Well, I finally did the number crunching for +haste vs. +crit. The results turned out as I expected them to – although not as strongly toward +haste as I expected them to, which was kind of surprising.
Going as far +haste as you can, you can get 1095 haste rating from gear, gems, enchants, and buffs. You can get about the same amount of +crit. However, 32.79 Haste Rating translates to 1% haste; 45.91 Spell Critical Rating translates to 1% crit. That difference is crucial.
With 1095 Haste Rating, you get about 33.39% +haste. Essentially, that means that in the space where you could cast 100 spells without haste, you can cast 133.39 spells with that much haste. (I’ll use Flash Heal as the baseline, since its casting time is the same as the Global Cooldown.) With about 1100 SCR, you get about 23.95% +crit. Without any +crit gear, I have 17.95% +crit for holy spells on my priest, so 1100 SCR would put me around 41.9% +crit for holy spells (36.9% for non-holy spells).
So in the time it takes me to cast 100 spells with my +crit gear (150 seconds for Flash Heal), I can cast 133.39 (call it 133 for neatness’s sake, and note that I’m rounding down) spells with my +haste gear. At 41.9% crit with +crit gear, 41.9 of those 100 spells will crit (call it 42); at 17.95% crit with +haste gear, 23.9 of those 133 hasted spells will crit (call it 24). Incidentally – or not, if you’re Matt – that’s 42 Divine Aegis procs for +crit gear, and 24 for +haste gear.
I’ll take a moment here to define H as the amount that a normal Flash Heal heals for.
With the +crit gear, that’s 58 casts that don’t crit, and 42 that do. Since critical heals give 150% normal healing, over 150 seconds, my +crit gear gives me 58H + 48(1.5H), or 121H.
With the +haste gear, I have 109 casts that don’t crit, and 24 that do. Over 150 seconds, I get 109H + 24(1.5H), or 145H.
In other words, with the gear that’s available on the live servers, stacking +haste provides 20% more throughput over a similar length of time than stacking +crit.
Oddly, the trick I talked about a few posts back – interweaving Power Word: Shield and fast heals to get the benefit of Borrowed Time – has sharply diminishing returns if your +haste is above 820, because the global cooldown can’t be reduced below 1 second. In other words, you can’t get more than 150 spellcasts into 150 seconds. In fact, from the point of view of only throughput, it’s better to not rely on Power Word: Shield at all, and just stack +haste and throw out Flash Heal and Penance as fast as you can. However, that’s not taking into account the mitigation of Power Word: Shield… which I’ll cover in another post.
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Comment by BobTurkey — March 2, 2009 @ 9:08 PM
Of course there are some pretty significant differences in maan use in your two examples.
Interesting never the less.
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Comment by Chris — March 4, 2009 @ 9:31 AM
@Bob,
Oh, absolutely. A priest who casts 50% faster also uses that much more mana. That’s why MP5 is my second-favorite stat. :)
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Comment by Actual Raider — March 23, 2009 @ 6:08 AM
I have to disagree strongly, you may get in more healing, I don’t doubt your numbers, especially if your cast timing is NON STOP with perfect timing, something the best DPSers strive for but just cant perfect.
But these numbers are from someone who must be holy, or does not raid. Your damage mitigation from your critical heals by way of divine aegis + inspiration + the fact that you are citing with your heals so often far outweighs the healing you gain. My Absorbed Damage from Divine Aegis alone is just insane. I am well geared with both sets and don’t find that much of a difference in my healing numbers but a huge difference in damage mitigation.
Why you do not even mention Divine Aegis is mind-boggling i do close to 400 Damage Mitigation Per Second with Divine Aegis on the MT. This does not take into account Inspiration or PW:S
There is a mod out there by the author of recount that extends recount.
http://wow.curse.com/downloads/wow-addons/details/recountguessedabsorbs.aspx
With all that said, knowing this is an old article, with Divine Aegis now stacking in 3.1 this theory of Haste over crit is almost laughable, almost is now, test your NUMBERS in a RAID instead of an OFFICE Setting OR at the very lease, forewarn new priest that this is just an interesting numbers game not a real world setting, and does not event take into account your skill tree.
