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Zusterke on Inspiration

January 12, 2010

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

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.

Math for buff duration uptime

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.

Inspiration Uptime

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

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.]

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15 comments

  1. Great post…. Zusterke shared his spreadsheet with me and I’m still trying to pour through it in time for the Dreamwalker encounter. Trying to figure out max HPS, and what gear/specs to use for her. He’s too smart for me! Good post!


  2. Nice write-up Zusterke.

    I think Zusterke should be writting my theorycafting posts. He’s much smarter than I. :-)

    Gobble gobble.


  3. Seri’s response:

    Oh look, a rainbow!


  4. […] on World of SnarkCraft has a wonderful piece with solid theory crafting on the benefits of the priest’s Inspiration […]


  5. […] on World of SnarkCraft has a wonderful piece with solid theory crafting on the benefits of the priest’s Inspiration […]


  6. Hey zus, nice to see you posting here again and getting linked on wow.com. ;)

    I’d just like to add that resto shamans can place the same buff on the tank, although for them it’s called Ancestral Fortitude. I’m unsure wether or not priests have an ability that makes them guarantee that a heal will be a crit therefor guaranteeing that Inspiraton/fortitude will be up on the target.

    Resto shamans have some leeway in that case. Tidal Waves will add 25% crit on the next two Lesser Healing Waves after using either a Riptide or a Chainheal, whereas Tidal Force will add 60% crit on the next Chainheal, Healing Wave and Lesser Healing wave for the next 20 seconds, reducing by 20% after each crit. Obviously Tidal Force, an ability on a 3 minute cooldown should not be considered, but a riptide or chainheal cast which form part of the normal spell ‘rotation’/choice of a shaman do have to be calculated in there somehow.

    So in that respect I think shamans have, due to class mechanics, favoured stats and talents a more reliable way of keeping Inspiration/Fortitude up on their target.

    Good to seeing you spread your knowledge to the priest community Zus! ;)


    • A comparison with the Shaman wasn’t entirely the goal of the article. If it comes to comparing the buff uptime between two tankhealers, in uptime there will be little difference. As little as 25% crit and 10 heals per 15s grant ~94% uptime. Doubling your crit can only yield small gains.

      The major difference is in the number of heals required to fire up the buff. The Shamans riptide+tidal wave talents will outweigh the only crit cooldown we have: ‘inner focus, 3m cd, 25% crit’ which I wouldn’t recommend to be used this way :)
      But if this buff is of such vital importance, it isn’t far fetched to spamheal the tank before the pull to get the buff running. I know I have done that on several occasions when I was healing your alt DK tank in ToC HC (5m) ;)

      Still, if you really want to duke it out with a priest in terms of tankhealing, I wouldn’t take a holy priest. IMHO they lose that fight hands down. Instead, challenge yourself with a Disc priest. With 40% crit and about 13% haste raidbuffed, the Disc priest can produce ~94.1% chance on inspiration in 4.3s using ‘Shield, penance, FHeal’. A Shaman with 40% crit and the spellcycle ‘Riptide, Lesser Healing Wave x 3′ would have 95.6% chance on Ancestral Fortitude. Not a huge difference but the shaman would need 38.5% Haste raidbuffed during that cycle unless I missed some passive haste buff they have.

      I’m not sure if this comparison is all that relevant though :)


  7. Less heals required to fire up the buff was indeed the point I was going for. :)

    I’m not going to get into another discussion with you on mana regen mechanics for priests vs shamans (we’ve done that for more then our fair share :D ), I just wanted to point out that the ‘mana cost’ of keeping the buff up will be lower for a shaman then for a priest since there are less casts required (sidenote that crits have a chance to regen mana for the shaman as well, lowering that cost).

    When all is said and done, the main goal will have to be healer synergy. Healers of all classes working together to play to their different strengths and compensate for individual class weaknesses.


  8. ‘less heals to maintain the buff’ makes me doubt the situation you want to apply this to. If it’s tankhealing, I assume the tank requires more heals than the absolute minimum to maintain inspiration/ancestral fortitude. Unless you plan to spread the buff as part of the healing strategy but I’m not convinced that is a sound basis for any healing strategy.
    Still a Disc priest would give you a run for your money: Penance gives 3 heals in 2s (unhasted), with 40% crit and a total 82% chance to proc on targets with weakened soul. That’s a pretty cheap spell (550 mana). It would require vast amounts of crit to push the Disc priest away. The Holy priest is lost though.


    • I’m not doubting the effectiveness of discpriests. What I am saying is that less heals to maintain or apply the buff allows for greater flexibilty. Lets say for instance that I am raidhealing and I see the tanks taking massive damage with no really big heals on the way. A quick critenhanced LHW will put the buff on the tank and make sure that since he will probably still be the target with the lowest relative health, the Ancestral Awakening proc will heal him as well. That should buy enough time for either a second LHW on my part or for the rest of the healers to top of the tank.

      Also, it needn’t neccesarily be a tank. Any raid member will benefit from less heals needed to proc the inspiration buff. Even when the tanks aren’t in need of a heal, there is nothing wrong with throwing a Tidal Waved LHW on the tank(s) to keep the buff on.

      Again, this is not meant to rate on class above the other. It’s just meant to show that Resto shamans, due to class mechanics and talents may have an easier way of putting that buff on a target then holy priests.


      • In casu supporting the tank I would agree that tidal wave shows nice synergy with this buff. The holy priest certainly has no comparable tool.

        The only form of ‘control’ the holy priest can offer is regularly healing the tank to apply this buff which some level of certainty, but that could conflict with his assignment.

        Not all is lost though. Unlike ES (correct me if I’m wrong), Prayer of Mending still triggers Inspiration. I should check if Empowered Renew can trigger Inspiration as well. Combined with CoH (much like the smart heal from Chainheal) we can expect a natural flow of heals on the tank, able to provide Inspiration. But this could certainly not be labeled as ‘controlled’ inspiration :)


  9. […] on World of SnarkCraft has a wonderful piece with solid theory crafting on the benefits of the priest’s Inspiration […]


  10. […] For an excellent theorycrafting post on Inspiration check out Zusterke’s effort on World of […]


  11. Alright, I double checked. ER doesn’t proc Inspiration. This would reduce the uptime for a priest that he would otherwise passively give.


  12. […] The second article is on healing UIs. You might recognize some of the people I interviewed. The first one I interviewed was Lilitharien. Yes, the same Lilitharien from Divine Aegis! Another familiar face you may recognize is Zusterke, who frequents the Plus Heal forums (and has guest posted on World of Snarkcraft). […]



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