Hello, it's my first post here. I've been lurking here for a while and I think it's time to give it a shot and try to contribute something, even if it's not 100% correct. I forgive in advance for oversights or imperfections as I'm pretty new to theorycrafting and holy paladins in general. I hope you can give constructive feedback so I can correct my mistakes.
What I've been trying to do is to lay down some napkin math as to get a rough estimate of stat values, with the exception of Spirit (which has already been discussed in detail in the previous pages).
For simplicity, my calculations assume full raid buffs, and no procs or cooldowns of any kind are involved.
My focus is on single target healing as it's the easiest to model.
Intellect
As stated by Nodrak, buffs give a 1.1025 multiplier to intellect in spellpower calculations, which in turn receive a 10% overall bonus. So the additional spellpower gained from X points of Intellect is derived from:
SP = ((INT + X) * 1.1025 + WEAP_SP) * 1.1 = (INT * 1.1025 + WEAP_SP) * 1.1 + X * 1.1025 * 1.1 = BASE_SP + X * 1.2127
So each additional point of intellect gives 1.2127 additional spellpower. INT is the unbuffed intellect of the character and WeaponSP is the spellpower on gear.
From now on, I start to get less confident about my calculations...
We know that
[Walk in the Light] gives a 15% bonus to all healing,
[Divinity] Gives a 6% bonus to all healing,
[Glyph of Seal of Light] gives a 5% bonus to all healing and
[Conviction] gives a 9% bonus to all healing (if we assume 100% uptime). Assuming all of these bonuses stack multiplicatively (EDIT: they don't. Even if the values are different, the relative results should stay the same), the overall bonus to healing is:
1.15 * 1.06 * 1.05 * 1.09 = 1.3951
Knowing this, and using the spell coefficients provided by Nodrak (base values are averaged), we get the following values for our single target healing spells:
FoL = (7328 + SP * 0.8632 ) * 1.3951 = 1.3951 * (7328 + BASE_SP) + X * 1.3951 * 1.2127 * 0.8632
HL = (4400 + SP * 0.432 ) * 1.3951 = 1.3951 * (4400 + BASE_SP) + X * 1.3951 * 1.2127 * 0.432
DL = (11733 + SP * 1.15306) * 1.3951 = 1.3951 * (11733 + BASE_SP) + X * 1.3951 * 1.2127 * 1.15306
HS = (2738 + SP * 0.2689 ) * 1.3951 * 1.3 = 1.3951 * (2738 + BASE_SP) + X * 1.3951 * 1.2127 * 1.3 * 0.2689 (Assuming 3/3 [Crusade])
WoG = (6399 + SP * 0.627 ) * 1.3951 * 1.1 = 1.3951 * (6399 + BASE_SP) + X * 1.3951 * 1.2127 * 1.1 * 0.627 (Assuming [Glyph of Flash of Light])
Following Nodrak's convention, if we set X = 100 Intellect, and if we ignore for now critical heals, the increase on the amounts healed by each spell will be (values are rounded):
+FoL = 146
+HL = 73
+DL = 195
+HS = 59
+WoG = 117
(I didn't account for the crit gained from +100 intellect, as it's not going to make a noticeable difference in such rough estimates.)
Even though I despise doing this, as the gains from crit, haste and mastery are relative to the amount of spellpower, some reference values for the aforementioned healing spells are needed. To do this, I set X = 0, INT = 4000 (a value attainable in mostly heroic dungeon gear) and WEAP_SP = 1729 to get 6752.9 buffed spellpower.
From this, the value of each uncritted healing spell can be easily calculated (values are rounded):
FoL = 18230
HL = 10208
DL = 27232
HS = 8259
WoG = 16318
Intellect, Haste and Mastery are indirectly affected by crit too. Even though my parses show higher crit percentages than expected (I'm hoping it's because of
[Divine Favor]), most raiders should sit at roughly 20% buffed crit. This gives a 1.1 multiplier to the gains of each stat, with the exception of crit, of course. And the average value of each heal, taking into account critical heals:
CFoL = 18230 * 1.1 = 20053
CHL = 10208 * 1.1 = 11229
CDL = 27232 * 1.1 = 29955
CHS = 8259 * 1.1 = 9085 (EDIT: This is wrong, it's not accounting for [Infusion of Light])
CWoG = 16318 * 1.1 = 17950
These reference values will be needed soon, but for now we can estimate the overall healing gains from intellect, taking into account 20% critical chance:
+FoL = 161
+HL = 80
+DL = 214
+HS = 65
+WoG = 132
Haste
I follow again Nodrak's convention of using 100 haste rating, corresponding to 0.78% haste.
