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Cataclysm Healing Priest Theorycrafting


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#41 Elimbras

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Posted 01 October 2010 - 04:15 PM

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

#42 Carnathagia

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Posted 01 October 2010 - 07:03 PM

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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#43 Ellyh

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Posted 01 October 2010 - 10:59 PM

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.

#44 Elimbras

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Posted 01 October 2010 - 11:50 PM

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.

#45 Svena

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Posted 02 October 2010 - 10:49 AM

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.

#46 Carnathagia

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Posted 02 October 2010 - 07:52 PM

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.


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#47 Ultimoron

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Posted 03 October 2010 - 07:38 AM

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).

#48 Viper45

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Posted 04 October 2010 - 10:20 PM

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.

#49 Carnathagia

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Posted 05 October 2010 - 06:57 PM

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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#50 Gamroll

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Posted 07 October 2010 - 01:30 PM

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?

#51 erragal

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Posted 07 October 2010 - 03:34 PM

One discipline smite priest is equal to a full healer (barring heavy raid healing encounters) and likely to be 15-20% of a dpser in the best case scenario. You won't be chain smiting the entire encounter, not anywhere close to that. Smite replaces your generic heal spell, gives controllable extra throughput and mana regen from archangel, and a lower penance cooldown through Train of Thought. The primary drawback is that you cannot control the target of your atonement heal.

The largest problem will be convincing the general public that an atonement-specced discipline priest is just a healer that adds a trivial amount of extra DPS.

#52 TrlstanC

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Posted 07 October 2010 - 03:58 PM

The primary drawback is that you cannot control the target of your atonement heal.


I never thought of this as a drawback for atonement, but rather a feature. It's supposed to heal the lowest health target (do we know if it's %health or abosulte health?), which still won't always be the optimum target for a heal, but is way better then a random target, and since the target is chosen at the end of the cast as opposed to the begining (like a regular heal) it's definitely possible that the target will be someone who took damage after the begining of the cast and would be a better target then whoever I would've picked out to cast a regular heal on, and could very easily be the optimum target given the timing.

Atonement smite healing is probably pretty worthless when high single target healing is needed, but could be the optimum strategy when there is consistent raid wide damage - even ignoring the DPS increase. Since the heals should always be going to good (if not always best targets) where as with prayer of healing there's always the chance for a misclick, or a change of priorities during the cast.

#53 Hegen

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Posted 07 October 2010 - 04:06 PM

The largest problem will be convincing the general public that an atonement-specced discipline priest is just a healer that adds a trivial amount of extra DPS.


I think you are a bit too early with your answer.

The thing is, if it really turns out to be a trivial amount, then serious priests shouldn't use a dps spec. It's not a good idea to trade healing talents and more importantly control for something trivial.

The true answer is that currently nobody outside of Blizzard knows what kind of dps contribution a smite spec healer will usually have - because nobody has seen Cataclysm raid encounters. These plus healing composition will dictate how large your percentage of smites will be. In 10 man, for example, a 2 healer setup will - probably - see a lot less smite use than a 3 healer setup. It may also be that even in a 2 healer setup a smiter can have pretty high smite uptime if the raid is melee heavy. We just don't know these things - yet.

The simple fact is this. We are told to concentrate more. But we can only do that if we are allowed to go considerably faster.


#54 Elimbras

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Posted 07 October 2010 - 04:53 PM

I hope for the spec that atonement picks either the lowest percentage health target, or the highest absolute deficit health target, and not the lowest absolute health target. This would lead to a lot of useless heal to pets / topped melees, when the tank is wounded but not close to death.

#55 erragal

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Posted 07 October 2010 - 05:35 PM

I think you are a bit too early with your answer.

The thing is, if it really turns out to be a trivial amount, then serious priests shouldn't use a dps spec. It's not a good idea to trade healing talents and more importantly control for something trivial.

The true answer is that currently nobody outside of Blizzard knows what kind of dps contribution a smite spec healer will usually have - because nobody has seen Cataclysm raid encounters. These plus healing composition will dictate how large your percentage of smites will be. In 10 man, for example, a 2 healer setup will - probably - see a lot less smite use than a 3 healer setup. It may also be that even in a 2 healer setup a smiter can have pretty high smite uptime if the raid is melee heavy. We just don't know these things - yet.


You do know that the discipline smite spec isn't a DPS spec, right? It's not in any way intended to be a DPS specilization. You're trading one set of healing talents for another set of healing talents, in order to heal in a different style/method. Control is given up for reduced cast time, increased mana regeneration, and potentially slightly greater throughput. Archangel and Power Infusion together allow you to have controlled throughput in high damage phases, or to take some burden off the other healers and allow them mana regen time.

The point is that if atonement healed INSTEAD of doing damage, it would still be a viable spec due to these factors. In fact, if the DPS became non-trivial it would quickly be changed in some way or you'd see atonement priests stacked endlessly.

#56 Zigizi

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Posted 07 October 2010 - 05:51 PM

I hope for the spec that atonement picks either the lowest percentage health target, or the highest absolute deficit health target, and not the lowest absolute health target. This would lead to a lot of useless heal to pets / topped melees, when the tank is wounded but not close to death.


