Tuesday, October 2, 2007

Comparing Healing Gear (Part 1)

There are a variety of ways to calculate the relative worth of each healing stats - from simple estimation to complex calculations based on your current stats. Theorycrafting junkie that I am, I of course go for the complex calculations.

The method I prefer is to calculate the maximum theoretical healing output with my current gear (the average amount healed per spell multiplied by the maximum spells I can cast in a given timeframe based on available mana reserves). I then calculate the percent improvement if I increase a single stat by one point. (For true accuracy, you can compare two pieces of gear directly - calculating total output while wearing one piece of gear compared the total output while wearing the other - but the results are very similar unless you're changing complete sets of gear at once.)

I'll demonstrate how to calculate total healing output in my first two posts and then explain how to calculate the percent improvement for each stat in Part Three. Part Four will include additional refinements such as applying weights to stats such as Stamina or Armor.

Required Information
In order to calculate total healing output, you need to know:

  • Your tooltip stats: Intellect, +healing bonus, spell crit, base mana pool, and mana regen rates (both combat and non-combat)
  • Length of fight: I use 7½ minutes as a good estimate.
  • Buffs/Consumables: Determine which buffs you expect to receive, along with your typical consumables. For my calculations, I assumed I would have/use: Gift of the Wild, Arcane Brilliance, Wisdom, Kings, [Flask of Mighty Restoration], [Superior Mana Oil], and [Blackened Sporefish]. I also estimated that I would use 3 [Super Mana Potion] in that 7½ minute timeframe.
  • Spell use: You'll need the minimum/maximum healed, mana cost, and casting time for your most commonly used spell (I use a weighted average of 5% HW, 5% LHW, 85% CH and 5% ES for my calculations based on my typical use of these spells as I feel it provides a little more accuracy). You also need to know the approximate amount of time during the fight you will be outside the 5-second rule (O5SR) and gaining out-of-combat (OOC) mana regen. I'll use 10% O5SR for my calculations, although in practice I'm generally higher.
Average Amount Healed
The basic formula is:
(Base Heal Amt. + Healing Bonus * Spell Coefficient) * (1 + 0.5 * crit rate) * (1 + 2% * ranks in Purification talent)
If using Chain Heal as your spell of choice, add:
* (1 + 10% * ranks in Imp. CH talent + 5% for the Skyshatter (Tier 6) 4-piece bonus)
  • Base Heal Amt. is obtained by averaging the minimum and maximum healed from your selected spell. If using CH, I suggest multiplying by 1.4 with the assumption that you'll heal an average of two targets every cast (each jump heals ½ as much: 1*1/3 + 1.5*1/3 + 1.75*1/3 = 1.4). Note that the [Totem of Healing Rains] adds directly to the base amount healed by CH, whereas the majority of Totems add healing bonus.
  • Healing Bonus is equal to your tooltip healing bonus.
    • If you have points in Nature's Blessing, you also need to factor in the effects of Mark of the Wild (+14 Int), Arcane Brilliance (+40 Int) and Blessing of Kings (+10% to all stats). Assuming 3 points in NB, this is equal to: (59.4 + 10% * tooltip Intellect) * 30%.
    • Include any spell-specific +heal effects (Totems, primarily).
    • If you use on-use trinkets such as [Lower City Prayerbook], add in their average effect over the long term: (+heal granted * length of effect) / cooldown (I'm bad at remembering to use my clickable trinkets, so I often multiply these effects by 50% to simulate the "wasted" opportunities.)
  • Spell Coefficient is equal to (base cast time/3.5). If using CH, multiply by 1.4 for the average effect of two players healed (yes, this will make your coefficient greater than 100%!). The coefficient for ES is 300% (30% each charge * 10).
  • Crit rate is equal to your tool-tip rate plus 1% for each rank of Tidal Mastery. You also need to factor in the three buffs listed above, which increases your crit by: (59.4 + 10% * tooltip Intellect)/70 * 1%.
For my current stats (1641 +heal, 543 Intellect and 8.99% crit), using [Totem of Healing Rains], [Totem of Spontaneous Regrowth], and [Totem of the Plains] as appropriate, and with no on-use trinkets, this works out to:
  • Base Heal (weighted average): HW*5% + LHW*5% + (CH + Totem bonus)*85%*1.4 (assuming 2 targets healed on average) + ES*5%*10 (10 charges per cast) = 2285*5% + 1112*5% + (884+87)*85%*1.4 + 270*5%*10 = 1460.3
  • Healing Bonus: Base + Bonus from buffs + Bonus from Totems (weighted by usage of respective spells) = 1641 + (59.4 + 10%*543)*30% + (88*5% + 79*5%) = 1683.5
  • Spell Coefficient (weighted average): HW*5% + LHW*5% + CH*85%*1.4 + ES*5%*10 = 3/3.5*5% + 1.5/3.5*5% + 2.5/3.5*85%*1.5 + 30%*5%*10 = 106.4%
  • Crit rate: Base crit + Tidal Mastery + Bonus from buffs = 8.99% + 5% + (59.4 + 10%*543)/70*1% = 15.61%
  • Multipliers: (1 + 2% * Purifcation ranks * (1-5%)) (Purification does not affect ES when cast on another player) and (1 + 10% * Imp. CH * 85%) (weighted by % used) = (1 + 2%*5*(1-5%)) * (1 + 20%*85%) = 128.1%
Plugging these numbers into:
(Base Heal Amt. + Healing Bonus * Spell Coefficient) * (1 + 0.5 * crit rate) * (1 + 2% * ranks in Purification talent) * (1 + 10% * ranks in Imp. CH talent)
(1460.3 + 1683.5 * 106.4%) * (1 + 0.5 * 15.61%) * 128.1% =
4,490 healed per average spell cast.

Continue to Part Two (Maximum Spell Casts)
Skip to Part Three (Stat Valuations)
Skip to Part Four (Refinements)


Anonymous said...

I am starting to like haste more since we are well into BT and MH. I’ve since lost my T5 4 piece bonus to T6 equivalent gear and am missing that 1.5 sec healing wave. I have to believe Blizzard is smart enough to “give” you what you need to survive the later instances. For example, you start to see +haste and +crit gear much more in BT/MH and you find that you need these more and more. There are some technical fights, but most of the fights are pretty fast paced and you are pretty much spamming heals the entire time. With mana tide, pots, buffs, and hopefully shadow priests, mana is rarely an issue for me. Mainly I need big heals quickly. I mainly gem for MP5 but also for int. A large mana base helps a great deal on fights that tend to ramp up; for instance Teron Gorefiend is easy in the beginning, but that last 3-4 minutes are crazy. I like to have a full and large mana pool going into this part of the fight.

As I said, Blizzard usually knows what’s going on and will generally provide you with what you need. I don’t even get into the theory craft; if it has a higher armor rating I generally consider it an upgrade.

Catwalk said...

Hey Draezele,

Just wondering when you might update the calculator to include Sunwell loots?

The calculator is terrific BTW.

Has anyone played with the HEP equation say to favor haste?