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Carnathagia

Cataclysm Healing Priest Theorycrafting

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Thanks, while obviously not a real run that still allows us to start looking at the value of surge of light. During your 212 sec test (3mins 32 secs) you cast a total of 99 spells and look to have clipped pennance once as you are one tick short as far as I can tell. This would probably function as a fairly good proxy for single target tank healing in a raid however.

You cast 64 smites and got 5 free flash heals which is above the expected 3.84 predicted by the average. You got a proc every 42.4 seconds.

A flash heal averages 8800 per sec and takes one GCD of about 1.3 secs (guess based on assumed haste) for a base heal of ~11440 so you got 57200 free healing which took 6.5 seconds to cast. If we used that time for more smites we would get about 3.5 smites in which represent 24850 healing and a moderate mana cost. Thus you get a whapping 32350 extra healing or about 152 hps boost along with the currently unquantifiable mana savings (archangel is possibly bugged right now).

This is a best case scenario and I would expect a 5 man or 10 man raid to have less time spent smiting and a proc rate closer to the average. Even as it stands at 40 secs procs are spaced to far out to be of much use and require heavy UI support to remember to use them in a real world environment.

At this stage I do not consider surge of light worthwhile for an attonement spec based on this parse. If someone wants to do the math on the mana savings I would be interested.

*edit* lastest build just popped up on MMO champ and atonement got dialed back.

Atonement now heals for 40/80% of the damage dealt, down from 60/120%. If the Priest is healed through Atonement, the effect is reduced in half.

This may make SoL more important as it significantly improves the delta in healing compared to smite but I remain very concerned about the proc being to unreliable and occuring at far too low a level.

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Or is it more of a situation spell like Pain Suppression?

Unless a glyph appears that significantly lowers its cooldown, Pw:B will be purely situational due to the 3 minutes cooldown, meaning you usually have it once in a fight (maybe twice if there's good opportunity early).

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Haste rating decreases the period length between ticks from channeled spells and heal over time effects according to the same formula, replacing the Base Cast Time with the channeling time or tick period. Durations are determined from the period times the number of ticks. Extra ticks are added at haste percentages where the duration with an additional tick is closer in absolute value to the base duration. This happens when (1+Haste*.01) = Base duration + .5 * tick period) / Base Duration. For instance, Renew gains an additional tick at (12 + 1.5) / 12 = (1 + 12.5 * .01).

I really don't know why you came up with such a confusing formula or what exactly your formula means. The way I see it, its very very simple. Please correct me if I am wrong. Edited due to the information in the two posts that follow

Base spell duration = B

Base tick interval (i.e. how long between ticks) = T(0)

Hasted tick interval = T(h)

Haste = H (this is a real number between 0 and 1)

Number of ticks with zero haste = m

Number of ticks with haste H = n

Int(), is an operator that returns only the integer part of any real number it operates on (this works in an excel spreadsheet)

T(h) = T(0)/(1+H)

Partial ticks are rounded to the nearest integer (less than half ticks are lost, more than half ticks are gained), hence

n = Int[ B/T(h) + 0.5 ]

With some rearranging and using the relationship m = B/T(0) we come up with

n = Int[m*(1+H) + 0.5]

This formula will give you the exact number of ticks for a given haste value. In other words the condition for haste adding a new tick is that the quantity (0.5+m*H) is an integer, i.e. when H = (I-0.5)/m, for I = 1,2,3, etc. This is the same as the formula in the thread you quoted.

[edited m=5 changed to m=4]

For renew with m = 4 you get a new tick when H = 0.125, 0.375, 0.625 and so on (0.25 intervals).

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

I don't understand the way you are calculating SoL gains Ellyh. Why are you comparing SoL flashes with smiting. That does not really help us understand the value of SoL. If you are running an atonement spec you will probably want 5 smites per 30 seconds. If you also cast h Heal spells per 30 seconds then the total number of SoL procing spells is 5+h. Assuming that you cast n procing spells between getting a proc and using it and that n is small (taking the average is not strictly accurate, but its good enough if n is small), which is a safe assumption given that you also have PWS, penance and train of thought then the chance of an SoL proc per 30 seconds is

S = (5+h)/n*(1-0.94^n) per 30 seconds.

As an arbitrary example lets take h = 5 and n = 2 which gives S = 0.582 procs per 30 seconds or 0.097 procs per 5 seconds.

In the time it takes you to cast a flash you could cast 0.75 heal spells. So you save 0.75 of the mana cost for heal spells and gain the benefit of the increased HPS of a full flash heal compared with 0.75 of a heal spell. Alternatively you save the full mana of a flash heal at the cost of a possible FH crit. From there you can calculate the mana gain and HPS gain/loss of SoL per 5 seconds.