Haste
should stack multiplicatively with the 9% haste given by
[Judgements of the Pure], the 3% haste given by
[Speed of Light] and the 5% haste given by raid buffs, so the buffed haste value is:
0.0078 * 1.09 * 1.03 * 1.05 = 0.0092
On a given timespan, 1% more haste will (on average) net 1% more healing, and applying this principle to the reference healing values calculated before (CFoL, CHL, CDL...) will get the increased healing for 100 haste rating:
+FoL = 184
+HL = 103
+DL = 276
+HS = 0 (Direct effect of haste on Holy Shock is null, as it's instant)
+WoG = 0 (Same as above)
Even though it may look like haste should give more benefits than intellect, it's important to remember the statistical distribution of the heals during the fight, as the lost throughput from
[Holy Shock] and
[Word of Glory] are far from negligible as they often account for 30% or more of overall direct heals.
Crit
Again, 100 crit rating is the reference value, which corresponds to 0.5578% crit.
Nothing relevant to my knowledge affect crits, so we can calculate the average increment given by 100 crit rating using the reference uncritted heal values (FoL, HL, DL...). Crits heal for 50% more so it's just a matter of multiplying by 0.005578 * 0.5:
+FoL = 53
+HL = 28
+DL = 76
+HS = 23
+WoG = 45
Crit seems incredibly awful, and is the main reason why I ask for feedback, as in my opinion it's not possible for a stat to have such a low value in comparison to haste or intellect.
EDIT:
[Infusion of Light] should increase the value of crit, by how much I still have to find out (thanks to Drekor for pointing that out).
And there's obviously the mana saving component of Crit (when it doesn't result in overhealing), altough we could say also haste can result in mana saving by allowing more frequent usage of efficient but weak heals. Crit also somewhat interact with mastery by allowing larger shield, and that can factored into the calculations by setting a reference mastery value as it's been done for intellect and crit (thanks to thedudeabides for pointing this out).
The value of crit is also slightly increased by
[Protector of the Innocent] healing through the beacon.
Mastery
Mastery rating has the same conversion factor of crit rating, so 100 mastery rating will buff
[Illuminated Healing] by 0.5578%. In the best possible case, the absorb can be seen as a "deferred" heal, healing a small part of the next damage taken. So the value of mastery can be calculated similarly to the one of crit, but using the reference "critted" heals (CFoL, CHL, CDL...):
+FoL = 112
+HL = 63
+DL = 167
+HS = 51
+WoG = 100
It's important to note that
[Illuminated Healing] doesn't proc from heals generated by
[Protector of the Innocent], the beacon and Holy Radiance, and given its short duration and the fact that the shield is easily overwritten, the effective value is much slower.
Weighting
To estimate the relative value of each stat, I define a distribution on the healing spells, to account for how much of a loss is for haste not affecting instant heals or mastery only affecting direct heals. This step is entirely arbitrary, as the distribution will vary greatly between different fights, but it wasn't my goal to provide absolute answers.
My chosen distribution is:
FoL 5%
HL 24%
DL 32%
HS 20%
WoG 19%
(Direct heals account for 50% of overall healing.)
So the weighted average of the incremental gains we estimated before are:
Int: +134
Haste: +122
Crit: +47
Mastery: +104 (Only direct heals)
Mastery: +52 (Direct heals account for 50% of overall healing)
Which gives a rough stat weighting of:
100 Int = 110 Haste rating = 285 Crit rating = 129 Mastery rating (100% direct heals) = 258 Mastery rating (50% direct heals)
If this is correct (and that's a big IF), it should allow some better theorycrafter to work out the other small details and maybe integrate Spirit to give a better overall picture. It should also be easy to put this stuff into a spreadsheet or software to allow customization for base intellect and spellpower values, crit and healing spell distribution. In any case, the math is very simple and it's easy to derive the values for specific configurations.