Assuming a single damage pulse arrives that takes players to low enough health that a PoH fully heals them, you get 0.6 in healing and 0.4 in the shield for X mana. N more PoH's with no healing but only leaving behind a shield is 1.0 + 0.4 * N. The more PoH's you cast, the less efficient the entire chain becomes. Now it is true that if you don't cast the PoH to sustain the DA that you lose it all, which leaves the efficiency at 0.6/X HPM. If you need one PoH to bridge it until the next damage pulse, then the efficiency is 1.4 / (2X) or 0.7/X. Barely more efficient than simply letting the DA expire. Two PoHs gets you to 1.8 / (3X) or 0.6/X -- this is where you were when the DA would have expired on its own. Three bridging PoH's and you're at 2.2 / (4X) or 0.55/X HPM.

Your math is incorrect in how you compute efficiency. The efficiency is Heals over Mana Cost. The general formula is .4 + 0.6/(N+1). This means, among other things, the more you cast it the less efficient it is (and that ignores the DA cap). This intuitively makes sense -- the more bridging PoH's you cast, the more their shield dominates the entire equation, driving it closer to efficiency of 0.4.

Using PoH to bridge DAs past a certain point is just wasting mana. Past two, it is less efficient than losing the entire DA on the original heal. Now what does cause it to make sense is if you are holding it for some larger burst to keep people alive -- but not for the HPM.

So it isn't efficiency. Now it is unquestionably going to be higher HPS to bridge like that (over letting it expire), but it isn't efficiency. But the real truth is that if you do have something you want to prepare for like that, you should use Spirit Shell instead, which is far, far, far higher efficiency *and* HPS than using DA for it.

Smite is certainly not hugely efficient as a pure healing spell, but it provides significant utility for damage, and definitely is worth casting in many cases. But you need to factor in Evangelism and Archangel when discussing its efficiency, as well as its Glyph; those both bring it up considerably. 20% more healing at 20% less mana is considerable, and if you use HF on cooldown, 20% more. Getting Evangelism up quickly means you can Archangel on cooldown and significantly increases your DPS. If you buy into the Atonement healing style, you need to be using Smite. There are healing styles that eschew it, but for really cutting edge progression, it probably is necessary.

The style you suggest is not likely to be effective in a mana-starved situaiton (which is what we will all be in). Do not confuse Dragon Soul at 35% with Mists' first tier when you're raiding in blues. Progression raiding requires a level of efficiency and teamwork that your proposed style will probably struggle with. Instead you should use Spirit Shell, not DA bridging, and focus more on not spending mana than on using it to somehow recoup an investment you're determined to make good on.

I'm using 60/40 to be heal/DA fractions. For my gear at 85, it's roughly 58/42 (134k EH total, 57k of which is a shield; raid buffed, it's 158k/66k). 60/40 is probably a reasonable ballpark estimate barring mastery stacking shenanigans (which wouldn't change it too much).

EH = PoH Heal + 0.3 * PoH Heal * (1.2 + mastery_from_rating) = PoH * (1 + 0.3*(1.2+x)) = PoH * (1.36 + 0.3 * x)

x will range from 0 to, say, 0.4 (40% bonus from mastery rating would require 16 mastery which needs ~2900 mastery rating at 85, which would be very very heavy mastery stacking and gemming).

So a ballpark estimate of 60/40 split between heal and shield seems about right for PoH/DA, at least for napkin math.

% of total heal from mastery = (.36 + .3*x)/(1.36 + .3*x). For x=.40, this is .48/1.48 = 32.4/67.6% split. A 2/1 ratio is an overestimation (it's looking at mastery-stacked end-of-expansion gear).

My calculation is correct. I am just using % numbers to compare. You calculate the exact same thing: I am averaging the % of the amount healed and dividing by the number of spellcasts. Its practically the same thing, no point in arguing semantics.