The value of SoL has to be ultimately compared with the value of other talents that you can get. The candidates are improved renew, mental agility and veiled shadows. My gut feeling is that veiled shadows will turn out to be the best option. SoL may be more useful for holy, due to serendipity

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Oh I see, so my assumption that you lose partial ticks was wrong. More than half partial ticks are gained and less than half partial ticks are lost. This is extremely easy to add to the formula. All you need to do is change it to

n = Int[m*(1+H) + 0.5]

Adding +0.5 to to a number operated on by the int() operator makes it round up to the nearest integer, which is exactly the behaviour we want. Basically haste adds an extra tick when the quantiy (m*H + 0.5) is a positive integer, i.e. the haste values can be found by substituting positive integers for I in the formula

H = (I-0.5)/m

Thus for renew with m = 4, [edited: m=4 instead of m=5]

I = 1 --> H = 0.5/4 = 0.125

I = 2 --> H = 1.5/4 = 0.375

and so on, so you get an additional tick at haste values of 10%, 30%, 50% and so on

As you can see the unhasted number of ticks is sufficient to completely determine the values of haste at which you get an extra tick, making the formula in your original post needlessly complicated (its also wrong due to a missing parenthesis).

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Havoc, I am just running a crude model of tank healing using smite instead of heal to get best case numbers for the value of surge of light. The numbers of casts are based off Carnathagia's log of healing a lifetapping warlock and would represent a best case performance for smite healing similar to when an off-tank and his healer take an obnoxious mob away for some private time while the rest of the raid deals with somthing more important. Specifically I want to determine the upper bound on likely numbers of SoL procs and take it from there to derive an approximate measure of the HPM and HPS improvements generated by spending points in SoL.

I was not using heal as pre todays build smite was higher hps than heal and with the shorter cast time procced SoL more often. I was also using a crude model where a SoL proc was instantly consumed rather than held for a spike but given the very low proc rates we are looking at I consider that this is a good first order approximation anyway as you will get very few overwrites of SoL procs while holding them.

Once I have time I want to redo the hps/hpm gain for SoL as a % gain over continuing to spam smite so that we can see the absolure upper bound of SoL performance. Again using the example parse I would expect that Mental Agility would be a superior mana talent than SoL and I need to math it out in this example.

I do not understand your proc calculation formula. What does n represent? In your example you are casting 7 potential proccing spell in 30 secs which is approximately a 35% chance of getting a surge this is a lot smaller than the 58% chance your equation calculates.

I get that figure by calculating the chance of NOT getting a proc which is 94% after once spell so for 7 casts we have 0.94to the 7th power. This is a 0.648 or ~ 65% chance of not getting a proc.

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I do not understand your proc calculation formula. What does n represent? In your example you are casting 7 potential proccing spell in 30 secs which is approximately a 42% chance of getting a surge this is a lot smaller than the 58% chance your equation calculates.

I think I did not explain n properly. Think of it as the number of SoL procing spells you might cast on average before considering whether to use an SoL flash. Effectively that means you are grouping your proc chances into groups of n casts rather than considering every cast. This is a better way to handle overwrites, which are going to be infrequent, but still noticeable, as my example demonstrates.

You might want to use heal instead of smite for two reasons (1) to heal the person who is not currently of lowest health (2) to save mana. Also you will probably prioritise PWS, penance, flash heal and greater heal over smite in any conditions when healing is challenging, but you will probably still want 5 smites/30 secs for archangel.

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Ok recaclulating the chance of not getting a surge for 10 casts in a 30 second period (22.5 secs casting pre haste) as your example indicates. We now get get 0.94 to the power 10 which is 0.538 or a 46% chance of at least one proc, still much smaller than the 58% proc chance your formula calculates.

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10 spells in groups of 2 = 5 double chances. You are not likely to cast 10 spells before considering an SoL proc, 1-3 is a more likely number on average. My understanding is that you don't have to cast 5 smites in a row in order to stack evangelism. You just need to cast 5 smites before your archangel CD runs down.

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Grouping does not matter as I am assuming 100% efficient usage of procs. The fact remains that in any group of 10 cast you only have a 46% chance of getting any procs to use at all. Therefor in 100 iterations you would get 46 with a proc to spend with about 20 with 2 procs to spend etc as a series (taylor series calculation?).

