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• CheshireCat · 06/14/07, 2:22 PM

I mentioned that I thought Inspiration was worthwhile without stacking crit upthread, complete with a classical Proof by Vigorous Assertion, with use of the Handwaving Corollary. But, since the thread is named "Holy Priest Theorycrafting", I thought some actual numbers might be helpful, so I drummed some up. The conclusions are, unsurprisingly, not as clear-cut as I had previously thought, but I think the conclusion holds up.

Purpose:

So, the question is, how important is it to have high crit in order to take advantage of Inspiration? How much benefit in Inspiraton uptime do you get from a 1% crit increase? How worthwhile is Holy Specialization?

Model:

The best way I came up with to model Inspiration uptime is to ask the question: How likely is it that a heal has crit in the last 15 seconds? (If there has been a crit, Inspiration is up. If not, it isn't. Therefore, the percent chance of that being true is also your percent uptime.)

The answer to that question is:

1 - (chance that no heals have crit in 15s)
1 - (chance not to crit)^(number of heals in 15s)
1 - (1 - average crit chance)^(number of heals in 15s)

Assumptions:

Between base crit and the Int that all our gear seems to be drenched with, I'm assuming that a priest that doesn't gear or spec at all for crit has a 6% crit chance. Mine is 6.14 in PMC/Kara gear with the Kazzak staff, for reference.

Our GHeals are 2.5s to cast, but we usually don't spam. Accounting for pauses, I think it's pretty fair to say we land one heal per priest every ~3s, or 4 in a given 15 second window. (I know, you can land 5 heals at 3s intervals in a 15s period, but in any randomly selected 15s window, which is what this model is based on, the chance is infinitesimal. 4 heals per healer per 15 seconds covers all casting periods from 3s to 5s. We can go back and adjust this assumption to a more spammy one if anyone objects, with the effect of making crit less important to uptime.)

Results:

For a single priest with the talent, then, uptime is:

1 - (1 - .06) ^ 4
1 - .94^4
1 - .781
.219 = 21.9%

For 2 priests with no extra crit, average crit is the same but there are twice as many heals landed in the same window. Uptime is 39%.

For 3 priests with no extra crit, uptime is 52.4%.

Now, what if we increase our crit with Holy Spec or gear? Remember, we're using average crit chance in the formula, so a 1% increase in 1 priests crit is worth (1/number of priests)% average crit.

For 1 priest, 1% crit increases the uptime to 25.2%, which is +3.3%, for (3.3/21.9) = 15% more uptime.
If there are 2 priests, 1% crit increases the uptime to 41.5%, +2.5% for 6% more uptime.
If there are 3 priests, 1% crit increases the uptime to 54.3%, +0.9% for 1.7% more uptime.

That first point of crit is the most valuable, since the more you crit the more likely you are to be overwriting a proc and contributing less than its full value to the uptime.

To prove it, consider if all priest were full Holy Spec for 11% average crit.

1 priest = 37% uptime.
2 priests = 61%
3 priests = 75%

Conclusions:

A) The more Inspiration-enabled priests in the raid, the less important an individual's crit rate is to overall uptime. My thoughts upthread on Inspiration being worthwhile regardless of crit chance were leftover from analysis done on 40-man raids. With 5 Holy priests in a raid, as was not uncommon, individual crit was basically immaterial. As that thread in General notes, though, stacking Holy priests is becoming less and less common, and in the solo case, increasing crit has noticeable effects.

B) There are severe diminishing returns on crit percentage as a means of increasing uptime. This is mainly because you start overwriting your own procs, so you don't get the full 15s of uptime for each crit. So, as a solo healer, the first crit percentage you add nets you a 15% increase in uptime, (to be clear, 3.3% more uptime for a proportional increase of 15%) but each point after that gets you a little less.

C) Combining the two, if you find yourself as the only Holy Priest in the raid frequently and you are often on MT healing duty, consider putting a point or two in Holy Spec. (I stand by my assessment that, unless all your tanks are near-cap druids, Inspiration is one of our best tank healing talents regardless of crit.) The first point or two pay pretty good returns in uptime. I would certainly not recommend pursuing crit on gear or even maxing out Holy Spec for the purpose of keeping Inspiration up.

