Mastery vs Intellect for Holy priests. The math.

[Gaussian]

I thought I'd post this to settle any debate over the value of mastery for holy priests.

To begin with lets remind ourselves what Echo of Light does.
Echo of light adds a 6 sec HoT to any direct healing spell on the target. The healing done over these 6 seconds is equal to a certain percentage of the direct healing spell in consideration. The percentage itself depends on your mastery rating. Each point in mastery, that is every 100 mastery rating (because 1 mastery point = 100 mastery rating), increases the Echo of Light effect by 1.25%.

There is quite some dilemma about how to gem and enchant correctly for holy priests. I myself have seen a variety of gem configs on priests in my server, some of them amusing while others not so amusing. Here's what you should know before you spend that gold of yours on enchanting and gemming your holy priest.

Suppose you have X intellect. For the sake of ease, let X be your spellpower too, and let any arbitrary healing spell you cast generate X amount of direct healing. The question is whether gemming for mastery, as opposed to intellect is worth it.

It should be obvious to anyone who is slightly mathematically inclined that mastery being a % scaling will at some point outweigh the linear gains generated by increments in intellect.

Again, for convenience suppose we are considering choosing between +20 intellect versus +20 mastery rating.
Note that +20 mastery rating = +0.25% healing to the Echo of Light effect. This is because 20 mastery rating is one-fifth of a mastery point (reminder that 1 mastery point = 100 rating), and since one mastery point produces an extra 1.25% Echo of Light healing, therefore 20 mastery rating would do one fifth of 1.25% which is 0.25%.
So finally it boils down to calculating at what point of intellect are we indifferent between an increase of +20 intellect versus +20 mastery rating. Suppose before choosing between the two we have a mastery rating which gives Y% extra healing through Echo of Light.
If we go for +20 intellect, the new Echo of Light effect = (X+20)*Y/100
If we go for +20 mastery rating, the new Echo of Light effect = X(Y+0.25)/100
On equating these two quantities, we get
20Y = 0.25X
Now lets put some numbers to X and Y.
Suppose Y is 15, then the X that equates the above is 1200. This means that if your mastery is generating 15% Echo of Light healing, then for intellect levels greater than 1200 you will do better in pure healing output by investing in mastery than you would by investing in intellect. I say pure healing output because you do lose out on a larger mana pool, and hence a bit of mana regen through replenishment effects. Notwithstanding, lets put these numbers in context.
Usuallly, the X quantity will be larger than your intellect stat because you would have some spellpower bonus from your weapon. This even larger X tilts the balance in favour of +20 mastery even further. It should be also clear that X=1200 is a very low threshold going by cataclysm (and even WOTLK!) gear levels. Any semi-decently geared priest would have the X quantity in excess of 5000.

Gemming mastery is the way to go .. yellow slots should take +40 mastery, red ones should take +20 int +20 mastery, blue ones should take +20 spirit +20 mastery.
Enchant your gear for mastery. The results in healing output are pleasantly surprising.

Good luck, and thanks for reading !

[Combatmedic]

Imo the biggets flaw about holy mastery, is its 60% overhealing..

[yurano]

If we go for +20 intellect, the new Echo of Light effect = (X+20)*Y/100
If we go for +20 mastery rating, the new Echo of Light effect = X(Y+0.25)/100

1) Echo of Light is approximately 50% effective.
2) Echo of Light healing does not vary linearly with intellect.
3) You are ignoring the effect of intellect on every other healing spell.

TL;DR
Echo of Light is the Holy Mastery, obviously mastery boosts Echo of Light the most. When Echo of Light is ~10-15% of your healing, Intellect will always be better.

[Gaussian]

When Echo of Light is ~10-15% of your healing, Intellect will always be better.

Have a look at
20Y = 0.25 X
again

Since Y is your Echo of light healing %. Lets say you are uber geared and so Y =25. The X that equates it is 2000. I'm not quite sure on what basis you say intellect works better for pure throughput.
Looking at 20Y =.25 X , again. It should be obvious whether you want to Boost .25 of X, where X is a four digit quantity; or would you rather boost 20 times Y, where Y is a 2 digit quantity.

obviously mastery boosts Echo of Light the most

Correct that to Mastery boosts echo of light only.

2) Echo of Light healing does not vary linearly with intellect.

Precisely why you're better off boosting Echo of light by leveraging the mastery effect which is non-linear (being a percentage scaling).