Your point about overlap is correct but only applies in the small % of cases where you get 2 procs in your 30 second window and they occur both withing the life time of the proc and before the proc is used. I would estimate this to be functionally close to 0 as most of the filler spells will be non-proccing onces such as shield, GH, pennance etc.

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Grouping does not matter as I am assuming 100% efficient usage of procs. The fact remains that in any group of 10 cast you only have a 46% chance of getting any procs to use at all. Therefor in 100 iterations you would get 46 with a proc to spend with about 20 with 2 procs to spend etc as a series (taylor series calculation?).

Your point about overlap is correct but only applies in the small % of cases where you get 2 procs in your 30 second window and they occur both withing the life time of the proc and before the proc is used. I would estimate this to be functionally close to 0 as most of the filler spells will be non-proccing onces such as shield, GH, pennance etc.

Ahhh I can see where you are going wrong. You are calculating the chance of getting at least one proc . That is not what you want to know. Basically you are not assuming 100% efficient use of SoL procs, on the contrary you assume that you get 10 chances to overwrite every time. This is why you are coming up with a 4.6% chance per spell of getting a proc instead of 6%. You want to know the number of procs . If you cast 100 procing spells with no overwrites you will get 6 SoLs on average since you have 6% chance per spell. Basically the correct way of calculating the number of procs is 0.06 procs per spell. Its just like calculating the number of criticals. If however you have groups of say 2 casts then you have 5.86% chance per spell, since there is now a chance to overwrite within the group of 2.

If you have a short window of opportunity to stack evangelism, you might decide to ignore an SoL proc. Also if you are casting back to back smite or heal, then you won't know you have a proc until you have already begun your next spell. I think having a way to handle overwrites is important. Its worth noting that n is an average so its not an integer. It could be 1.5 or 1.2 even. It will depend on your exact pattern.

edit: If you want to assume 100% usage then the calculation is dead simple:

SoL procs per 5 seconds = 0.06*5*n/T = 0.3*n/T, where n = number of procing casts over over a period of T seconds.

If you are casting 7 procing spells per 30 seconds that would be 0.07 procs per 5 seconds 7% of an fheal per 5 seconds.

I think if you just cast PWS every 10 seconds, that is 5% of a PWS every 5 seconds. I think mental agi will end up being of similar value to SoL for an archangel spec, but I think veiled shadows will be a lot better than both

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In your spreadsheet tab Talents and Buffs cell D25 needs to be updated to

=SUM(C22,B19,D19,B16:E16,C13:E13,B10:E10,B7:E7,B4: D4)

the actual change is B16:E16 from B16: D16

I'm having to put a space between : D16 since the forum is converting the :D into a smile

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OAll you need to do is change it to

n = Int[m*(1+H) + 0.5]

Additionally, the haste caps are easy to compute:

you get k more ticks for a hot/dot that has m ticks at 0% haste if your haste is higher than (2k-1)/2m.

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Umm, well with today's note, all your calculations are probably going to have to go out the door anyway...

Spell Changes in 13117

# Atonement now heals for 40/80% of the damage dealt, down from 60/120%. If the Priest is healed through Atonement, the effect is reduced in half.

I don't have a PTR account, but I'm guessing disc priests were indestructible in PvP, hence the nerf.

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and so on, so you get an additional tick at haste values of 10%, 30%, 50% and so on

The problem is that you gain additional renew ticks at 12.5% haste and 37.5% haste. I just retested to confirm this, at 12.46%, 12.51%, 37.33%, and 37.62% haste values. The behavior follows that Renew will have as many ticks as will make the duration the closest in absolute value to 12. I would love to see a formula that will give the number of ticks for a given haste value.

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How many ticks does base renew (without haste) currently has ? Glyphed and unglyphed ? The value you present match perfectly with a 4 ticks renew.

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Renew is base 4 ticks, 3 second period, 12 second duration. The Glyph of Renew is now 10% additional Renew healing. That was the problem. Thank you, I didn't see it earlier.

n = Int[m*(1+H) + 0.5]

h=0.124, m=4

int[4*(1.124)+5] = int[4.996]

h=0.125, m=4

int[4*(1.125)+5] = int[5]

h=0.373, m=4

int[4*(1.373)+5] = int [5.996]

h=0.375, m=4

int[4*(1.375)+5] = int [6]

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I have been working on the value of surge of light for a disc atonement spec and the proc overwrite issue and have concluded the following points:

• even playing very badly the loss of procs from accidental overwrites is very low, maybe 12% worst case which is about 0.1 ppm

• Even at high smite/heal usage it is only very very marginally better than 2/3 mental agility in terms of mana efficiency but is unreliable and spiky by comparison.

