The main thing you gain from reaching a haste breakpoint, is that your DoT now lasts noticeably longer. In this example, it goes from 13.86 seconds to 16.15, making it last 2.3 seconds longer. This does add a large chunk of DPS (at least, large for a single point of haste rating) in the form of more time for Mind Flay. Over the course of a 6 minute boss fight, you would cast VT 25 times at 29.9% haste, or 21 times at 30% haste, saving you 4 GCDs, or 2 Mind Flays, adding about 200 DPS over the 6 minute fight. Imagine if we always gained that much from a single point of haste rating! I'd be dealing 400k DPS easily.

Seriously though, these breakpoints are small enough and rare enough that they don't play a huge role in our DPS or determining out stat weights on "normal" fights. They become supremely important if we can't always keep our DoTs up all the time, such as when we're multi-DoTing, being CC'd, fighting targets that move out of range, or using a DoT that has a cooldown or another reason we can't refresh it in time built-into the spell. In Mists, our Devouring Plague is going to require Shadow Orbs to cast, and you can be sure we won't have the resources to keep that up full-time. In that case, an extra tick translates directly to extra damage from the DoT in question.

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