I would assume that they would use similar logic to other "low health" targeting abilities, such as a Shaman's Ancestral Awakening.

#57 Hegen

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Posted 07 October 2010 - 06:38 PM

You do know that the discipline smite spec isn't a DPS spec, right? It's not in any way intended to be a DPS specilization. You're trading one set of healing talents for another set of healing talents, in order to heal in a different style/method.
...
The point is that if atonement healed INSTEAD of doing damage, it would still be a viable spec due to these factors.


The atonement spec is the one PvE discipline dps spec, whether you use it for pure dps or for healing. There just aren't other talents in the disc tree that improve dps. Also, this wasn't the point I was making.

Regarding the second point: again, we still don't know that. It's just your assumption based on how you interpret today's beta numbers regarding raid encounters that nobody has seen. Even if you assume all numbers are final (which they aren't - there's still 2 months to go), it's not reasonable to make definitive statements regarding a full raid tier that we have no clue about.

The simple fact is this. We are told to concentrate more. But we can only do that if we are allowed to go considerably faster.


#58 lufe

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Posted 12 October 2010 - 07:03 AM

If you are going for a Disc Atonement+Evangelims+Archangel build, I recommend using this Smite macro:

#showtooltip Smite
/cast [@mouseovertarget, harm] [@mouseover, harm] [@targettarget, harm] [harm] Smite


It always ensures a successful cast, whether you are aiming at an enemy or a tank/melee, with your target, or mouseover.

#59 JMBattista

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Posted 12 October 2010 - 08:43 PM

My wife plays a disc priest and was curious about the relative value of mastery vs. INT for the sole purpose of improving PW:Shield, and since I did not find anyone trying to work out the math here I tried to do it, it appears to be roughly:
MR = SP / 1.15 - 1329.407
IE your mastery marting must be as high as MR there for INT to be worth more in terms of increasing shield's absorb value than Mastery Rating will increase its absorb value - within the assumptions of for base values / talent boosts below.

BV = 3498 // Base Value
C = 0.418 // PW:S coefficientT
TB = 1.1 // Talent boost, not assuming twin disciplines.

MB = 1.20 + MP *0.025 // Mastery Boost
MP = <user value> // Mastery Points
SP = <user value> // Spell Power ~= intellect, as stacking int gives 1:1 spell power

( (BV + (SP * C) ) * TB ) * MB = final value

This is a function of 2 variables (SP and MP), seen more clearly when represented as:
( (3498 + (SP * 0.418) ) * 1.1 ) * (1.20 + MP * 0.025)
( 3847.8 + (SP * 0.4598) ) * (1.20 + (MP * 0.025) )
4617.36 + 3847.8 * (MP * 0.025) + (SP*0.55176) + (SP * 0.4598) * (MP * 0.025)
4617.36 + (96.196 * MP) + (SP*0.55176) + (SP*MP*0.011495)

Using calculus we find that:
df/dMP = 96.196 + SP*0.011495
df/dSP = 0.55176 + MP*0.011495

Taking a second derivative gives us a 0, so there is no 'acceleration' to either Mastery or Spell Power. The first derivatives prove the intuitive assumption that the value (for purposes of power word shield) of mastery scales based on the amount of spell power you have and that the value of spell power scales based on the amount of mastery you have.

You need 179.28 Rating to equal a point of mastery @ 85 (note that MP is in terms of points not rating). So MP = MR/179.28 gives:

value = 4617.36 + (96.196 * MR / 179.28) + (SP*0.55176) + (SP*MR/179.28*0.011495)
df/dMR = 0.5365… + SP*0.0000641175 = MRincrease
df/dSP = 0.55176 + MR*0.0000641175 = SPincrease

(SPincrease) * additionalINT * 1.15 // increase per point of int
(MRincrease) * additionalMR // increase per point of mastery


Set additional INT and MR to 1 (same stat cost) and set the two functions equal to each other to find out the proper values to have SP as valuable as MR

SPincrease * 1.15 = MRincrease
SPincrease = MRincrease / 1.15
0.55176 + MR * 0.0000641175 = 0.5365/1.15 + 0.0000641175/1.15 * SP
MR = SP / 1.15 - 1329.407

#60 Niimue

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Posted 13 October 2010 - 12:03 AM

I compared your formulas to those available on the PTR for level 80 and found some differences from your equations, as below:

(1) The coefficients given for Lightwell and Serenity seem to already have spiritual healing in them. To keep the formulas as written, the coefficients should be 0.308 for Lightwell and 0.525 for Serenity. It's likely that your base values are over by 15% as well, for the same reason (I was unable to confirm for level 85).

(2) Similarly, if you pull out Shield Discipline, the coefficient for PW:B should be 5 (this corresponds to the spellbook values).

(3) The coefficient for Aspire was 0.238 and the Aspire HOT was 0.075 per tick.

(4) I found the coefficient on Desperate Prayer to be 0.496, and not 0.318.

(5) Spiritual Healing should be removed from the equation for Penance since you can't have both!

Hope this is helpful. Please note again that the above observations were off Level 80 test realm. It's unlikely, but possible, that the coefficients change at level 85.




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