# Cataclysm Healing Priest Theorycrafting

### #21

Posted 30 September 2010 - 06:59 PM

Reason for this is that best case as a newish level 85 you will get about 35 smites max if chain casting this spell. At a 6% proc rate this is 1.8 procs/min of SoL. However it is unlikely that even the best geared priest will be able to get much above 50% of time spent smiting so that cuts us down to 0.9 PPM as the smite priest is unlikley to be casting much Heal, the only other spell that benefits from SoL.

### #22

Posted 30 September 2010 - 07:11 PM

### #23

Posted 30 September 2010 - 07:34 PM

5 min encounters - if you use shadowfiend within the first minute the talent would give you a 2nd use. If you are using that much mana in the first minute to warrant using your shadowfiend, then it would be worth it.

5+ to 8 min encounters - you will get the same number of shadowfeind uses with or without the talent. The choice in this case is dependant on wether you need the mana sooner in certain encounters.

9+ min encounters - you will see benefit of an extra shadowfiend use from the talent here as well.

Point being it's a poor choice for most disc specs considering our other options for 4 talent points. Not to menion how little mana the shadowfiend is returning on beta atm. I could see a pvp disc priest going for twisted faith, but that may not even be so. With minimal hit needed to cap pvp spell hit.

**stupidity**!

### #24

Posted 30 September 2010 - 07:56 PM

I was able to sustain this for ~3 minutes, with 50% of my mana remaining at the end. My opening was Smite x5, Power Infusion, Archangel, Shield, Penance, Inner Focus + Greater Heal; then Power Infusion and Archangel on cooldown, Penance on cooldown, Power Word: Shield -> (Borrowed Time) Greater heal when Weakened Soul drops, sometimes delayed if I could get Penance with Borrowed Time, Surge of Light procs, and then Smite as filler.

Stats

[TABLE]Intellect | 3622

Spirit | 2103

Spellpower | 5874

Haste | 10.7%

Crit | 10.7%

Mastery | 11.4 (28.5%)

Combat Regen | 2087

[/TABLE]

I used Glyph of Divine Accuracy, but not Smite.

Jovavich - Arcane/Fire Mage

### #25

Posted 30 September 2010 - 08:32 PM

### #26

Posted 30 September 2010 - 08:51 PM

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.

### #27

Posted 30 September 2010 - 08:53 PM

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).

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.

### #28

Posted 30 September 2010 - 10:02 PM

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

### #29

Posted 30 September 2010 - 11:20 PM

Hamlet describes the relation in this post. But I like how your model outputs the number of ticks.

Jovavich - Arcane/Fire Mage

### #30

Posted 30 September 2010 - 11:54 PM

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).

### #31

Posted 01 October 2010 - 12:01 AM

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.

### #32

Posted 01 October 2010 - 12:17 AM

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.

### #33

Posted 01 October 2010 - 12:24 AM

### #34

Posted 01 October 2010 - 12:28 AM

### #35

Posted 01 October 2010 - 12:36 AM

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.

### #36

Posted 01 October 2010 - 01:26 AM

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

### #37

Posted 01 October 2010 - 03:27 AM

=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 into a smile

### #38

Posted 01 October 2010 - 01:33 PM

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.

### #39

Posted 01 October 2010 - 01:41 PM

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.

### #40

Posted 01 October 2010 - 02:20 PM

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.

Jovavich - Arcane/Fire Mage

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