I gave you a very specific example with spirit shell. After spirit shell is absorbed you still have people to heal so you will have left over aegis. I have shown that its potentially worth keeping it alive using the minimal number of PoHs. It will increase your HPS dramatically, and it can even boost your HPM [edit: depending on the overheal you get from PoH. Spirit shell is a 1 minute CD and you will still cast no spirit shell pohs after the raid stops taking damage during the top up, so again you have aegis worth keeping alive. Unfortunately spirit shell does diminish the value of aegis stacking (if its up) in cases where all spirit shell must be applied before the spike hits (i.e. spike is only 1 hit). If that is the case its a really bad fight for disc.

This is one of the major issues disc has at the moment. PoH without aegis being absorbed has abysmal efficiency. Hopefully blizzard will understand this and let spirit shell refresh aegis, but we will see.

Remember that PoH can also overheal, which increases the value of the aegis you have stacked. 70% to 65% is a drop of roughly 7.2%, but that is with zero overheal on the original PoH. Since aegis is a 15s buff you can potentially (safely) extend to 25s after the intial stack is established (not when the damage hits but the actual first aegis stack is established). If you have cast 2 PoHs on a group, The you can extend it for roughly 25s with a gain in HPM, or you can extend it for 37s with a 7.2% loss in HPM

Basically we can conclude that I am right. As long as you don't need to cast a lot of PoHs, once you use it to heal a spike its worth keeping aegis alive for a certain amount of time depending on the left over stack. If the fight allows you to do that it makes sense to do it.

PoH = base*(1+crit*(1+0.9*(1+mastery)+0.3(1+mastery))

% of total heal from mastery = (crit*0.9+0.3)*(1+mastery)*100/(1+crit)

Adding in 5% crit and 30% mastery this comes up to 42.71%

The % of aegis is 42.71/1.4271 ~ 30%

Crit increases that value quickly because PoH crits are roughly 50% aegis.

In raids we can have 37% mastery and probably 10% crit due to the crit buff. In that case it would be 32.7%. With that Casting a full healing PoH and then a 100% overheal poh to keep the aegis alive has an efficiency of 132.7/2 = 66.35%, nearly the same as letting the original PoH expire (67.8%). However even PoHs that are not cast with the sole purpose of keeping aegis alive can overheal, sometimes a lot, which greatly raises the value of keeping your aegis alive.

[edit2] With 470 scaled gear I have 12.55% crit and 47.78% mastery, which brings the aegis percentage to 35%. This means casting one extra PoH to keep aegis alive increases your HPM.

about 60-70% of our heals is PWS, aegis and spirit shell, making mastery a very good secondary stat for disc. Aegis stacking is going to be even more important as our gear improves since mastery and crit will go up.

Summary: Keeping aegis alive is crucial to maitaning both high HPS and can even be a gain HPM depending on gear/conditions.

If you don't agree I am happy to run a little simulation for you.

[edit] Serrif pointed it out correctly that I am wrong about the amounts. Its 42% of the actual heal amount not 42% of the whole PoH. So its 42% of the heal, which means its 0.42/1.42 = 30% of the PoH value. I will revise the calculations.

The correction means that you can use less PoHs to keep a stack alive, but the results are qualitatively similar. The inefficiency of using PoH to stack aegis is mitigated by the fact that it keeps aegis you stacked by healing alive.

I open this subject because i am really confused about my result and would have a confirmation from you if i am wrong or right.

Objectif of calculation was, at the begginning, to simply calculate the %haste needed to gain additionnal cast of PoH when using Spririt Shell.
It is simple (for example 100%-7/6 = 16.67% haste to win 1 cast of PoH for 15sec) but i wanted to find a standard formula to use it on every repetitive event like Fiend, MindBender (if they follow haste effect), Hymn of hope, renew, etc... from others classes....