[zindsoros]

Again, for convenience suppose we are considering choosing between +20 intellect versus +20 mastery rating.
Note that +20 mastery rating = +0.25% healing to the Echo of Light effect. This is because 20 mastery rating is one-fifth of a mastery point (reminder that 1 mastery point = 100 rating), and since one mastery point produces an extra 1.25% Echo of Light healing, therefore 20 mastery rating would do one fifth of 1.25% which is 0.25%.
So finally it boils down to calculating at what point of intellect are we indifferent between an increase of +20 intellect versus +20 mastery rating. Suppose before choosing between the two we have a mastery rating which gives Y% extra healing through Echo of Light.
If we go for +20 intellect, the new Echo of Light effect = (X+20)*Y/100
If we go for +20 mastery rating, the new Echo of Light effect = X(Y+0.25)/100
On equating these two quantities, we get
20Y = 0.25X
Now lets put some numbers to X and Y.
Suppose Y is 15, then the X that equates the above is 1200. This means that if your mastery is generating 15% Echo of Light healing, then for intellect levels greater than 1200 you will do better in pure healing output by investing in mastery than you would by investing in intellect. I say pure healing output because you do lose out on a larger mana pool, and hence a bit of mana regen through replenishment effects.

Interesting post, but I must point out the failure in your math. In the quoted portion you compare the added Echo of Light effect from 20 int to that of 20 mastery. With that in mind, all you have shown is that mastery increases Echo of Light more than intellect does beyond 1200 int, which I dont think anyone was trying to argue. If we consider instead the added healing from 20 int vs 20 mastery we have the following.

If we go for +20 intellect, the new Echo of Light effect = (X+20)*Y/100 + 20*spell coefficient (for simplicity I will use 1)
If we go for +20 mastery rating, the new Echo of Light effect = X(Y+0.25)/100
On equating these two quantities, we get
20Y + 2000 = 0.25X

Once again assuming Y = 15, we conclude X = 9,200, showing that Int is in fact the superior stat for increasing healing done. Now assuming instead a spell coefficient of .5 we would find X = 5,200, a number much closer to being able to be hit, but still out of reach for current gear levels. Conclusion is that in no way is 1 point of mastery better than 1 intellect since it not only gives higher output, but also has other added benefits

[Gaussian]

Once again assuming Y = 15, we conclude X = 9,200, showing that Int is in fact the superior stat for increasing healing done. Now assuming instead a spell coefficient of .5 we would find X = 5,200, a number much closer to being able to be hit, but still out of reach for current gear levels. Conclusion is that in no way is 1 point of mastery better than 1 intellect since it not only gives higher output, but also has other added benefits

I am unable to link you the wowwiki page on spell coefficients, but:

Spell coefficients for Circle of Healing, Prayer of healing, renew fall in the .5 ballpark.
I disagree with your description of 5200 as a number out of current gear levels. I have 359s on all slots except shoulder and wand, and my X is 7400 when I last checked (with inner fire).

Thanks for your post

[Deleted]

I am unable to link you the wowwiki page on spell coefficients, but:

Spell coefficients for Circle of Healing, Prayer of healing, renew fall in the .5 ballpark.
I disagree with your description of 5200 as a number out of current gear levels. I have 359s on all slots except shoulder and wand, and my X is 7400 when I last checked (with inner fire).

Thanks for your post

Note that 20% of PoH's healing and and 87% of Renews healing isn't affected by Mastery while it is affected by Intellect. 100% of Lightwells healing isn't affected by mastery either. (based upon logs that can be anything from 20-30%+ of your healing that isn't affected by Mastery at all.)

Additionally I'd much rather have my direct healing than a 6 sec hot when someone is in danger of dying.

Also the mana gain from intellect is huge, around the value of 1 pt of spirit depending upon the length of the fight. So basically int is around the value of 1 spi+2 mastery (at least). Not much question there if you're asking me.

[zindsoros]

I am unable to link you the wowwiki page on spell coefficients, but:

Spell coefficients for Circle of Healing, Prayer of healing, renew fall in the .5 ballpark.
I disagree with your description of 5200 as a number out of current gear levels. I have 359s on all slots except shoulder and wand, and my X is 7400 when I last checked (with inner fire).

Thanks for your post

Sorry, after checking my math I realized I was completely wrong. In fact, the relationship between the value of spellpower and mastery is independent of spell coefficients. This is simply because mastery loses value at the exact same ratio as spellpower does with respect to the coefficient.

As an extra note you seem to be switching your definition of X from intellect to spellpower, so from here on I will use it exclusively as spellpower, since it is more relevant to the problem. In addition I will work just with the healing increase due to int/mastery.

