Mad Priests on Madmortem

Ok, first off: None of the pages above have been correctly updated for lvl 80 – yet!

However, due to my first raiding adventures at 80 (yeah, naxx is a joke…) I began to wonder how intellect w/ all the shiny new buffs compares to intellect, espacially as my intellect value was still comparatively low.

The first hurdle is just finding out, what the formula is at 80. However, Ratingbuster has been updated long since (thanks Whitetooth!), so after a bit of browsing through their files, the formula becomes obvious:
(0.001 + spi * 0.005575 * sqrt(int))*5
Since we are not interested in modularity or other levels than 80, we can simplify this with a clear conscience:
0.005 + spi * 0.027875 * sqrt(int)
Another simplification we can make is dropping the leading 0.005, since we really do not care about the total value, but just the increase one point of either spirit or intellect will give us.
spi * 0.027875 * sqrt(int)
This is just about one tenth of what we need though, since especially intellect gains most of its value through correlated effects like replenishment or critical strikes that trigger serendipity or holy conc.

Replenishment

causes up to 10 party or raid members to gain 0.25% of their maximum mana per second

We are going to make a couple of assumptions at this point: First and foremost, we will assume replenishment is always up (this requires a certain amount of shadow priests, ret paladins, etc in range and causing damage). Second, we will assume a rather boring 14/57/0 build, since I am not really interested in disc priests at this point Of course raid buffed ‘n’ stuff is also assumed.
So, what do we gain from one point of intellect?
The mandatory 1 int = 15 mana rule has to be modified by kings, so we will have to say 1 int = 16.5 mana.
Therefore:
1 int = 15 mana + mana from kings
1 int = 16.5 mana
1 int = 16.5 * 0.0025 * 5 mp5 from replenishment
1 int = 0.20625 mp5 from replenishment

Shadowfiend
The shadowfiend ideally does 15 hits each regenerating 4% of your maximum mana – this means you have a “mana regen” of
1 int = 16.5 mana
1 int = 0.6*16.5 / 5 min
1 int = 0.165 mp5 from Shadowfiends

Holy Concentration
Researching this was pretty annoying, because I oversaw one thing: Although the factor is 0.00006 – each class gets a different amount of crit chance granted “for free”…
However, the result is pretty simple:
1 int = 0.00006 crit
Note, that this equals to 0.006% in case you were wondering

Now, what do we gain from this?
Essentially we have to look at two different cases: AoE healing and single-target healing.

During AoE healing, we ideally will hit 6 targets (CoH glyph & hunter pet in your group rocks…), but due to all those pesky problems with range (and actually having someone with a pet in your group and in range) we will assume an average of 5 hits.
Why are we talking about this? Because you can procc SoL of a CoH hit!
1 int = 0.00006 crit
1 int = 0.00006 * 5 targets
1 int = 0.00006 * 5 * 0.5 chance for SoL to procc
1 int = 0.00006 * 5 * 0.5 * 625 Mana per Flash Heal
1 int = 0.1125 mana
Now, there is another problem: First, there is no set timeframe for this. It could be one CoH or PoM with a casttime of 1.5 and one instant flash heal with GCD – but you could also be using PoH with its 3 second cast time and pushing a 1.5s flash heal after it. Also, you are hardly ever constantly casting.
Second, not every SoL procc will (and should!) be used. If the group needs to be healed (hey, that IS the point of AoE healing…) throwing a flash heal just because it is cheap might not be a very good idea.
Due to those problems I will assume that the 0.1125 mana is gained over 10 seconds, therefore leaving us with
1 int = 0.046875 mp5 from crit during AoE healing

During single-target healing, SoL hardly changes, the main difference here is that now we only have one target:
1 int = 0.046875 / 5 mp5 from SoL during single-target healing
1 int = 0.009375 mp5 from SoL during single-target healing
However, during single-target healing we can also procc Holy Concentration – and we are going to assume that we will use up that charge with greater heal.
1 int = 0.00006 crit
1 int = 0.00006 * 0.45 chance for HC to procc
1 int = 0.00006 * 0.45 * 1050 Mana per GHeal
1 int = 0.02835 Mana
Since we have to assume that we procced this cast of a gheal and we are going to use it with a gheal our 10 seconds are very valid to assume again:
1 int = 0.014175 MP5 from HC during single-target healing
1 int = 0.009375 + 0.014175 = 0.02355 mp5 from crit during single-target healing

As summary we are going to assume the lower value of 0.02355 mp5 from crit, because we should not assume to be always AoE healing.

Hymn of Hope
Restores 8% MaxMana w/ 5 min cd… Yep:
1 int = 0.08 * 16.5 /60 = 0.022 mp5

Int-regen from spirit-based MP5
Ok, the title is pretty idiotic, but the idea is that intellect also improves our spirit-based mana regen!
1 int = spi * 0.027875 * sqrt(int + 1) - spi * 0.027875 * sqrt(int)
1 int = spi * 0.027875 * (sqrt(int + 1) - sqrt(int))
That rather annoying formula above misses that spirit based MP5 only works IC… To make this comparable we are going to assume a 75% time spent in combat and also 3/3 meditation.
1 int = 0.027875 * spi * (sqrt(int + 1) - sqrt(int)) * 0.75 * 0.3 + 0.027875 * spi * (sqrt(int + 1) - sqrt(int) * 0.25
1 int = (0.75 * 0.3 + 0.25) * 0.027875 * spi * (sqrt(int + 1) - sqrt(int))
1 int = 0.013240625 * spi * (sqrt(int + 1) - sqrt(int))

Full Int based Regen!
Ok, now we simply have to add all our values up!
1 int = 0.013240625 * spi * (sqrt(int + 1) - sqrt(int)) + 0.02355 + 0.165 + 0.20625 + 0.022
1 int = 0.013240625 * spi * (sqrt(int + 1) - sqrt(int)) + 0.4168
Ok, but now, what is bigger, better, meaner?

Sprit-Regen
For spirit we can steal most of the work from above
1 spi = 0.013240625 * (spi + 1 - spi) * sqrt(int)
1 spi = 0.013240625 * sqrt(int)

So, what is better?
Well, to answer that we will simply calculate at which point int becomes better than spirit (and vice-versa)
0.013240625 * sqrt(int) = 0.013240625 * spi * (sqrt(int + 1) - sqrt(int)) + 0.4168
sqrt(int) = spi * (sqrt(int + 1) - sqrt(int)) + 31.478877
spi = (sqrt(int) - 31.478877) / (sqrt(int + 1) - sqrt(int))

WTF dude?
Yep, just my point.
The problem is, simply put, that spirit is more worth the more int you have – and the more spirit you have, the more int is worth! Below is a table with intellect and spirit values… What you do is look up your (raidbuffed!) intellect value und then, if your spirit value is HIGHER, you would ideally take more int. If your spirit value is lower than the one in the table, you want to grab more spirit.
Easy, huh?

Notice something?
Yeah, 1 point intellect regenerates more mana than 1 point spirit!