I observed something quite interesting. The renew glyph always removes just 1 tick and boosts the remainder by the same amount regardless of haste.

For those who dont understand what this means

At 4 ticks Glyphed = unglyphed
At 5 ticks glyphed = 4*33 = 132%, while unglyphed = 125% i.e. glyphed heals for 5.6% more
At 6 ticks glyphed = 5*33 = 165% while unglyphed = 150% i.e. glyphed heals for 10% more

For me with 9.42% haste PWS (25.83% haste) nets me one extra tick, while PWS+PI (51% haste) gives two extra ticks.

The reason why this is so intersting is this. Renew does not consume borrowed time, so basically you can cast PWS and 4 hasted renews if you have even a little bit of haste. If you have 10% base haste you can cast 5 hasted renews per borrowed time.

What does this mean

In inner will for me renew heals for 5253 or 6987 if glyphed. Total values including crit and aegis are 5253*4*1.1821 = 24 838 and glyphed heals for the same amount.

With borrowed time however glyphed renew heals for 33037 ,while unglyphed renew heals for 31048

In inner will renew costs 3535 mana and with my values GCD is 1.371 or 1.167 with borrowed time.

If I cast PWS + 4 renews with the glyph the total cast time will be 1.371+4*1.167 = 6.039 seconds and total healing will be 49213 + 4*33037 = 181 361. Total mana cost is 3535*4+9600*0.85 = 22300. HPM: 8.133

flash heal under these conditions heals for 33284 without crit and aegis and costs 9600 mana.

Casting 1 PWS and 4 flash heals on 4 targets (assuming they don't have grace, which you can expect for non tanks), heals for 49213 + 4*33284*1.1820 = 206580 in inner will or 217529 in inner fire. Cast time = 1.371*4+1.167 = 6.651 sec Total mana cost is 46560 in inner will and 48000 in inner fire.

HPCT of PWS+4xrenew inner will = 30 032 for 22300 mana
HPCT of PWS+4xflash inner will = 31 060 for 46560 mana
HPCT of PWS+4xflash inner fire = 32 706 for 48000 mana

If you are under PI, then things get even worse, since you can now fit 5 renews in a single borrowed time and renew will tick 5 times. So HPCT = 255 694.25/6.142 = 41 630.5 for 17840 mana

For PWS+5flash HPCT is
Inner will: 245921.44/6.712 = 36639 for 37248 mana
Inner fire: 36639*1.053 = 38581 for 38400 mana.

For those of you who might be wondering, spells that have a base cast time consume borrowed time even if they are made instant through talents and glyphs. They also don't benefit from inner will (e.g. glyphed holy fire and FDCL flash)

In order for this analysis to be complete we also need to look at PoH.

13593+5290 (aegis) = 18883 with aegis

I am calculating total healing with PoH including crit and aegis by determining the crit boost with 60% aegis and then adding 30% aegis for all non crits:




13593*(1+0.0877+(0.9*0.0877+0.3)*1.2974) = 21468 per target

PWS + 3 PoH = 371 233 healing (5 targets inner will) or 390 908 (5 targets inner fire). Total cast time: 1.5/1.0942+2*2.5/1.0942+2.5/1.2583 = 7.927 sec 46 831 49 314

HPCT PWS+3PoH (5 targets inner will) = 46831 for 32160 mana
HPCT PWS+3PoH (5 targets inner fire) = 49314 for 33600 mana

Incidentally HPM with inner will is 11.54 while with inner fire it is 11.63. So it takes 3 PoH casts per PWS to break even mana wise, if we ignore overheal. PoH is ofc an expensive spell. For cheaper (the cheaper the better) spells you need more casts to break even. However when factoring in overheal, which pretty much eats a sizeable chunk of the HPS benefit from inner fire, Inner will is pretty much certain to be better HPM.

To show that its worth casting PWS straight PoH spam is 46981 HPS in inner will or 49471 HPS in inner fire. Compare that with the values for PWS+3PoH they are practically the same as with PWS+3PoH. Ofc with PWS+2PoH you need to be in inner will, so you lose like 5% HPS. HPM for PoH alone is 14.94 (inner fire).Once overheal is accounted for however PWS has no overheal under heavy raid damage you end up with higher HPS and massively better HPM. With one rapture proc per 2 PWS you are up to 13HPM already in inner will. So very little overheal (15%) is needed to make PWS+3PoH better HPM. PWS + 5PoH might seem like it would be the most HPM, but it will most likely not be. The reason is that its not guaranteed that PWS will be absobed immediately and just 1 PWS per 12s is likely to lose a lot of rapture procs.

The HPM for PWS+4renew for comparison is 8.133.

