*v3.3*

Time to look at haste. Haste is a trickier creature to calculate as there are two main aspects to it:

- More haste allows faster casting which means more throughput
- More haste also increases the chance that a spell will be cast just-in-time to prevent death. The so called ‘saving cast’.

The saving casts can not be quantified as far as I am aware as it is dependant on factors such as player skill and latency. We can however estimate the additional throughput that haste grants.

## Sections

- Introduction
- Mana regeneration including Spell Power and Stamina
- Mana pool
- Haste rating
- Critical rating
- Summary including LootRank and Pawn values

Assumptions:

- Flash Heal is being spammed (1887 base heal, 80.68% co-efficient and 1.5s cast time)
- Discipline has 2774 spell power
- Holy has 3092 spell power
- 32.8 Haste Rating equals 1% Haste
- Caster currently has zero haste. The effect of moving from 0% to 1% haste is slightly greater than moving from 6% to 7% haste. However the effect on weighting is very small.
- 30% over-heal
- Borrowed Time and Serendipity have been ignored as only FH is being spammed.
- Surge of Light procs are ignored.

Firstly we calculate the MP5 value of a Flash Heal. We calculate this so we can figure out how much an additional FH, enabled by haste, is worth.

`Flash Heal MP5 value = (base heal + (SP * SP co-efficient)) * SP MP5 value * (1 - overheal %)`

Flash Heal MP5 value is 5775 for discipline and 6134 for Holy.

Secondly we need to calculate the number of additional casts 1 Haste Rating allows.

`Cast time for 1% Haste = Base Casting Time/(1 + (% Spell Haste / 100))`

Cast time for 1% Haste = 1.5/(1 + (1 / 100))

` Cast time for 1% Haste = 1.48149`

Extra casts for 1% Haste = 1.5 - Caste time for 1% Haste

Extra casts for 1% Haste = 1 .5- 1.48149

Extra casts for 1% Haste = 0.014851

Extra casts for 1% Haste (%) = Extra casts for 1% Haste/ Base cast time

Extra casts for 1% Haste (%) = 0.014851 / 1.5

`Extra casts for 1% Haste (%) = 0.990099%`

Extra casts for 1 Haste Rating = Extra casts for 1% Haste / Haste Rating per Haste

Extra casts for 1 Haste Rating = 0.009901 / 32.8

Extra casts for 1 Haste Rating = 0.030186%

So for each 1 Haste Rating you get 0.030186% additional casts. Not much eh? Thirdly we bring the parts together to calculate how much MP5 value 1 Haste Rating brings.

`Haste Rating MP5 value from additional healing = FH MP5 value per second * extra casts for 1 Haste Rating`

`Haste Rating MP5 value (Disc) from additional healing = 5775 / 1.5 * 0.030186%`

Haste Rating MP5 value (Disc) from additional healing = 1.1621

Haste Rating MP5 value (Holy) from additional healing = 6199 / 1.5 * 0.030186%

Haste Rating MP5 value (Holy) from additional healing = 1.2344

Now this additional healing throughput comes at a cost. Casting more Flash Heals heals for more but also consumes more mana. So we need to deduct the additonal mana consumption.

`Mana consumption per haste rating (MP5) = Flash Heal mana cost * extra casts for 1 Haste Rating / Flash Heal cast time * 5`

`Mana consumption per haste rating (MP5) (Disc) = 528 * 0.030186% / 1.5 * 5`

Mana consumption per haste rating (MP5) (Disc) = 0.5312

Mana consumption per haste rating (MP5) (Holy) = 621 * 0.030186% / 1.5 * 5

Mana consumption per haste rating (MP5) (Holy) = 0.6248

Final value of haste rating is additional healing minus additional mana cost or:

**Haste Rating MP5 value for Discipline = 1.1621 – 0.5312 = 0.6309****Haste Rating MP5 value for Holy = 1.2344 – 0.6248 = 0.6096**

Using this model, at about a spell power to MP5 ratio of about 1:1 the additional throughput generated by haste rating is equal to the the additional mana cost of casting the spells. Thus at ratios less than these I suggest a floor value of 0 for haste rating MP5 value be used instead of a negative value.

Next is critical rating.

Does this also ignore Imp. Flash Heal for Discipline? I assume so, but it wasn’t mentioned, so I felt a bit hurt. :(

Yes this ignores talents. I should actually stop being lazy and add all the talents for both specs.

At what point should I lower the value of haste? I’m at 716 haste rating right now, which gives me a 1.1 second flash heal with raid buffs (wrath of air totem).

What I am asking:

– Should I value haste the same past the point of a 1 second flash healing during hero?

– Should I value haste the same past the point of a 1 second flash heal outside of hero?

Edit/Update:

The reason I am asking if haste carries a degenerating value is because a lot of gear either holds haste or spirit, and I’m having to choose between the two. Based on your previous stat weighting, haste carries the upper-hand, and do to this I have things like Merlin’s Robe rather than Royal Moonshroud Robe. Should I keep choosing haste>spirit, even with my flash heals getting close to 1 second? I don’t want to waste my frost badges, know?

Edit/Update 2:

Actually, I’ve been wondering why I have more intellect than spirit when you weight spirit>intellect. I’m almost 100% sure that it is because haste>spirit in the weighting. Most gear either carries spirit or haste, from what I’ve been looking around at lately… Problem?

Um im a Sp that stacks haste instead of crit. I seem to pawn hardcore I too have merlins robe and several hast gems my haste is 810 at least I think mindblast roks at lightning speed. Now my question is am i doing something wrong I was told sp stack crit. Like i said me and most of the ppl on my server think im not a bad sp, Would i do better stacking crit or if it aint broke dont fix it? I know how to play the way my toons set up is that more important than choosing crit like everyone else?

