Priest Theorycrafting – Critical Rating (Part 5)

v3.1

  1. Introduction
  2. Mana regeneration
  3. Mana pool
  4. Haste rating
  5. Critical rating
  6. Summary

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.

Assumptions:

  • Flash Heal is being spammed (1887 base heal, 80.86% co-efficient. 1.5s cast time)
  • Discipline has 1950 spell power
  • Holy has 2147 spell power
  • 45.91 Crit Rating equals 1% Crit
  • 167 Intellect equals 1% Crit – Due to Disciplines Mental Agility talent they only require 145 Intellect per 1% Crit
  • 30% over-heal
  • Divine Aegis is 70% consumed.
  • Surge of Light procs are 70% consumed
  • Inspiration prevents 5% damage (for 25% armour buff) and has a 40% uptime

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 (0.6) 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+(1950*80.86%))*0.6*0.5*(1-0.3)
FH Crit MP5 value (Disc) = 726.65
FH Crit MP% value (Holy) = 760.01 (Holy FH crits are bigger)

1% FH Crit MP5 value (Disc) = 7.2665
1% FH Crit MP5 value (Holy) = 7.6001

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

  • Discipline
    • Crit rating MP5 = 7.2665/45.91 = 0.1583
    • Intellect MP5 = 7.2665/145 = 0.0500
  • Holy
    • Crit rating MP5 = 7.6001/45.91 = 0.1655
    • Intellect MP5 = 7.6001/167 = 0.0455

Divine Aegis

Discipline priests have an additional effect that triggers on healing critical hits. Divine Aegis creates an additional 30% of the 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 + (1950 * 80.86%)) * 0.6 * 1.5 * 0.3 * 0.7
Divine Aegis FH MP5 value = 653.9891

1% DA FH MP5 value = 6.5399

Divine Aegis Crit Rating MP5 value = 6.5399/45.91 = 0.1425
Divine Aegis Intellect MP5 value = 6.5399/145 = 0.0450

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.

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*50%*70%/100
SoL MP5 per 1% crit = 7.245

SoL Crit Rating MP5 value = 7.245/45.91 = 0.1578
SoL Intellect MP5 value = 7.245/167 = 0.0434

Inspiration

The 25% armour buff from Inspiration grats about 5% damage reduction.  Using numbers for Patchwerk 25 for a priest with 22.72% critical rating there is about 40% uptime.  This equates to 0.09% damage reduction per 1% crit.

Over the course of a 6 minute fight the one of the tanks takes approximately 1,000,000 points of damage.

Damage prevented = damage reduction % x damage actually received.
Damage prevented = 0.09% x 1,000,000
Damage prevented = 880.281 (per 1% crit)

Next we calculate the number of Flash Healing spells saved by the damage reduction (including the 30% overheal).

FH healing = (base heal +(SP*SP co-efficient)) * (1 – overheal %)
FH healing (Disc) = 2523
FH healing (Holy) = 3122.7 ( I realise i’ve missed some of the the Holy talents which increase this number.  They will slightly decrease the MP5 value, but not significantly)

Number of Flash Heals saved by Inspiration = Damage prevent / FH healing
FH saved (Disc) = 0.3488
FH saved (Holy) = 0.2819

Flash Heal Mana cost (Disc) = 528
Flash Heal Mana cost (Holy) = 621

Inspiration MP5 (per 1% crit) = FH saved x FH healing / Fight time * 5
Inspiration MP5 (Disc) = 2.5581
Inspiration MP5 (Holy) = 2.4314

Inspiration Crit Rating MP5 value (Disc) = 2.5581/45.91 = 0.0557
Inspiration Intellect Rating MP5 value (Disc) =
2.5581/145 = 0.0176

Inspiration Crit Rating MP5 value (Holy) = 2.4314/45.91 = 0.0530
Inspiration Intellect Rating MP5 value (Holy) =
2.4314/167 = 0.0146

Next bringing it all together.

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7 Responses to Priest Theorycrafting – Critical Rating (Part 5)

  1. I applaud your ability to do so much number work… honestly, my brain just hurts when I think about it. 😦

  2. melsana says:

    I’ve enjoyed reading this whole series. I’ve decided to put the calculations into my own spreadsheet so I can play with the “assumptions” to make them match my playstyle/stats a little better.