• Even at high smite/heal usage 2/3 points in Darkness for 2% haste is a better throughput tool.

• Even at high smite/heal usage you will average just over 1 proc per minute.

End result is that even in the most favourable circumstances I can envisage SoL is always the wrong talent to take no matter what you need be it efficiency or throughput. I have not done the math for a holy smiter but assume similar results would obtain.

Math Follows for those that care.

All math is done at 0 hastefor convenience of calculating but all values scale 1-1 with haste so the conclusions should be sound.

Overwriting procs

First lets look at the issue of calculating the proc over-write. Formulas previously in the web don't seem correct to me and give strange numbers when I run them so we re-derive the formula from principles.

C = number of proccing casts (heal & smite)

N = average number of proccing used before using the Surge of Light

Pc = proc chance: currently this is 0.06 per cast

P = total average number of procs (C * Pc) = (C * 0.06)

Pl = procs Lost

Pr = procs remaining (P - Pl ) This is the value we most want.

Note: When playing a priest well the value of N should never be more than 1 because the HPM and HPS of spending the surge is much greater than the HPS/HPM of either smite or heal. The value on N is only one if you are chain casting smite/heal and don't have time to react to a proc until 1 cast after it is triggered. This is a minimum of 1.5 seconds even with high haste and is well within the capabilities of good players.

Procs Lost.

A proc is lost whenever the spell following a proc also causes a proc. Therefore for a single spell immediately after a proc Pl = 0.06 * N (proc chance * probability of the spell cast being capable of causing a proc)

For a series of casts C the number of procs lost is therefore Pl = 0.06 * N * P the number of procs lost is proportionl to the total number of procs occuring.

From above we see that:

Pr = (P - Pl )

Pr = (C * 0.06) - Pl

Pr = (C * 0.06) - (0.06 * N * P)

Pr = (C * 0.06) - (0.06 * N * C * 0.06)

Pr = (C * 0.06) - (0.0036 * N * C)

Using this formula we can now determine the total number of procs that will occur over a period of time with C proccing casts and a N probability of following a proc immediately with a proccing cast.

For the purposes of determining the value of the surge of light talent I am taking a hypothetical priest with 5000 spell power casting 20 proccing spells per minute which takes up 40 seconds or 2/3 of the casting time. This is about as high a number of casts/min as I believe it would ever be possible to get in real raid play and can be taken as the absolute best case scenario for the value of surge of light.

I am assigning a best guess value of N as 0.8 because you are more likely to cast proccing spells consecutively. Thus the number of procs this priest gets to use is.

Pr = (C * 0.06) - (0.0036 * N * C)

Pr = 20*0.06 - 0.0036 * 0.8 * 20

Pr = 1.2 - 0.0576

Pr = 1.1424 usable procs per minute.

Even if we say the priest is playing incredibly badly with an N value of 2 they will still get 1.056 procs per minute or 92% of what our optimally playing priest got. They even get 88% of the theoretical maximum number of procs to spend. The reason we loose so little is because of the low absolute proc chance which is why we all hate the talent in the first place.

Value of SoL as a mana saving tool.

For our hypothetical priest we have 1.1424 procs in a one minute period. The mana cost saved is what would have been cast if we were not spending a GCD on the SoL procs. So taking the more expensive spell (smite) and assuming we are chain casting we must work out the mana/sec of casting smite and apply that saving to the 1.5 sec gcd of spending the surge.

According to my sources a L 85 priest has 20590 base mana at 85 and Smite costs 3088 mana with a 2 secs to cast. So for every surge we save 1.5/2 * 3088 mana.

So in one minute our hypothetical priest has therefore saved 1.1424 * 3088 * 1.5/2 = 2645 mana or 220 mp5 in todays terms.

However if the priest had instead put those 2 points into mental agility they would have made savings on PoM and shield which most priests cast as close to cooldown as possible.

if we assue 4 shields and 5 PoMs per minute (not unreasonable to me) the 7% mana savings on these spells is

4 * 3912 * .07 + 5 * 3706 * .07 or 2392 mana saved. This is 199 mp5

It is clear that 3/3 mental agility is going to be much better than SoL and even 2/3 is better when you are casting fewer proccing spells.

Value of SoL as a throughput tool

Taking the same priest as before with the same casting pattern how does SoL compare to taking 2/3 darkness (1% haste per point)

This priests average flash heal will be 10539 healing.

If you were not casting a SoL we assume you are casting Smite as it is lower throughput than heal and gives the biggest value to SoL.