This analysis explains why using PWS/renew/pom/holy fire and penance and ignoring SpS and heal is so effective. Its significantly higher HPM than SpS and significantly higher HPS than heal, even if you have FDCL or not. Once you get past the 1st haste break point for renew, BT renew will heal for as much as a flash heal for roughly 1/3rd the mana! For stationary deficits on 4 targets this BT renew in inner will is currently the most efficient strategy, especially if you have enough haste to get 5 ticks with borrowed time.

Inner will is better HPM and a noticeably reduced mana drain per second compared with inner fire unless you are spamming SpS without divine insight. This is especially true if you have FDCL

EDIT: Recalculated for 30% aegis.

Love the analysis, love the info on how glyphed Renew works. But then again. We won't be casting BT-Renew chains and even less BT-PI Renew chains nor will we (likely) be stacking haste nor does this calculation include the fact that Renew by far is the most overhealing spell in out arsenal (SpS not yet tested enough) nor apparently takes into account that heal will profit from grace (though it does not on Beta yet) or did I miss something.

I don't understand this calculations. What are we supposed to be casting for 30+K mana and 40+K Heal? Am I missing a digit in Healing? Secondly: Your calculation implies we should be a) using PW:S on CD during AoE Damge and b) stay in Inner Will to do so? Did you calculate the double dipping of aegis with crit?

Please walk me through that: 33284*1.1821 is 39345 ((ah got that one, 51148 assumes Grace))

And what why is there a 1.6 in your calculation for flash heal. Totally confused.

Yep I forgot to add the 1.3 multiplier. I amended the post.

You are also correct in that my calculation is not quite right I applied the mastery to the whole of the crit multiplier not aegis! Lets define mastery%/100 = mastery and crit%/100 = crit

A critical heal is 100% larger from the heal part and an additional 30% of the crit as aegis. That means 30% of a crit is 60% of a normal heal, hence a crit from disc is 160% larger than a normal crit. Since we have mastery its the benefit of aegis is increased to 60%*(1+mastery%/100) so a crit from disc is 100%+60%*(1+mastery%/100).

Thus the crit multiplier is 1+[1+0.6*(1+mastery)]*crit = 2+0.6*(1+mastery). For 8.77% crit and 29.74% mastery that is

1+(1+0.6*1.2974)*0.0877 = 1.1560

So the effect of crit is smaller than I calculated. And the correct flash heal value excluding overheal and including grace is:

33284*1.156*1.3 = 50019.2

That also means the values in the above post are slightly higher than they should be. I will amend them.

I don't see a reason to not cast a renew chain if there is an opportunity. Everytime you PWS it makes sense to renew the tanks (if there are two) and/or people who have a DoT on them or have a significant deficit. Even during aoe healing it makes sense to use renew occasionally.

HPCT = healing per cast time. Its basically the HPS and total mana cost of a PWS+3PoH sequence. My calculations show that there is effectively no difference in HPS/HPM between straight PoH spam and PWS+3PoH. My calculations show that PoH+3PWS spam is better than straight PoH spam if PoH has any overheal.

I did calculate the double dipping, in fact I overestimated it, because I made the same mistake of applying mastery to the heal part of the crit as well as aegis. I need to recalculate it

This is the formula I am using

base*[1+crit+(1+mastery)*(0.9*crit+0.3)]

Not that this formula can be rearranged to read:

base*[1+(1+0.9*(1+mastery))*crit+0.3*(1+mastery)]

This shows that the "double dipping", is not really a double dipping. The crit behaviour of PoH can be thought of as having a higher crit multiplier for direct heal part of the spell but no benefit at all from crit for the absorption part of a non-crit PoH. This is what the formula suggests. The 0.3*(1+mastery) part is the absorption part and as you can see it not influenced by crit at all. The crit multiplier for the direct heal however is dependent on mastery, but it turns out that it rises very slowly. Crit never performs as well for PoH as it does for normal spells. At high levels of mastery PoH in fact performs quite poorly.

For example look at my values

Normal heals gain 15% from crit and aegis but PoH gains 21468/18883 = 1.137, just 13.7%.

Crit looks massive when you are just looking at the base heal, but that is only a Part of PoH. The automatic aegis applied by PoH must be thought of as part of the base heal, since its always applied and it does not benefit from a crit as much as the direct heal part of PoH.

The crit multiplier for a normal spell is [2+0.6*(1+mastery)], while the crit multiplier for PoH is {2+1.2*(1+mastery)/[1+0.3*(1+mastery)]}.

Yes that is correct. I had a look and it seems that there is no mastery breakpoint. Crit for PoH never performs as well as it does for other spells. In fact the higher your mastery the less well it performs compared to our other direct heals. However its important to realise that this just means that crit does not benefit PoH as much as it does normal spells. I haven't looked at crit in comparison to haste and mastery. I suspect crit is not going to be a great stat for PoH however, because its value for PoH is effectively static. The crit modifier increases extremely slowly for PoH.

