The new EH: beyond physical damage

I’d hope you’ve seen this thread on maintankadin, it’s been fairly regularly mentioned around the blogosphere and twitter.

Theck has worked out a new formula for effective health which accounts for magic or non-physical damage. This is significant because the usual EH formula assumes just physical damage and armour, basically, whereas the New EH accounts for magic, bleeds and resistances.

At the time of writing this, artifact 19 (in the Conclusion) is the formula:

                  (1-X-Y)           X               Y
EH = H*D/d = H*-------------- + H*-------- + H*--------------             (19)
               (1-Ma)(1-Mt)       (1-Mt)       (1-Mg)(1-Mr)

He’s said that:

The take-home message of these formulas is that armor loses effectiveness linearly with the percentage of “regular” physical damage intake for a given fight.

In other words, for a fight with only 50% non-bleed physical damage, armor is reduced in effectiveness by 50%. If an armor trinket is worth 100 stamina on a purely “regular” physical fight, it will only be worth 60 stamina on a fight with 15% bleed damage and 25% magic damage (60% “regular” physical).

I asked Theck to confirm how we’d use this to compare Unholy talents for damage reduction (which is 6% on all magic damage) to Frost’s 2% flat reduction on all damage plus 3% melee avoidance. He answered (page 3, about half-way down):

“The easiest thing to do is to just take the EH equation, choose a particular fight (i.e. X and Y), and plug in your health H and armor A, along with the mitigation factors Mt, Mg, and Mr.

For the 2% flat damage mitigation talent, add 0.02 to Mt and Mg before calculating.

For the 6% magic reduction talent, add 0.06 to Mg before calculating.”

I haven’t done that EH calculation yet.

The result would be you could work out the EH of a Frost and Unholy tank, if all gear was otherwise the same (ie. just the talent differences), as they’d be in different fight-types, say one with 10% magic damage and another with 20%.

Any fellow geeks want to, go ahead, it’s pretty easy: just stick it into Excel if you’ve no maths tools. Let us know here.

Wrathy is going to start tabulating the different damage mixes in ToC and ICC, which means the New EH can then be used to help select gear and talents by applying the formula, to in turn improve survival in the new ICC content.

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7 comments to The “total EH”: beyond physical damage

  • I’m actually kind of interested to see if this will help bring some of the more dogmatic EH tanks to a higher level of performance.

  • Gravity
    Twitter: gravitydk

    I wonder. I will tell Reynard about this so he can put it into TankTotals, that might help.

  • Well, the issue is that it’s going to be on a per encounter basis, which is as it should be. An identical gear set gets you different mileage on Patchwerk than it does on Hodir. The parameters will be shifting in every fight, and while I have no experience in coding addons, I imagine that that would be brutal to code.

  • Gravity
    Twitter: gravitydk

    The other variables in the formula, I didn’t note in the post:

    • His hits deal raw damage D. If your physical mitigation is M, then the damage that shows up in the combat log is d.
    • Ma is the mitigation due to armor, defined below
    • Mt is the mitigation applied to physical damage due to talents
    • Mg is the mitigation applied to magical damage due to talents
    • Mr is the mitigation applied to magical damage due to resistances
    • X is the percentage of our damage intake that’s from bleed effects,
    • Y is the amount of damage taken from magical sources, (and 1-X-Y is the “leftover” amount due to regular physical damage)

    You’d notice the formula has three bits to it (terms), which are added together. The first term is our EH against “regular” physical attacks multiplied by the percentage of our damage intake that those attacks represent. The second term is our EH against bleeds, multiplied by the percentage of our intake due to bleeds. And the third term is our EH against magical damage multiplied by the percentage of our intake that’s magical.

    In other words, EH is properly calculated as the weighted average of our EH against all damage sources, with the weight factors simply being the percentages of our intake that those sources represent.

    You can get X and Y from a combat log parse.

    Ma is defined below, where A is your armour:

    Ma = A/(A+K)
    K = 467.5*L - 22167.5

  • R

    Hey Gravity,
    Was going to reply to you here, but I figured I might as well post on the original Maintankadin thread (page 7). Hope you had a good trip!

    • Gravity
      Twitter: gravitydk

      Hiya Reynard, I’m glad you chipped in there, it was the right place for such a solid contribution. Settling going well. My sleep nearly back to normal (work at 430am today), and all the many logistics of a new house are a bit daunting.

  • I should probably point out that I made a slight mistake in my advice to you.  In all likelihood those talents are multiplicative rather than additive, unless they’re modifying existing talents.
    In other words, rather than add 0.02 or 0.06, you’d multiply the denominator by an extra factor of (1-0.02) or (1-0.06).
    Example: if you get 15% mitigation from other sources, and a talent adds 5% mitigation, your net mitigation is (1-0.15)*(1-0.05) = 0.8075, rather than (1-0.15-0.05)=0.80.

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