Articles like this just upset me because is spreads misleading information to new priests.
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Comment by Chris — March 23, 2009 @ 6:50 AM
“Actual Raider”, for the record, I have completed Kel’thuzad 25 and Sarth+2D as a Discipline priest.
You’re more than welcome to disagree with me, but please don’t do it here until you’ve learned to keep your dick in your pants while you’re posting. Nobody cares how big it is.
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Pingback by And the Award Goes to… | World of Matticus — March 29, 2009 @ 10:16 PM
[...] promising healing blog formed in 2009, I nominate @etherjammer. He’s come to the conclusion that haste is indeed better than crit going forward into 3.1 for Discipline Priests. His weekly link posts are an excellent source of reading material if [...]
Comment by Zusterke — March 30, 2009 @ 5:20 AM
“my +crit gear gives me 58H + 48(1.5H), or 121H.”
This should be 58H + 42(1.5H). Result is correct though.
I disagree with the maths as it doesn't take into account DA, for example:
– The crit does 150% of the healing
– DA takes 30% => 30%*150% = 45%
So you nearly double (195%) the value of a crit.
Secondly, you do not use the proper stat weights. For 1095 haste rating, you can get 1314 crit rating. Assuming you stick to the same iLVL of gear, you get more crit. So, we need to compare:
– 1095 haste rating, giving 33.39% haste, with a base crit of 17.95%
– 1314 crit rating, giving 28.62% crit, for a total of 46,57% crit
Using your formula you get:
– 150H, for your Haste set.
– 144H, for your Crit set.
That's 4% difference only. However, this isn't the complete picture. You're still not taking into account the uptime of inspiration. The uptime is calculated with the following formula:
Uptime = 1 – (1 – crit)^n
where crit is your critchance and n is your amount of spells cast within the duration of your uptime (15 seconds).
With 46.57% crit this is:
Uptime = 1 – (1- 46.57%)^10 = 99.81%
With 33.39% haste and 17.95%:
Uptime = 1 – (1 – 17.95%)^13.339 = 92.86%
This uptime provides a 25% increase in armor. Taking my guild's pally with 23587 armor, his armor increases to 29483.75 and his mitigation from 58.64% to 63.93%.
That's a 5% decrease in damage to be healed which would require a 5% increase in hps otherwise. The haste package only offers 4%, so you need 1% extra to get to the same value.
If you take into account that:
– Borrowed time gives a hard cap and a diminishing return of haste
– crit heals more for the same amount of mana, thus increases mana efficiency
– Divine Aegis procs increase the mana returned through Rapture
However, I would not canonize these maths just yet. Clearly, there are far more factors involved in healing than the example here comprises. At least, I hope I've indicated that Haste > Crit is not always true.
Haste gives the biggest direct healing throughput, but Crit shows more synergy with a bunch of talents. Even so, it would be wrong to think that one stat beats the other at all times. Just look at your hps formula:
<total hps> = <base hps> * (1+(50% + 45%) * crit%) * (1 + haste%)
Both crit and haste multiply the hps. This effective means that haste and crit work in tandem. Logically, this can be seen as:
the more haste, the more spells you cast, the more chances on a crit you can get.
While the exact balance of haste and crit may vary depending on the situation, at least this formula says that some crit and some haste will give better results than dropping either stat completely. Not using exact science here, but I bet that a comparable amount of haste as crit (say, both 20%) will score best. However, you start with your base crit from intellect, which for int stacking disc priests is quite high. That's why, at first, haste may give the biggest gain untill they have a comparable %.
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JP Reply:
May 13th, 2010 at 12:05 PM
@Zusterke, thats quick alot Mr. Mathmetician =) Just a straightforward “Crit is better than haste” or “Haste is better than crit” would be nice
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Comment by Zusterke — March 30, 2009 @ 5:26 AM
It seems I forgot to use the uptime of the inspiration buff with respect to the mitigation. In total, the inspiration gives 4.4% more mitigation with the crit set, compared to the haste set.
