Priest Theorycrafting for 3.3 – Critical Rating (Part 5)

v3.3

There are three areas which are affected by Critical Rating. There is the base 50% additional healing which results from a critical and then there is then one talent for each of the healing schools which is crit based. These are Divine Aegis for discipline and Surge of Light for holy.

Sections

  1. Introduction
  2. Mana regeneration including Spell Power and Stamina
  3. Mana pool
  4. Haste rating
  5. Critical rating
  6. Summary including LootRank and Pawn values

Assumptions:

  • Flash Heal is being spammed (1887 base heal, 81% co-efficient. 1.5s cast time)
  • Discipline has 2774 spell power
  • Holy has 3096 spell power
  • 45.91 Crit Rating equals 1% Crit
  • 167 Intellect equals 1% crit. However as we are including talents and Blessing of Kings the amount of intellect on gear required for 1% crit is 132 for discipline and 151.8 for holy
  • Base 30% over-heal with 50% for critical hits
  • Divine Aegis is 70% consumed.
  • Surge of Light procs are 90% consumed

Base Critical value

Healing spells that critically hit heal the target for 150% of their normal healing value. To calculate the value of this additional healing we assume that the caster is using Flash Heal and use the attributes associated with that spell. To determine its value as MP5 we equate the total heal for the FH as MP5 based on the SP to MP5 ratio (2.0:1) and then calculate how much is additional healing is due to the critical. Over-healing is also taken into account.

Flash Heal Crit MP5 value = (base heal + (SP * SP co-efficient)) * SP MP5 value * proportion from crit * (1 - over-heal %)
FH Crit MP5 value (Disc) = (1887+(2774*80.68%))*2*0.5*(1-0.5)
FH Crit MP5 value (Disc) = 2062
FH Crit MP5 value (Holy) = 2190 (Holy FH crits are bigger)

1% FH Crit MP5 value (Disc) = 20.6253
1% FH Crit MP5 value (Holy) = 21.9081

These numbers are now converted to Critical Rating and Intellect values:

  • Discipline
    • Crit rating MP5 = 20.6253/45.91 = 0.4493
    • Intellect MP5 = 20.6253/132 = 0.1562
  • Holy
    • Crit rating MP5 = 21.9081/45.91 = 0.4772
    • Intellect MP5 = 21.9081/151.8 = 0.1443

Divine Aegis

Discipline priests have an additional effect that triggers on healing critical hits. Divine Aegis creates an additional 30% of the total critical heal value as a damage absorption bubble. To calculate its MP5 value we need to once again assume Flash Heal is being cast and then calculate the MP5 value of the Flash Heal and the associated Divine Aegis.

Divine Aegis FH MP5 value = (base heal + (SP * SP co-efficient)) * SP MP5 value * 1.5 * DA bonus * DA consumption rate
Divine Aegis FH MP5 value = (1887 + (2774 * 80.68%)) * 2.0 * 1.5 * 0.3 * 0.7
Divine Aegis FH MP5 value = 2598

1% DA FH MP5 value = 25.98

Divine Aegis Crit Rating MP5 value = 25.98/45.91 = 0.5661
Divine Aegis Intellect MP5 value = 25.98/132 = 0.1969

Divine Aegis, under a Flash Heal spamming scenario, provides a lot of extra throughput at this level of gearing. High spell power and high critical hit chance grant Divine Aegis quite a lot of value in this model.

Surge of Light

Holy also have a critical based talent which creates MP5 value. Surge of Light provides free Flash Heals, 50% of the time, following a spell critical.  However the free Flash Heal can not result in a critical hit so it effectively only occurs 33% of the time.

SoL MP5 per 1% crit = Spell mana cost / cast speed * 5 * proc rate * consumption rate / 100

SoL MP5 per 1% crit = 621/1.5*5*33%*90%/100
SoL MP5 per 1% crit = 9.315

SoL Crit Rating MP5 value = 6.15/45.91 = 0.1339
SoL Intellect MP5 value = 6.15/151.8 = 0.0405

Inspiration

There is one more ability we can have a go at estimating the value off and that is Inspiration. This talent provides a buff to healing targets which reduces damage received by 10%. At first glance this doesn’t sound like much, but when you consider that a tank can take 1 million (1,000,000)points of damage in a eight minute boss fight the 10% damage reduction starts to add up.

Assumptions:

  • Inspiration reduces all physical damage received by 10%
  • Uptime is about 60%. Single target healing uptime is about 90%, but raid healing uptime is about 40%. To make the calculations simpler i’ve assumed a middle of the range 60% uptime.
  • 30% critical chance
  • MP5 value per Flash Heal is 2062 for Discipline and 2190 for Holy. This is calculated in my critical rating theorycrafting post for 3.3.
  • Mana cost of Flash Healing is 528 for Discipline and 621 for Holy

Damage reduction per 1% critical chance = 10%*60%/30 = 0.20%
Damage reduction = 0.20% * 1000000 = 2000

Flash heals saved per 1% critical for:

Discipline = 2000 / 2062 = 0.9697 Flash Heals
Holy = 2000 / 2190 = 0.9129 Flash Heals