    I’m a holy priest so I am only worrying about the calculations for Holy.

    Anyway.. I was doing just fine until I got to the part about Inspiration. In all the other sections you get very detailed and show all your work (just like math class). But in the Inspiration section you seem to leave chunks of math out and I’m having a hard time following.

    I’m not really sure how you calculated “0.09% damage reduction per 1% crit.” I took a guess and did 5% * 40% / 22.72% but then I get 0.09 not 0.09%. Which makes my Damage reduction off by a factor of 100.

    Also when you calcualte the Flash Heal amount, I’m getting a number closer to the Disc (but not exactly). So I’m not sure what I’m doing wrong.

    When I calculate the FH saved I obviously get close to the Disc number listed.

    Finally when I calculate the “FH saved x FH healing / Fight time * 5” I get a REALLY different number. If I fudge out the 100 factor mentioned earlier (ie use your number) I get 12.23 not 0.3(since my FH value is closer to the disc) or 0.2. Again, since you don’t show your work in this calculation, I can’t figure out what I’m doing wrong. As far as I can tell I’m following the equation you have listed exactly.

    Of course these two differences greatly affect my Crit Rating MP5 and my Intellect MP5 from Inspiration.

    Any chance you could expand on the math equations in a bit more detail to help me figure out where I’m going wrong.

    Thanks.

  3. BobTurkey says:

    Glad you’ve found it useful Melsana.

    Inspiration was added as a bit of an afterthought which is why it might be a bit less elegant than the other areas.

    re: “5% * 40% / 22.72% but then I get 0.09 not 0.09%”

    Your numbers are right. Because you are working with percentages the answer will be a percentage to. To simplify imagine 10% of 10%. 10% x 10% = 1% not 1.

    I’m not sure about your FH healing bit. Are you including the 25% of Spirit as spell power that Holy get from Spiritual Guidance? Also I made a slight deviation from my other posts (the dangers of tacking bits on at the end) and included glyphs and talents in both the total healing and mana cost for FH.

    So I included +10% healing from Spiritual Healing talent, +20% spell power to FH from Empowered Healing and -10% mana cost from Glyph of FH. This resulted in FH numbers of 621 mana cost and 4461 healing instead of the base 690 mana and 3619 healing.

    If you get the 0.09% problem sorted the exact FH healing/mana numbers you use are less important as the effect is very minor on the stat weighting. Having said that i’m happy to try and help.

    Gobble gobble.

  4. melsana says:

    Hmm. I understand what you are saying with the percentages but I’m still not getting the right answer… let me show my work.

    Let me remove the % , so it becomes

    .05 * .40 / .2272 = 0.088

    So then if you put the % back on the answer it = 8.8%

    Am I missing something… it has been a few years since I took a math class.

    —-

    As for the FH, I wasn’t including the Holy talents or glyphs, since they weren’t specified in the write up, I missed that. It makes sense. So thanks.

  5. BobTurkey says:

    The 0.05 * 0.4 bit is correct (5% times 40%). However you need to divide by 22.72 to get the damage absorption per 1% crit. The number your getting is the damage absorption per 100% crit.

    Maths class is a long way behind me too. I’m sure there is a good maths type explaination why I did it the way i did it, but I don’t remember it.

  6. firebert says:

    I’ve worked it out.
    Inspiration MP5 (per 1% crit) = FH saved * FH mana cost / fight length * 5
    You’re working out mana, not how much you’re healing.
    This puts the Inspiration MP5 from ~12 to ~2, and sorts out the related ratings.

    Also, I’ve spreadsheeted all of this, in preparation for the Replenishment nerf, with twenty-odd variables based upon your character’s stats and assumptions.

    If the target is not moving, Shadowfiend can get 10 hits in.

    Thanks for the walkthrough 🙂

    Firebert

  7. BobTurkey says:

    Your welcome.

    I do all my calculations in a spreadsheet also. I’ve considered posting it somehow, but i’ve been too lazy so far. Plus its kinda messy.

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