One other thing of importance is that in looking over your original post I noticed you claimed 100 mastery rating = 1 mastery point. This is simply false, in reality it takes 179 mastery rating to get 1 point of mastery at 85. This means 20 mastery rating increases your mastery effect by .14, not .25

Healing gained from 20 intellect (increase in Echo of Light + increase due to spellpower), Z represents the spell coefficient
Z*(X+20)*Y/100 - Z*(X)*Y/100 + 20Z
or simply
Z*(20Y/100+20)

Healing gained from 20 mastery
(XZ)(Y+.14)/100 - XYZ/100
or simply
.14XZ/100

Equating these 2 we have
Z*(20Y/100+20)=.14XZ/100
Z cancel, showing spell coefficients have no impact, leaving us with
20Y/100 + 20 = .14X/100
or
20Y + 2000 = .14X
Again assuming Y = 15 we now see X = 16,428.5 spellpower. As an additional note increasing mastery to Y = 20 raises the required X for int and mastery to be equivalent to 17,142.9, while with Y = 0, X = 14,285.7 so under no realistic scenario is it possible for mastery to come anywhere close to being equal value to intellect in output.

Going back to seeing how much healing is added from each source, assuming X = 7.4k and Y = 20,
Added healing from 20 int
Z*(20Y/100+20) = Z * 24
Added healing from 20 mastery
.14XZ/100 = Z * 10.36
This clearly illustrates that intellect is worth more than twice mastery. Some extra math will tell you that you need 46 mastery rating to get the same output increase as you get from 20 intellect.

[Ynna]

Well, the debate wasn't really Mastery vs. Intellect.
Furthermore: Intellect affects everything we do. Then there's the thing with a lot of Mastery being overhealing.
Add to that that Healing has always been rather difficult to math out I'm not very sure this will change how Holy Priests will gear.

[Arlee]

Ummm, not to be captain obvious or anything but.... It should have been a tipoff something was wrong when you came up with a secondary stat being more important than a primary stat... if that actually were the case that would have meant blizz totally broke their game

[Peppercat]

I'm really sick and tired of people trying to provide 'math' to settle something which doesn't need to be settled.

Int > Mastery.

I'm not going to flame anyone who thinks otherwise, but...if you're going to let napkin math giving someone a largest x scenario be the deciding factor to how you reforge/gem, you're a moron.

[Zodisius]

I don't see why your getting so upset over math. This has been around for a long time and has played a huge factor in deciding which is better for the min/max people out there. I'm all for a bit of math and trying to figure out which is better, but people have already shown that Int>Mastery. Walking in here and saying "giving someone the largest x scenario" and then saying they would be a "moron" if they tried to min/max doesn't help. I could say, "I'm sick and tired of people saying haste makes me crit more often. Crit increases my crit chance so I will crit more often! It doesn't need to have math to figure that out!" Even though math has shown that haste is better and allows you to crit more often because you can cast more spells in a period of time. People are always going to be looking at the math and deciding which is better. No reason to bash.

[Grizzlokk]

The keyword is 'math' with the quotes. Nobody has a problem with solid math, it is outlandish claims like the OP has made that is the problem. Even if it was solid math that showed something we already know, it would be better.

[Töasty]

Not sure if this is really pertinent to this discussion but:

One issue with mastery that I have noticed, is there are break points where mastery does not bump up the % of echo of light until certain points, it appears to be at the x.00 and x.50 points of mastery rating. So basically if you have x.49 mastery and can reforge the mastery on one piece of gear to haste and still be > x.00 mastery, you will still get the same % of echo of light and will gain a little haste. Better to utilize stats than waste them.

[Deleted]

Not sure if this is really pertinent to this discussion but:

One issue with mastery that I have noticed, is there are break points where mastery does not bump up the % of echo of light until certain points, it appears to be at the x.00 and x.50 points of mastery rating. So basically if you have x.49 mastery and can reforge the mastery on one piece of gear to haste and still be > x.00 mastery, you will still get the same % of echo of light and will gain a little haste. Better to utilize stats than waste them.

That's just the tooltip - the actual value scales without break points.

[underdogba]

Each point in mastery, that is every 100 mastery rating (because 1 mastery point = 100 mastery rating), increases the Echo of Light effect by 1.25%.

1 mastery point = 179.28 mastery rating (source: http://elitistjerks.com/f15/t29453-c..._85_cataclysm/), therefore your argument actually proves that Intellect is better.

Furthermore, Intellect cannot be judged only by looking at its impact on Echo of Light. To answer the kind of question you're trying to answer, you have to create some kind of model that takes into account everything a typical Holy Priest is going to do in a fight based on plausible casting assumptions.

[ramennoodleking]

And today I had to Guardian Spirit my tormented body for fear I might a die a little more inside as I weep bitterly for some of the holy priests out there in the wide World of Warcraft.

[[-Spiritus-]]

Furthermore, Intellect cannot be judged only by looking at its impact on Echo of Light. To answer the kind of question you're trying to answer, you have to create some kind of model that takes into account everything a typical Holy Priest is going to do in a fight based on plausible casting assumptions.

...which is why healcraft is such a royal pain in the you know what.