Basically the crit modifier of PoH is

{2+1.2*(1+mastery)/[1+0.3*(1+mastery)]}, while for our other spells it is [2+0.6*(1+mastery)]

So the crit modifier for PoH when taking aegis into account is lower and rises more slowly with mastery.

I'm note sure I can follow you on this statement. Unless something got changed in the beta I overlooked, both crit and mastery are highly more effective for Prayer of Healing than our other spells, which is quite easy to prove:

Let v be the base healing value (that is, the amount we hit, not crit, for on average), c the crit rate, d the divine aegis factor (depending on mastery something around 0.4 for most of us) and the average healing value including crit and divine aegis.

The average healing done by any of our direct healing spells is then






Now for Prayer of Healing, we get one Divine Aegis bubble for the hit itself, and another if we crit - but those two with the higher (critted) base value






Now the derivative of will always be higher than that of , scaled to v we get:




As for mastery, the difference is even bigger:




We see that for every value of d, the benefit of crit for Prayer of Healing is higher than for any direct heal, as is with mastery.

It does not seem to me that you have not proved what you set out to. I will discuss what I think you have done a little later.

My analysis is certainly correct. In fact the final formula you posted for PoH, which is equivalent to mine behaves exactly the way I predicted. The easiest way for your to see it is to plot it vs crit and you will see exactly what happens.

For now let us look at the crit behaviour of PoH by focusing exclusively on the above 4 equations as they tell us all we need to know.

For a direct heal the crit multiplier is


For PoH the crit multiplier


By inspection you can immediately see that the crit multiplier is automaticaly lower(!!) than for a direct heal. There exists no value of mastery for which the crit multiplier for a direct heal is smaller than the crit multiplier for PoH

To help visualise it lets say that D is 40%

For a direct heal the crit multiplier is


For PoH the crit multiplier


Thus a PoH crit is 2.5714 times larger than a PoH hit, while a direct heal crit is 2.8 times larger (!!). I am sure you will agree that having a lower crit multiplier means that PoH benefits less from crit.

Just in case you dont here is the proof: Thus if our amount of crit is C, the benefit to PoH will be (1+C*2.5714), while the benefit to direct heals will be (1+C*2.8). You can clearly see that the benefit of crit for PoH is simply not as high.

To demonstrate mathematically how mastery and crit interact for PoH. Lets look at the limit of the crit multiplier as D goes to infinity.

For direct heals there is no limit, while for PoH it is obvious that the limit is 4. At 2.57 we are already quite close to the asymptotic limit so as mastery increases the crit multiplier for PoH is going to increase quite slowly compared to that of a direct heal, which will increase quite fast.

I confirmed this in game. Just check the values I posted for PoH and flash heal or feel free to recalculate them yourself from the base healing values I provided. You will see that the crit multiplier for PoH is lower exactly as I predict.

So we can clearly demonstrate that your result is wrong. A question is why it is wrong. Looking at the rest of your equation I can immediately see the problem. The problem lies in the way you have normalised the rate of increase. To explain:

, is the absolute rate of increase. This tells us roughly the absolute amount of healing added by an increase in crit for a given level of mastery, which is not very useful, because (a) it directly depends on the amount healed by the spell and (b) it does not tell us the % increase. To find the relative rate of increase i.e. the rate in the % increase in healing amount, we need to normalise for the non crit heal amount. You have correctly attempted to normalise this in the two formulas I quote above. However you have chosen the wrong thing to normalise to. 1/u is the normalisation factor for a direct heal, but not for PoH. The correct normalisation factor for PoH is 1/[u*(1+D)].

Let us now correctly calculate the relative rate of increase with crit for PoH and direct heals:




We can clearly see that the relative increase in PoH with crit is always smaller than it is for direct heals. So the answer is no PoH does not double dip with crit. It always benefits PoH less than it does direct heals and the more mastery you have the bigger the difference(!!).

I am afraid this is also incorrect for the same reason. When you do it correctly you find that mastery has diminishing returns for PoH, but it does not have diminising returns for direct heals.

This analysis does not tell us whether crit or mastery are good for PoH compared to haste. That is something completely different. However they do tell us how these two stats behave. For the allowed values of mastery, PoH pretty much has a fixed crit multiplier (ranges from 2.3333 to roughly 2.6), so the value of crit does not benefit from mastery. The value of mastery itself clearly has diminishing returns, so even if it does turn out to be better than haste (I don't think so), it is highly likely that at a certain level it will drop below it.

