Zusterke strikes again! This time, he delves into numbers to discuss that basic Priest talent: Inspiration.
Inspiration

Inspiration is a welcome tool, whether you’re making art or healing the tank. Most combat parsers check the uptime of this buff, showing the value of this talent. Sadly logs do not tell us how inspiration evolves with respect to crit and how we can manipulate our healing to work with inspiration. That needs to worked out differently, with pretty colors and graphics.
Inspiration uptime
“Theory”! Ha! Scared you, didn’t I? Due to heavy reader loss last time I wrote a guest post, I promised I’d stop aiming my theory at the readers and put the loaded math down. Still, for sake of completion I present the formula for inspiration uptime. The credit for this formula goes to Dagma at PlusHeal for he taught me both formula and its proof. The faint of hearth are invited to close their eyes for a second, it will not be pretty.

Hits denotes the amount of (inspiration able) heals within the buff’s duration that we cast on the target. C denotes critical strike chance.
You may open your eyes again. We have 2 things that effect our chance to proc inspiration: critical strike chance and the amount of spells we cast on the target. This pretty rainbow below shows us by how much. Sadly, there is no pot of gold at the bottom end of this rainbow, only rotten potatoes for that’s where our inspiration ends.

Each line corresponds to an amount of heals on our target. Crit quickly boosts our inspiration uptime and as little as 20% gives a good uptime for spammy scenarios. For 25% crit we obtain 90% uptime when healing the target 8 times or more within 15 seconds. That’s easy with FHeal and/or penance, our tankhealing tools. Higher crit gives better uptimes, but the benefit from crit diminishes. The difference between 30% and 35% crit is only noticable if we heal the target less frequently. Beyond 35%, the benefit of crit is very low.
A grain of salt for these potatoes
I love theor.. eh.. rainbows but it isn’t 100% reliable. Critical heals are still random. The numbers above give ‘expected values’ but in practice your buff time could differ a little. Still, the more crit we have, the more reliable our inspiration becomes.
Another factor that effects our outcome is how you heal. The formula assumes that our heals are equally spread over time. In-game, this is rarely the case. This could influence your uptime both in a positive and negative sense. While the numbers above remain good indications, they are not 100% on the spot.
Counting on Inspiration
Tankhealers are seldom confronted with this question… but support healers or OT healers might: how often do you need to heal your target to proc inspiration? The answer for pessimists is “infinitely many times”. For all optimists out there, we can work out your chance to proc inspiration depending on how often you heal the target. *crushes door* Here’s theory! While I would enjoy a reign of math terror, you are spared another formula. The chance to proc inspiration, depending crit and your number of attempts, can be calculated with exactly the same formula as above. Consequently, the same rainbow shows you how reliable your chances are to proc inspiration and we can draw the same conclusions.
Inspiration and Surge of Light

Surge of Light offers a free flash heal, but one that cannot crit. For our global inspiration uptime, it could be noted that SoL has a negative impact. But if we check the graph above, we can see that 1 heal less does not greatly affect our uptime. What’s more: in tankhealing scenarios it is likely to be a proc from a critheal on our tank. It would thus be the same heal that resets the inspiration timer and we should have about 15s time to ‘use’ that FHeal and cast more spells on our tank.
While I doubt the lack of inspiration or the gain of SoL has ever caused a wipe, there is a small risk that SoL procs from PoM or CoH that crits on a player, other than your target. In the (inconceivable) case that this proc would hinder your healing, a holy priest could use Binding Heal on the target as work around. But I have rarely been in a position where this would make a difference.
TLDR, aka the conclusion
For inspiration we note that 20% crit is sufficient to provide a reliable inspiration uptime in a tankheal scenario. More crit is welcome as it gives more freedom of how often we need to heal the tank but there is a diminishing return. At 30% crit, this diminishing return becomes strong and beyond 35% crit it weighs heavily. These numbers are raidbuffed. They should be taken with a grain of salt, so adding or dropping 1% won’t make a tremendous difference. If I remember correctly Jov always promoted 20% crit as minimum for holy priests. I guess I just added a piece of the proof she’s right. (and I’ll probably never hear the end of it) [You just said my two favorite words: Jov's right. Of course you'll never hear the end of it! -ed.]


So, we need a minimum amount of spirit to support our intellect. This condition is very easy: for 1000 intellect, we only need 308 base spirit or 324 spirit unbuffed. It is fairly safe to assume a holy priest will have that amount of spirit and thus intellect beats mp5.
Round 1: Disc priest
Given 1065 intellect unbuffed, spirit can beat mp5 when raidbuffed. Starting raiders without sufficient intellect on their gear may find mp5 slightly more performant at first, but spirit will gradually outscale mp5 by the time they leave naxx 10m and the spellpower bonus from spirit makes the stat preferable quite early in the content.

Does this make sense? Like… any sense? It does! Basically this comparison tells us that we can stack a boatload of intellect before spirit catches up. For example, with 0 spirit, the optimal value for intellect is 2025! Well, intellect clearly wins this one!
Keep in mind that these are basestats and thus spirit should be a tad higher. Still, it’s quite clear that spirit has lost some considerable ground to intellect! That is, for 20% HC Uptime, 90% FSR and no specific synergy with your manabar regen abilities. Do check that other ratio’s, with some more spirit or some intellect also score quite well as optimal (less than 10% difference).
The regeneration model of WoW has seen a lot of changes with patch 3.1: spirit/intellect regeneration was nerfed outside the five second rule, the shadowfiend is buffed,
Having checked dozens of WWS parses, it seems Replenishment ticks 75-95% of the time (see screenie). I consider 85% an average which yields me: 85%*1.25% = 1.0625% of my manabar as mana every five seconds.
We can calculate the percentage of maximum mana per 5 seconds we get for both Disc and Holy priest. We can use that percent to calculate how much mp5 per point of intellect we get from manabar based regen but here we must take into account the bonus on intellect accordingly: 

These values probably like an odd mix of Thalassian and Chinese so let’s simplify them. We assume 90% time spent inside the five second rule and for holy priests we add 20% Holy Concentration uptime (see image). This is a bit pessimistic but it’s better to play safe. Holy priests tend to have a notably higher mana consumption when raidhealing and most raidhealing spells do not trigger holy concentration.
Taking into account buffs from talents and 

1. I’m a lazy item enhancer. Seriously,
4. In the spirit of tracking improvements, I flash healed my way through Molten Core before I learned what downranking was. (This was before Flash was good for anyone but pallies, fyi.) My knowledge of my class consisted entirely of “I read the tooltips on my spells and talents” through 6 months of pre-TBC raiding. A few friends eventually took me under their wing, and introduced me to a whole new world of not-sucking.

First, let’s talk Discipline. I have none, obviously, but I’m talking about talents here. The Discipline tree has long been the redheaded stepchild of our family, but with 3.0 it is looking to become an extremely viable single target healing spec.
At one time, I had 10 Priests under my purview. Although there have been a few casualties, we are still legion; the Priest class is the largest in our guild and it’s my job to evaluate both the Holy and Shadow Priests. I’ve always been Holy, so when I took on a class lead role I knew I had my work cut out for me. Fortunately for you, you can now benefit from all of my hard work. By following these guidelines, you can whip those Shadow Priests into shape… or at least find out what sort of shenanigans they’ve been getting away with.