This narrows the distance between the stats, though there are still far more facts to take into account. Eventually, a lot depends on the player's style.
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Comment by Chris Anthony — March 30, 2009 @ 9:17 AM
Thanks for the comment. I'm actually not finished with the train of thought I started in this post, for just the reasons you specify – there is something to be said for crit, and between talents and Borrowed Time, there is a haste cap that can be reached easily with current gear. (I've also been convinced in other comments that Intellect is probably a better investment than MP5.)
Do you mind if I ask where you got the item budget values for haste and crit? The table I was looking at valued them about the same.
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Comment by Alarric — March 30, 2009 @ 11:05 PM
I am terribly confused by your postings here. Your assumptions on the number of casts maxed with haste are terribly flawed. Numbers are only useful when they are implemented in a real enviornment. Sure haste might be better if all you did was cast FH on the targets … but who does that? And is that the most efficient healing strat to use? You seem to think so, but Penance is single handedly one of the best heals in the game, and it benefits more with crit than with haste. On another note, with DA stacking in 3.1 …. the arguement then moves to the accepted range of thought, which is a balance between crit and haste.
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Comment by Zusterke — March 31, 2009 @ 12:20 AM
That is indeed a mistake. As soon as I read your question, I double checked my information and sources on item budget. I got 12 crit = 10 haste yesterday but I must have made a mistake. My reference sheets and sources are telling me 1 crit = 1 haste today. I hope they stick to that tomorrow ;-)
That would require some rework of my calculations *sigh*
But I bet it still shows that 'some' crit +haste is better than no crit + lot of haste or a lot of crit with 0 haste. IMO, the most interesting question is not whether this is true (the formula says the answer is yes) but if there will ever be need to gear for more crit than you get from intellect.
Of course, this is all assuming a FH spam scenario.
As for investment in intellect: yes, it is probably better than mp5. While this may go against the religion of many disc priests, even spirit beats mp5 when you have over 1200 intellect.
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Comment by Chris Anthony — March 31, 2009 @ 6:45 AM
Alarric, thanks for commenting. It seems like the switch to Disqus wiped out the previous comment thread, which is a shame, because I already addressed this there. ;)
I'm aware that this isn't a realistic scenario or Discipline priests. The goal here was not to say that I think Discipline priests should just spam Flash Heal (I agree with you that that's ridiculous) but to provide a baseline for raw throughput.
I actually am not finished with the train of thought that I started in this series of posts, but I've been weighed down recently with work and Real Life, and I haven't had a chance to move on to the next station, so to speak. In short, though, my ideal Discipline priest strategy is to mitigate as much damage as possible with Power Word: Shield (in order to keep Borrowed Time up) and to supplant that mitigation with Divine Aegis (which now takes into account overhealing and will stack – which might cause some interesting confusion for mitigation meters – but which has a maximum mitigation). Penance is a big part of that plan as well. But like I said, I haven't finalized it yet, which is why I haven't posted more about it. :)
I hope that helps with your understanding of this post!
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Comment by Chris Anthony — March 31, 2009 @ 6:50 AM
Thanks for clarifying that. Many of the tools that I use date back to BC, and I haven't found good replacements for them for Wrath (assuming that they need to be replaced!), so I honestly wasn't sure of the stat weights.
You're almost certainly right that some +crit and some +haste is better than either extreme. I didn't intend to imply that Discipline priests should want gear that was all +haste all the time; my post was really a reaction to the Discipline priest guides I've seen that claim that the best strategy is to stack +crit as high as you can, with +haste as a spackle to fill in the itemization gaps. I think that attitude is contributing to a lot of misconceptions about Discipline priests, and I'm trying to correct it.
Like I said, I'm not actually finished with this idea yet, but I've been buried by work and Real Life and haven't had a chance to work out the kinks in it.
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Comment by Zusterke — April 1, 2009 @ 12:31 AM
I'll keep checking your blog then ;-)
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