However all this ignores a critical factor, mastery and crit increase HPM, while haste doesnt. Also mastery ignores overhealing pretty much while crit and haste don't. The jury is not out on whether mastery and crit are good or bad stats for PoH. I suspect that mastery is good, while crit is bad. However two things is absolutely clear. (1)PoH does not double dip from crit and gains very little benefit from mastery. (2) Mastery has diminishing returns, but has a better interaction with crit than normal spells.

FYI some info on Spirit Shell changes
- It now stacks @60% Priest HP (up from 40%)
- It will now apply Grace

I am afraid that is also wrong. I urge you to carefully read my whole post, rather than just that bit. You did not calculate the absolute rate of increase. What you attempted to calculate was the relative rate of increase, but unfortunately you made a mistake and the formulas you came up are completely wrong. I am sorry to say that no conclusions whatsoever can be drawn from your analysis.

If you want to look at the absolute rate of increase in the healing produced by PoH with respect to crit:

PoH: Base_{PoH-no aegis}*(1 + 3d)

Direct: Base_{direct}*(1 + 2d)

This is a kind of meaningless value. The absolute increase is not really that important. The relative increase (what you tried to calculate) is what matters.

To show you why, lets say that you have a spell that heals for 1000 000 and adding X% crit you get an absolute increase in healing of 100. Compare that with a spell that heals for 100 and adding x% crit, it produces an absolute increase of 50. What you are trying to say is because the increase for the first spell is 100 compared to 50 for the second spell, in real world terms the first spell benefits more from crit.

hat however is completely wrong. For the 1st spell if you cast the spell 10 times you will get 10,000,000 healing. Adding x% crit will increase that healing to 10,001,000, which is effectively no different than what you had without that crit and all the stat budget points you spent on it were utterly wasted.
For the second spell casting it 10 times nets you 1000 healing, but when you add x% crit you get 1500. In contrast to the 1st spell that x% crit increased your healing massively.

In the same way if we look at absolute rate of increase for say 50% mastery with my value of spell power.

Rate of increase with crit {PoH} = 13523*5*(1 + 1.5) = 169037.5

Lets do the same for flash heal

Rate of increase with crit {flash} = 33284*2 = 66568

The base healing of flash is 33284, while the base healing for PoH is 13523*5*(1+0.3*1.5) = 98041.75

That means a 1% increase in crit rate raises flash from 33284 to 33949.68 (i.e. +665.568) which is a 2% increase

In contrast a 1% increase in crit rate raises PoH from 98041.75 to 99732.125 (i.e. + 1690.375) which is a 1.7% increase. I.e. if you are spamming PoH and you take 1% crit you will see a 1.7% increase in healing. If you are spamming flash on the other hand you will see a 2% increase in healing with crit. In other words flash heal benefits from crit 18% more than PoH does.

In other words taking 1% crit has a much higher value for spaming a direct heal like flash, compared to PoH. This is because the absolute rate of change is based entirely on a higher crit multiplier for the direct heal part of PoH and it ignores the absorption part of PoH, which is quite frankly huge. The difference becomes higher and higher as mastery gets larger, because aegis becomes a bigger and bigger part of PoH.

Yes, I do not deny any of these points made, nor did I ignore the majority of your post.

It is indeed true that my calculations are not suited to compare our different spells on how they are increased by crits. As I already said, my original formalism was used for Prayer of Healing exclusively, and I never examined the proper interaction with other spells. Using v to normalize the derivatives was used to cancel out any talents or other effects, and is not suited per se for anything more. I did not make the point I intended to.

That being said, the fact that Prayer of Healing crits are a lower relative increase (and absolute, if counting v (1+d) as the 'hit') than for our direct healing spells seems to me as a pure academic endeavour. Otherwise one could think you argue that Prayer of Healing is a weaker spell because it scales weaker than the rest due to its baseline Divine Aegis. While the scaling statement is mathematically true, it is a dead end gameplay-wise:

Consider Prayer of Healing works like in Wrath of the Lich King, creating a Divine Aegis bubble of size d*2v on every crit. We'd have equal scaling behaviour.
Now add a constant bubble d*v (not d*2v) on every hit/crit (kinda the way it was in the first Cataclysm days). The relative increase by Prayer of Healing just got weaker for every %crit, yet would you say the spell scales weaker in general? This very effect gets even bigger by its actual behaviour with 2*d*2v bubbles.

In other words: The notion of this "weaker" scaling is due to some additional effect we have on non-crits. One could argue of course that because of this mechanic we are at a disadvantage to Holy or other classes not using this effects to achieve their proper output, but that's another round of number crunching. And on this one, one should not underestimate the fundamental benefits of absorbs (as well as its downsides of course), which we completely ignore in our current calculations.

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