Formula i have reached is :
Number of times of event = ENT [ 1 + (Time effect - delay)/Time between event ]
where
Time between event = base Time between event / (1+%Haste)
delay = base delay / (1+%Haste)


==> Number of times of event = ENT [ (base Time between event - base delay)/base Time between event + (1+%haste)* base number of time of event ]
With :
base number of time of event = Time effect / base Time between event
base delay = can be 0 if the first tic is immediate after the cast (ex :Mindbender), GCDu (if it is 1GCDu =1,5sec after the cast), time casting (if it is a heal which as to be cast (ex : PoH for SS claculation)

Means also that :
Additional times of event = ENT [ (base Time between event - base delay)/base Time between event + %haste* base number of time of event ]


NOW, the problem i have ;


For exemple for Renew :
Time effect = 12 sec
Delay = gcd (because the first tic is done 1 gcd after the cast) = gcdu / (1+%haste) = 1,5* /(1+%haste)
Time between event = Base time betwwen event / (1+%haste) = 3 / (1+%haste)

So, we arrived on the well known formula of Renew which is number of TIC = ENT [0,5 + 4*(1+%haste) ]
or also the well known formula "Number of additional TiC = ENT ( 0,5 + Base Number of Tic *%haste)

Then, based on this last formula "ENT ( 0,5 + Base Number of Tic *%haste)" which defines the number of additionnal tics, i see everywhere, more or less, the following table which define breakdowns for haste :

3 Base Tics : 16.67% 50.00% 83.33%
4 Base Tics : 12.50% 37.50% 62.50% 87,50%
5 Base Tics : 10.00% 30.00% 50.00% 70.00% 90.00%
6 Base Tics : 08.34% 25.00% 41.67% 58.33% 75.00% 91.66%
7 Base Tics : 07.14% 21.43% 35.72% 50.00% 64.29% 78.57% 92.86%
etc...


That means (and i take this data until this date) for Hymn of hope which is a 4 Tics base class, that the additional tic will be reach at 12,5% of haste like the renew.

BUT When using the standard formula i gave ,the result is different because the formula used is :
Additional times of event = ENT [ (base Time between event - base delay)/base Time between event + %haste* base number of time of event ]

Means that for Hymn of Hope, additional tic is reached for 18,75% Haste instead of 12.5% :

base Time between event = 2 sec
base delay = 1 GCDu = 1.5 sec. (first tic is given after 1 GCD)
base number of time of event = 12/3 = 4

1 = ENT [ (2-1.5)/2 + 4*%haste ] ==> %haste = 0.75 / 4 = 18.75%
(except if the base delay is not 1 GCDu but 1 sec ==> in this cas, we have 12,5%)



My Conclusion is that it is wrong to use this table and "ENT ( 0,5 + Base Number of Tic *%haste)" is true only if the "base delay" is half of the "base Time between event".


And for additionnal cast of PoH under SS, i have my result now with the généric formula which matchs to the simple calculation "%haste needed for PoH under SS = 100% - [Number of cast per 15sec / Base number of cast per 15sec]" :

6 casts 2.5 Sec base for 15sec of SS stack period
Generic formula gives same result : 16.67% 33.33% 50.00% 66.67% 83.33% 100.00% when i take :
"Additional times of event = ENT [ (base Time between event - base delay)/base Time between event + %haste* base number of time of event ]"



Sorry, for this long explanation and thank you for your feedback !
(did i miss something ?)

Blizzard has changed channeled spells specifically. With 33% haste I still get 4 ticks and no more and the total channel time is 6s.

With 33% haste I also have mind sear finish channeling in 3.75 seconds and getting 5 ticks (one every 0.75s).

Channelled spells no longer get extra ticks. I don't think this is a big. Its probably a new design. Maybe blizzard does not want the HPM of channeled spells to increase with haste.

Mindbender and shadowfiend no longer benefit from haste either.

They definately did benefit from haste until just after we got the new spirit shell. I actually tested it, because I wanted to be sure about the formula.

Thank.
I made a complete mistake and i just see IG that hymn of hope did not depend on haste no more.

For Mindbender and fiend , it is very stange because i have noticed the same thing as you about haste which has no impact (done after recording the log or heard the attack) BUT a lot of people told me that they have seen and verify IG (5.05 cata) that haste (on equipement) scales on pets.
depending on haste on equipement and haste proc with trinket, they have confirmed to see mindbender returns 14 to 15 tics.
I do not understand since i do not find same result but it is strange because people who has told me that are serious player.