Inspiration MP5 per 1% critical = (FH mana cost * FH saved) / fight duration * 5
Discipline Inspiration MP5 per 1% critical = (528 * 0.9697) / 480 * 5 = 5.3334
Holy Inspiration MP5 per 1% critical = (621 * 0.9129) / 480 * 5 = 5.9053

Inspiration Crit Rating MP5 = Inspiration MP5 per 1% critical / Crit rating per 1% crit

Inspiration Crit Rating MP5 for discipline = 5.3334 / 45.91 = 0.1162
Inspiration Crit Rating MP5 for holy = 5.9053
/ 45.91 = 0.1286

Inspiration Intellect MP5 = Inspiration MP5 per 1% critical / Intellect per 1% crit (remembering to include talents and buffs)

Inspiration Intellect MP5 for discipline = 5.3334 / 132.0158 = 0.0404
Inspiration Intellect MP5 for holy =
5.9053 / 151.8182 = 0.0389

Edit: For an excellent theorycrafting post on Inspiration check out Zusterke’s effort on World of Snarkcraft.

Final critical related stat weightings are:

Discipline

  • Critical rating
    • Base critical rating MP5 weighting = 0.4493
    • Divine Aegis critical rating MP5 weighting = 0.5661
    • Inspiration critical rating MP5 weighting = 0.1162
  • Intellect
    • Base Intellect MP5 weighting = 0.1562
    • Divine Aegis Intellect MP5 weighting = 0.1969
    • Inspiration Intellect MP5 weighting = 0.0404

Holy:

  • Critical rating
    • Base critical MP5 weighting = 0.4772
    • SoL critical rating MP5 weighting = 0.1339
    • Inspiration critical rating MP5 weighting = 0.1286
  • Intellect
    • Base Intellect MP5 weighting = 0.1443
    • SoL Intellect MP5 weighting = 0.0405
    • Inspiration Intellect MP5 weighting = 0.0389

Finally next we conclude with the summary.

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16 Responses to Priest Theorycrafting for 3.3 – Critical Rating (Part 5)

  1. Codi says:

    At first I was confused until I realized that what you are doing here is working with stat weights, not actual MP5 numbers. You might want to make that distinction a bit more clear. 🙂 Shaman work with the idea of Healing Equivalency Points (HEP) that I’ve adapted for my own uses, where the base HEP is MP5 the way yours are, but they aren’t -called- MP5 so as not to confuse people. (Because obviously spellpower doesn’t actually give MP5!)

  2. BobTurkey says:

    Yes equating everything to MP5 is prety much the same thing as HEP.

    I could have equated it to spell power, which is more like HEP.

    Gobble gobble.

  3. Arrelliana says:

    Do my eyes decieve me or is critical strike becoming more valuable than haste now?

  4. Fidtz says:

    This is very interesting, especially since I am now used to lots of haste!

    Shouldn’t Holy Concentration should be included here for Holy?

  5. Dahk says:

    “Inspiration reduces all damage received by 10%”

    Inspiration reduces physical damage only by 10%. It does not reduce magical damage at all.

  6. BobTurkey says:

    @Arrelliana – in my opinion it has always been more important although I aim for a balance.

    @Fidtz – HC is under mana regen.

    @Dahk – good point. I’ll fix that.

  7. xeonio says:

    It’s late so forgive me if this is a bit slow. I know the calculations take into account overhealing for flash heal but when you mix in Divine Aegis doesn’t that increase the potential overheal? Kind of like the debate over how haste is weighted since it was only being looked at for its bonus to throughput.

    Under the Base Crit Value…

    “1% FH Crit MP5 value (Disc) = 28.87
    1% FH Crit MP5 value (Holy) = 30.99
    These numbers are now converted to Critical Rating and Intellect values:

    * Discipline
    o Crit rating MP5 = 28.31/45.91 = 0.6290
    o Intellect MP5 = 28.31/132 = 0.2187
    * Holy
    o Crit rating MP5 = 30.43/45.91 = 0.6681
    o Intellect MP5 = 30.43/151.8 = 0.2020”

    I understand the math that gives you the 1% FH Crit MP5 Value but then you go to convert them and I don’t know where those numbers come from. Discs 1% FH Crit mp5 value = 28.87 but in the conversion you have 28.31? Same happens with Holy being a different number. Then you reference those numbers later and you go back to the 28.87 and 30.99.

  8. BobTurkey says:

    These are wrong:

    “1% FH Crit MP5 value (Disc) = 28.87
    1% FH Crit MP5 value (Holy) = 30.99”

    Should say:

    “1% FH Crit MP5 value (Disc) = 28.31
    1% FH Crit MP5 value (Holy) = 30.43”

    This is what happens when I make slight changes, like extending the fight duration from 6 mins to 8 mins, at the last minute and after the post is drafted.

    re:over-heal and Divine Aegis i’ve assumed 70% of DA are consumed. DA creates a shield that is only consumed on the next damage. It is not immediately wasted like normal over-healing. Does this answer your question?