You ought to check out the post over at Life In Group 5, as it deals explicitly with the ‘diminishing returns’ of Haste as it relates to a short cast spell (in this case Lesser Healing Wave) and a long cast spell (Chain Heal), with curve adjustments for raid buffs.

http://lifeingroup5.com/

@Will – I’m not an expert on haste but i’ll give you some answers.

“Should I value haste the same past the point of a 1 second flash healing during hero?”

I’d personally never gear based on heroism. Its too small a factor in a fight to be gearing around.

“Should I value haste the same past the point of a 1 second flash heal outside of hero?”

Probably not. I’d reduce the haste weighting to zero because your global cool down will be 1 second also.

@Chuck – I’m no shadowpriest expert (check out shadowpriest.com), but haste is much better than crit I believe. I’m stacking haste for the DoTs though not faster Mind Blast.

If you’r doing good DPS as you are Chuck i’d be very careful about changing without doing some research.

@shatterhoof – I had a quick look but I couldn’t find a post about haste there. Can you link the actual post please?

Gobble gobble.

I would think the post Shatterhoof is referring to is: http://lifeingroup5.com/?p=96.

In essence, the argument I presented is that the more points you invest in haste, the less value you gain (in terms of casting speed increase). This makes haste seem to have diminishing returns. However, when you plot cumulative haste against theoretical HPS, you see a linear progression. The ultimate conclusion is that the actual benefit of haste lies somewhere in between those two scenarios.

I didn’t look at haste’s weight against mp5, however I do think it would be an interesting evaluation to make since, as you note, haste is typically held as a negative mp5 value (but obviously at a different level for us chain healing machines.)

Great read and great food for thought!

Oh thanks Vixsin. That is an interesting post.

[…] priorities for those new characters! Priests — new 3.3 theorycrafting from BobTurkey– Part 4: Haste Rating Part5: Critical Rating Part 6: Summary Hunters — Jaedia’s ICC raiding loot list. […]

This calculation is odd. I guess what conflicts with my views (and I’m shortsighted in that matter ;)) is the part where it’s all translated to MP5. I would just compare throughput stats and go from there.

Of course, my view doesn’t help to build weight stats.. The great part about this method is that it correlates the manacost from Haste with the benefit from Haste, something I just cannot do with my methods.

As for the Haste comments from Vixsin, I agree that the time benefit from haste reduces with every point you have but I disagree that this is a correct measurement. Haste gives procentual throughput. 1% haste = 1% Throughput. While the time aspect of each cast is not irrelevant, I’m guessing we deem it “true” because we consider time a valuable aspect to saving a life and this aspect has indeed a diminishing return. But in reality there is no diminishing return to haste in throughput.

If you wish to compare the value of Haste up to a point where others become more interesting, then it should be weighed out against SP.

When it comes to crit we can easily show that, without additional bonuses in throughput, crit will never catch up haste:

HPS = base_hps * (1+Haste%) * (1+ 50% Crit%)

value_haste = base_hps * (1+50% Crit%)

value_crit = 50% * base_hps * (1+ Haste%)

value_crit > value_haste WHEN

=> 50% * base_hps * (1+ Haste%) > base_hps * (1+50% Crit%)

=> Haste% > 100% + Crit%

So unless your haste is 100% more than your crit, haste beats crit in throughput.

SP works the opposite way: 1 SP on a 1.5s spell with 20% bonus always gives 0.97 more healing, but while 100SP might give a 9.7% bonus in throughput, your next 100SP will give less than 9.7% even though it gives the same amount of healing.

The diminishing effect in time from haste is weighed against the diminishing effective heal of SP. So ‘Haste has a diminishing return’ is a good start and a good argument, but it’s not enough imo :)

I’m really not happy with the very last bit of this thread. I bracketed off the

(mana cost * 0.03…%) / (cast time * 5)

and it gave a tiny disadvantage to Haste instead of 1 haste knocking off half the value of it.

Thing is. I don’t know if that’s right.

By my numbers, Haste: 1.3827, and the mana reduction from haste could either be 0.0244 or 0.6096, first with brackets and second without.

Halp?

I thought you had me for a while there but…

Mana cost per cast = 528

Additional casts per haste rating = 0.030186%

Additional mana cost per haste rating = 528 * 0.030186% = 0.1593

Next we normalise to MP5. Flash heal (in this example) has a 1.5s cast so additional mana cost per haste rating per second = 0.1593 / 1.5 = 0.1062

To allow equation with MP5 we calculate the additional mana cost to cost per 5 seconds = 0.1062 * 5 = 0.5312 (i’ve rounded but your numbers should be very similar).

(mana cost * 0.03…%) / cast time * 5 is correct as you calculate the brackets, then the division then the multiplication (BODMAS), but if you want to add brackets you could write it as:

(((mana cost * 0.03…%) / cast time) * 5)

Hope this helps.

Gobble gobble.

Does help. Skimping on brackets means I have to rely on BODMAS, which further screws up numbers.

My numbers won’t look much like yours for haste. I’ve made the assumption that haste distributes uniformly the more you stack. (Obviously it doesn’t, but there’s no other way I can think of keeping the value of Haste moving as my gear changes.) I’ve just set my base cast time for Flash Heal as 1.27s and modify it every time my haste gear changes.

Other things that came to mind were the 3% racial Spirit bonus humans get, and the oft-looked-over +2% Intellect meta that usually shift things about.

But we’re theorycrafters. It’s what we do.

Hope you enjoy this lolwalltextcrit.

Firebert

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