Smite for this priest heals for 3567 pre crit using the info from the very latest built (80% of damage - healing)

again normalizing for cast time we get 1.5/2 * (10539 - 3567) * 1.1424 = 5973 extra healing per minute. This is 99 hps gain.

This is a 5.5% increase in throughput over non crit smite spam but smite is our worst hps spell by a large margin. 2% haste on our greater heal gives a 112 hps gain and 140 hps gain on flash heal. These haste gain will only get bigger as crit increases so my conclusion is that even at high SoL proc rates 2% haste is a better throughput tool than surge of Light.

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There is two points for SoL, (which I agree, is not really good talent):

1/ If you lack both hps and hpm, 2 points in Sol seems to be better than 1 in haste and one in Mental Agility. Recall also that if we have some "triage" time and are short on mana, additionnal hps is a slight increase in hpm, because we need less often to use other heals than Heal / smite with atonement.

2/ SoL is an instant, and experienced healers know the value of instant heals, though this value should decrease in Cataclysm if the raid spend some time wounded and death are less instantaneous. In fact, the instant nature of SoL is the main reason many holy priest use this talent nowadays ! I must say however that current SoL is fairly reliable. It will not be always available, but it's uptime is high enough for you to consider the option when you need it. Values around 1 ppm makes it absolutely not reliable.

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Currently on the PTR divine aegis max absorb has a direct correlation with spellpower (Int). With 4569 spellpower the most absorbs I can accrue is 6508. (at level 80) It seems mastery is not affecting divine aegis at the current time.

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I can't speak for the PTR, but Beta does not exhibit this behavior at all. Divine Aegis absorbs are 30% of the critical heal amount * Absorption Mastery. It will continue to stack when refreshed with whatever value it held previously. It capped out for me at 20% of my total health (17035 with 85175 HP and 15411 with 77055 HP). Multiple Divine Aegis' from different Priests will not stack, but instead create 2 separate buffs, which can each stack up to 20% of the casting Priests' health.

With 27.7% mastery, Penance critical for 7481 produced 7481*0.30*1.277 = 2865 Divine Aegis

Seconds later, a 8965 critical Heal added 8965*.3*1.277 = 3434 additonal absorption to my Divine Aegis for 6300.

divineaegislog.jpg

divineaegislog2.jpg

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The current value for Atonement on the PTR is the same as Smite so the formula [(653:732 + SP * .714) * Twin Disciplines] from the OP applies to i

Also, Prayer of Healing has had its cast time reduced, so its HPS should be slightly higher (in the region of 1000 more than current live values, other stats notwithstanding).

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Value of SoL as a throughput tool

Taking the same priest as before with the same casting pattern how does SoL compare to taking 2/3 darkness (1% haste per point)

This priests average flash heal will be 10539 healing.

If you were not casting a SoL we assume you are casting Smite as it is lower throughput than heal and gives the biggest value to SoL.

Smite for this priest heals for 3567 pre crit using the info from the very latest built (80% of damage - healing)

again normalizing for cast time we get 1.5/2 * (10539 - 3567) * 1.1424 = 5973 extra healing per minute. This is 99 hps gain.

This is a 5.5% increase in throughput over non crit smite spam but smite is our worst hps spell by a large margin. 2% haste on our greater heal gives a 112 hps gain and 140 hps gain on flash heal. These haste gain will only get bigger as crit increases so my conclusion is that even at high SoL proc rates 2% haste is a better throughput tool than surge of Light.

With the change to Atonement granting 50/100% I used Ellyh's numbers and got 1.5/2 * (10539 - 4459) * 1.1424 = 5209 extra healing per minute. This is ~87 hps gain. 2% haste is still better in my opinion.

Seems like our last two points are pretty easy to find homes for... Veiled Shadows for mana issues or Darkness for throughput.

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Here is the latest version of the spreadsheet. (Updated in OP also)

  • A few error fixes.
  • The upcoming updates to Atonement at 50% per point and the reduced cast time of Prayer of Healing are added.
  • The raid buffs and debuffs should be working, and Smite will benefit from appropriate target debuffs.
  • Surge of Light is added to the formulas and to the options, which if selected will calculate your available procs and use them all within your rotation. As demonstrated by Ellyh, the result is quite small, and I haven't modeled lost simultaneous procs.

If you have any feedback for the spreadsheet and its modeling, feel free to PM me or post here.

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I have a question in regards to the value of the damage and healing done by smites. Will the value of the healing + smites from 2 atonement priest be comparable with the value of the DPS and healing of one pure DPS and one pure healer?

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