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  10. xeonio says:

    “re:over-heal and Divine Aegis i’ve assumed 70% of DA are consumed. DA creates a shield that is only consumed on the next damage. It is not immediately wasted like normal over-healing. Does this answer your question?”

    Not really. My argument is that the increased crit causes more DA (which is good) but since you have more DA its more likely that a heal will overheal (because of DA still being up).

    With DA causing such a heavy weight this makes the 4p t9 bonus quite huge doesn’t it? I tried replacing the .3 in the equation with a .4 and the difference between .3 and .4 was .1886. I don’t really know how to equate that into a value that would give the rough estimate of what 4p t9 is worth.

  11. BobTurkey says:

    Hi Xeonio,

    Usually you won’t just be healing someone unless they need their green bar to go up some. The presence or absence of DA doesn;t effect this I don’t think.

    Has anyone confirmed if the 4 pc T9 is 40% rather than 33%?

    But otherwise, yes your thinking is correct. However to counter that i’d say that both the T10 set bonuses are also aimed at tank healing, although the 2 pc T10 isn’t that good.

    Persoally i’m using 4pcT9 any time i’m tank healing ATM.

  12. xeonio says:

    Ya know I didn’t think of that… I thought it was just a flat 10% increase on top of what we already did. That is very interesting.

  13. Zusterke says:

    The healing from Crit is a bit iffy. It’s great to take into account 30% overheal, but you added the same amount of overheal to SP as you did to crit in that formula. If you assume the crit bonus overheals more often (which is not unreasonable), you would have to change the formula to:
    Flash Heal Crit MP5 value = (base heal + (SP * SP co-efficient)) * SP MP5 value * (100% – overheal% + crit% * portionfromcrit * (100% – critoverheal%))

    SoL
    SoL MP5 per 1% crit = Spell mana cost / cast speed * 5 * proc rate * consumption rate / 100

    I’m not sure this is correct. Assume a 100% consumption rate and 100% crit:
    621 / 1,5 * 5 * 50%
    Spamming FHeal costs us:
    621 / 1,5 * 5
    of which SoL refunds half by your formula. This isn’t correct. SoL only refunds 1/3. If I cast 99 Fheals, with 100% crit, then 66 will be crits of which 33 will proc SoL and 33 heals will be the actual SoL proc being consumed. Your formula would be correct if the FHeal from SoL itself could crit (and proc SoL) or if SoL would refund the mana directly.

    I would calculate the value from inspiration differently too 😦 The uptime for your inspiration buff on a target is:
    Uptime = 1 – (1-p)^n
    where
    n = hits/triggers of the buff
    p = chance to proc the buff
    This formula shows a strong increasing diminishing return. Your method assumes the value of crit is linear for inspiration. The problem with this is that, assuming your stats you should have 19.5% crit raidbuffed without gearing for crit on your holy priest. Checking single target healing on a tank, you’ll notice that at 20% you already have a 90% uptime and anything between adding 1% or 80% crit can at most add another 10% uptime. This would sink the value you obtained a lot 😦
    Of course, you could assume you’re not spamhealing the tank which is perfectly viable as holy priest… but then the base number of damage you took is quite an overestimation on the damage taken by dps. Furthermore this assumes the damage is physical.

    I think crit is overestimated here.

  14. BobTurkey says:

    Yes you are right. There is likely to be more overheal for crits. Especially for Holy.

    You are also right about SoL. I’ll drop the 50% to 33%.

    You are also correct on Inspiration.

    The stat weights are based on a set of assumptions for the casters current statistics. As these statistics change the stat weights change. For example compare these numbers with my 3.2 and 3.1 stat weights.

    None of the stat weights continue to be accurate once you modify the underlying assumptions.

    I suppose I have misled readers a little though. If you have exactly the % crit i’ve used in my assumptions them my stat weights will be correct (mostly) however the crit rating stat weight i’ve provided is only really accurate for the next point of critical rating. Beyond that the weightings will change.

    Also as Dahk pointed out above Inspiration only works for physical damage. Not all damage.

    Gobble gobble.

  15. Zusterke says:

    It’s true that the assumptions influence the results a lot. Your assumptions seem a bit optimistic imo for a holy raidhealer who prefers to use Renew over FHeal but it would seem fairly accurate for a holy or disc priest who’s regularly healing the tank.

  16. Karrah says:

    I don’t think we should try to factor inspiration into our stat weighting because of the nature of the mitigation it offers: it only works on physical damage. You have 2 very different situations: either you’re healing the raid in that case the uptime of inspiration will be low on your targets but it doesn’t matter as the raid isn’t taking physical damage; or you’re healing a tank in which case you’ll be focusing on 1 or 2 targets and inspiration will be up almost 100% of the time even with a low 20% crit (the probability to have not crit at all over 15 sec, casting a heal every 1.5 sec, is 10% at 20% crit and 2% at 30% crit).

    So my conclusion is that while inspiration is a great talent the effect of increased crit rate should be negligible where it matters. The high weights you’re derivating are mainly coming from your assumption of an average 60% uptime which doesn’t make much sense due to targets on which physical damage occurs.

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