Thursday, October 4, 2007

Comparing Healing Gear (Part 3)

Once you calculate your theoretical healing output, it is relatively simple to modify the general formula to increase each stat by one point for an adjusted total output. The relevant stats for our analysis are: +Healing, Intellect, Mana pool, spell crit rating, Mana/5, and Spirit. You can then use these adjusted numbers to compare the absolute increase in healing output, the percent improvement each stat provides, and the relative values of each statistic.

Once again, the general formula for healing output is:

[(Base Heal Amt + Healing Bonus * Spell Coefficient) * (1 + 0.5*crit) * Multipliers] / [(Mana Pool + Mana Sources + ((Mp5*I5SR) + (OOC regen*O5SR)+ Add. Mp5) * 60/5 * Length) / Mana cost]
I won't clutter this posting with the math for each stat (that's what spreadsheets are for!), but will instead list the calculated improvement each would provide with my current gear using the following formula:
(New output - Base output) / Base output * 100
Healing
This stat is the easiest to adjust for:
[(Base Heal Amt + (Healing Bonus + 1) * Spell Coefficient) * (1 + 0.5*crit) * Multipliers] / [(Mana Pool + Mana Sources + ((Mp5*I5SR) + (OOC regen*O5SR)+ Add. Mp5) * 60/5 * Length) / Mana cost]
  • Percent improvement: 0.033%
Intellect
Intellect has several effects on this formula. It increases your base mana by 15, with a slight additional effect on your Mana Tide returns (not shown), and increases your crit by 1/70%. Each point of Nature's Blessing will also add 10% to your +healing, and for Elemental Shaman, Unrelenting Storm will convert it into 0.02 mana/5 per talent point. Assuming you'll receive Blessings of Kings (adds 10%), this results in:
[(Base Heal Amt + (Healing Bonus + 0.11*NB ranks) * Spell Coefficient) * (1 + 0.5*(crit + 1.1/70%)) * Multipliers] / [((Mana Pool + 16.5) + Mana Sources + ((Mp5*I5SR) + (OOC regen*O5SR)+ (Add. Mp5 + 0.022*US ranks)) * 60/5 * Length) / Mana cost]
  • Percent improvement: 0.063%
Mana
Very straightforward (with a miniscule effect on Mana Tide regeneration):
[(Base Heal Amt + Healing Bonus * Spell Coefficient) * (1 + 0.5*crit) * Multipliers] / [((Mana Pool + 1) + Mana Sources + ((Mp5*I5SR) + (OOC regen*O5SR)+ Add. Mp5) * 60/5 * Length) / Mana cost]
  • Percent improvement: 0.003%
Spell crit rating
Each point of spell crit rating improves your crit by 1/22.1%:
[(Base Heal Amt + Healing Bonus * Spell Coefficient) * (1 + 0.5*(crit + 1/22.1%)) * Multipliers] / [(Mana Pool + Mana Sources + ((Mp5*I5SR) + (OOC regen*O5SR)+ Add. Mp5) * 60/5 * Length) / Mana cost]
  • Percent improvement: 0.021%
Mana/5
Another easy one:
[(Base Heal Amt + Healing Bonus * Spell Coefficient) * (1 + 0.5*crit) * Multipliers] / [(Mana Pool + Mana Sources + ((Mp5*I5SR) + (OOC regen*O5SR)+ (Add. Mp5 + 1)) * 60/5 * Length) / Mana cost]
  • Percent improvement: 0.167%
Spirit
Spirit increases a shaman's mana/5 regeneration outside of combat by ½.
[(Base Heal Amt + Healing Bonus * Spell Coefficient) * (1 + 0.5*crit) * Multipliers] / [(Mana Pool + Mana Sources + ((Mp5*I5SR) + ((OOC regen + 0.5)*O5SR)+ Add. Mp5) * 60/5 * Length) / Mana cost]
  • Percent improvement: 0.008%

Analysis
Looking at the various improvements, you can easily see that mana/5 provides the biggest improvement in overall healing ability. Dividing each by the improvement provided by one point of +heal, you get the relative "value" for each stat.