I think , i have also made a mistake for the generic formula i gave even for Renew because "base delay" for renew is 3sec instead of GCD.
and my formula does not match real result.

Could you check where i am wrong to apply :

==> Number of times of event = ENT [ (base Time between event - base delay)/base Time between event + (1+%haste)* base number of time of event ]
With :
base number of time of event = Time effect / base Time between event
base delay = can be 0 if the first tic is immediate after the cast (ex :Mindbender), GCDu (if it is 1GCDu =1,5sec after the cast), time casting (if it is a heal which as to be cast (ex : PoH for SS claculation)

Means also that :
Additional times of event = ENT [ (base Time between event - base delay)/base Time between event + %haste* base number of time of event ]

When I tested it just after we got the new spirit shell, fiend scaled with haste. After a certain point blizzard changed it.
Haste definitely no longer benefits fiend. However external buffs do apply to the fiend. So totems increasing attack speed and heroism or pet haste buffs definitely affect fiend attack speed and hence they may give a better return if everything lines up properly.

I tried it dozens of times and its definately 11 attacks. The fiend is ready to attack the instant its summoned and unless the opportunity is denied it does.

===================================================================================

On a sidenote, PoH has been nerfed recently. It now no longer applies the base 30% aegis to crits. Crits only apply 30% of a crit as aegis and no other aegis...

The PoH now has a crit multiplier of exactly two, so the formula is now

base*(1+0.3*(1+mastery))*(1+crit)

This further reduces the value of keepinga aegis alive.

I have tried also during several hours and main results are 11 attacks.

But you cannot close your eyes about the log i have linked.(alone, without buff on a dummy low level)

Try N°2 at 0H26 ==> 12 tics !
and we can reproduce it at 14 or 15 tics with haste above 40% and 50% (with haste proc trinket)

I have dont link the video i have done with Fraps also during these log, but when you wotch it frame by frame, you can verify that mana jumps are conform with log recording.

There is something unclear or unstable about attack of pet et mana return.

I cant access the log I don't have a google account.

to verify what you said I did an experiment, I proced by DS haste trinket, used PI and PWS which boosted by haste to 95%. Mindbender gave me back 14 attacks. I wonder if blizzard fixed the haste scaling!

[edit] ~Yes they did!! Mindbender now scales with haste. I used PWS and I got 12 attacks. So mindbender now scales with haste! I will investigate the scaling [/edit]

At 16% haste I get 12 attacks.

At 33% haste I still get 12 attacks. (PWS)

At 39% haste I still get 12 attacks. (Power Infusion)

at 60.1% haste I get 14 attacks (haste trinket)

Thus mindbender now scales only with haste rating, it does not scale with any buffs that increase spellcasting speed or spell haste. Only effects which increase both spellcasting and melee attack speed affect mindbender. So haste rating on gear, bloodlust, the attack speed totem etc, all increase mindbender attacks, but buffs, which increase spellcasting speed, but not melee attack speed have no effect.

I tried it quite a bit looking at the log and here is what I found. I think that when the mindbender casts shadowcrawl that attack is completely unhasted.

the log looks like this (with 60% haste):

...:44 I cast mindbender
...:44 attack1
...:44 mindbender casts shadowcrawl
...:46 attack2
...:47 attack3
...:48 attack4
...:49 attack5
...:50 attack6
...:50 mindbender casts shadowcrawl
...:51 attack7
...:52 attack8
...:53 attack9
...:54 attack10
...:55 attack11
...:56 attack12
...:57 shadowcrawl
...:57 attack13
...:58 attack14
...:59 attack15

I expect 1 attack every 0.9375seconds, but I get 15 attacks and 3 shadowcrals in 15 seconds. However if each shadowcrawl attack is unhasted this is what I expect:

Which matches perfectly with what I see on the log.

If I turn shadowcrawl off as soon as the mindbender is summoned I get 16 attacks.

So basically it looks like shadowcral attacks are the reason why haste does not quite work the way we expect with mindbender.