06/14/07, 2:22 PM	#143 (permalink)
• CheshireCat These are not the hammer. Pynn Human Priest <Exile> Whisperwind	I mentioned that I thought Inspiration was worthwhile without stacking crit upthread, complete with a classical Proof by Vigorous Assertion, with use of the Handwaving Corollary. But, since the thread is named "Holy Priest Theorycrafting", I thought some actual numbers might be helpful, so I drummed some up. The conclusions are, unsurprisingly, not as clear-cut as I had previously thought, but I think the conclusion holds up. Purpose: So, the question is, how important is it to have high crit in order to take advantage of Inspiration? How much benefit in Inspiraton uptime do you get from a 1% crit increase? How worthwhile is Holy Specialization? Model: The best way I came up with to model Inspiration uptime is to ask the question: How likely is it that a heal has crit in the last 15 seconds? (If there has been a crit, Inspiration is up. If not, it isn't. Therefore, the percent chance of that being true is also your percent uptime.) The answer to that question is: 1 - (chance that no heals have crit in 15s) 1 - (chance not to crit)^(number of heals in 15s) 1 - (1 - average crit chance)^(number of heals in 15s) Assumptions: Between base crit and the Int that all our gear seems to be drenched with, I'm assuming that a priest that doesn't gear or spec at all for crit has a 6% crit chance. Mine is 6.14 in PMC/Kara gear with the Kazzak staff, for reference. Our GHeals are 2.5s to cast, but we usually don't spam. Accounting for pauses, I think it's pretty fair to say we land one heal per priest every ~3s, or 4 in a given 15 second window. (I know, you can land 5 heals at 3s intervals in a 15s period, but in any randomly selected 15s window, which is what this model is based on, the chance is infinitesimal. 4 heals per healer per 15 seconds covers all casting periods from 3s to 5s. We can go back and adjust this assumption to a more spammy one if anyone objects, with the effect of making crit less important to uptime.) Results: For a single priest with the talent, then, uptime is: 1 - (1 - .06) ^ 4 1 - .94^4 1 - .781 .219 = 21.9% For 2 priests with no extra crit, average crit is the same but there are twice as many heals landed in the same window. Uptime is 39%. For 3 priests with no extra crit, uptime is 52.4%. Now, what if we increase our crit with Holy Spec or gear? Remember, we're using average crit chance in the formula, so a 1% increase in 1 priests crit is worth (1/number of priests)% average crit. For 1 priest, 1% crit increases the uptime to 25.2%, which is +3.3%, for (3.3/21.9) = 15% more uptime. If there are 2 priests, 1% crit increases the uptime to 41.5%, +2.5% for 6% more uptime. If there are 3 priests, 1% crit increases the uptime to 54.3%, +0.9% for 1.7% more uptime. That first point of crit is the most valuable, since the more you crit the more likely you are to be overwriting a proc and contributing less than its full value to the uptime. To prove it, consider if all priest were full Holy Spec for 11% average crit. 1 priest = 37% uptime. 2 priests = 61% 3 priests = 75% Conclusions: A) The more Inspiration-enabled priests in the raid, the less important an individual's crit rate is to overall uptime. My thoughts upthread on Inspiration being worthwhile regardless of crit chance were leftover from analysis done on 40-man raids. With 5 Holy priests in a raid, as was not uncommon, individual crit was basically immaterial. As that thread in General notes, though, stacking Holy priests is becoming less and less common, and in the solo case, increasing crit has noticeable effects. B) There are severe diminishing returns on crit percentage as a means of increasing uptime. This is mainly because you start overwriting your own procs, so you don't get the full 15s of uptime for each crit. So, as a solo healer, the first crit percentage you add nets you a 15% increase in uptime, (to be clear, 3.3% more uptime for a proportional increase of 15%) but each point after that gets you a little less. C) Combining the two, if you find yourself as the only Holy Priest in the raid frequently and you are often on MT healing duty, consider putting a point or two in Holy Spec. (I stand by my assessment that, unless all your tanks are near-cap druids, Inspiration is one of our best tank healing talents regardless of crit.) The first point or two pay pretty good returns in uptime. I would certainly not recommend pursuing crit on gear or even maxing out Holy Spec for the purpose of keeping Inspiration up.