Relative "value" of healing stats for Draezele
Healing1.00
Intellect1.93
Mana0.08
Spell crit0.64
Mana/55.07
Spirit0.25

How to use this information is really up to you. When comparing gear, I usually calculate the percent improvement I would receive based on the increases in stats (just adding them up, basically). I find that this is a good judge of whether an upgrade is worth taking or whether I should pass it along to someone else who could put it to better use.

Before I move on to the final section, I want to highlight a few things about this analysis:
  • This calculated output assumes you are casting nothing but healing spells. No totems, no Purges, no Earth Shocks, etc. More time (and mana) spent casting non-healing spells reduces the effective amount healed per spell cast since they have a healing amount of zero (this reduces the effects of Healing and spell crit, primarily - Intellect's major effect is on the number of spells able to be cast).
  • The relative value of mana/5 and +healing are inversely proportional: The more mana/5 you have already, the more valuable additional healing becomes; the more healing you have already, the more valuable additional mana/5 becomes. If you stack one preferentially, it becomes less and less effective, so you ideally want to have a balance of the two.
  • There are several reasons why my calculated value for mana/5 in PvE gear is significantly different from the 11:1 ratio calculated by my guildmate Phaelia. Aside from any differences in our characters' current stats (and stat balance as mentioned above), shaman have a much lower base mana efficiency for their spells. Adding more mana can be thought of as "throwing good money after bad." Casting slightly more mana-efficient spells therefore has a greater effect than casting more spells (in comparison to a druid's Lifebloom, for example, which is already incredibly mana-efficient - "retardedly" so, according to Phae). Healing styles also play a major role. Shaman have no instants and no heal-over-time spells, so it's a little harder for us to "use up" our pool during any fight that requires frequent movement.
  • As always, use common sense when applying these numbers. If you find yourself continually running out of mana, you probably need more mana/5 or Intellect, even though the improvement "value" may be lower. Likewise, if your tank keeps dropping while you still have most of your mana bar, you may want to focus more on +healing. These values don't mean anything in a vacuum, so don't just use them blindly.
Continue to Part Four (Refinements)
Go back to Part One (Average Heal Amt.)
Go back to Part Two (Maximum Spell Casts)


Also see Comparing Healing Gear (Revisited) for further discussion.

4 comments:

Kenny said...

Hello,

I'm trying to understand your formula in an attempt to stand upon the shoulders of giants and adapt this for Holy Paladin healing.

In the Fight 1 section, when you calculate Total Healing, Healing, Intellect, etc, you have a section of the formula that calculates how much extra healing you'll get from crits.

(1 + 0.5*($B$5 + 5% + (59.4 + 0.1*$B$3)/7000)))

I don't understand what the last section of this formula is doing...

What is 59.4? where is the 7000 coming from? I've noticed that the 59.4 value is different for each of the things calcuated (Healing, Intellect, etc), so I'm wondering where this number comes from. Any help would be appreciated, thanks.

Draezele said...

$B$5 is your tooltip crit, where 5% is from talents (not included on the tooltip). The rest of the formula represents the increased crit gained from Arcane Brilliance and Blessing of Kings (54 * 1.1 and your current Int * 0.1). The 7000 represents that 70 Int = 1% crit.

(Sidenote: this formula is incorrect, it should be 80 Int per 1% for shaman).

Kenny said...

Thanks Draezele, that helps a ton. One last question, the 59.4 value (the int buffs modifier) is different in the Intellect row:

Healing is 59.4
Intellect is 60.5
Spell Crit is 59.4
etc..

Was this an oversight or is there a reason the Int row has a different modifier?

Thanks again.

Draezele said...

The Intellect row calculates the additional amount of healing after raising Intellect by one. 59.4 + 1 Int * 110% (for Kings) = 60.5.

Glad you're finding my work helpful!