Let's do some napkin math (retrospective edit: very-large-napkin math):
- You have 45k max health.
- Bosses melee for 15k.
- Scenario: you take a hit that reduces you below 35% (we'll call it 15k) and are at risk of being oneshot by the next 15k attack.
- Health distribution before the possibly deadly attack is somewhere between 1 and 15k, uniformly distributed.
- Blocking/block value is ignored. Note that correcting for block would favor Blood Draining (bosses, on average, hit for less compared to the static heal from Blood Draining, and you're less likely to be below 35% over time so Blood Draining will, on average, have a higher stack).
- We'll say you have a 45% chance to be hit (or "block" for 0 damage).
- Blade Warding (onestack) is up 26% of the time (first source (saying 26%, derived from logs), second source (saying 30.6%, derived from modeling))
- Blade Warding (two or more stacks) is up a negligible portion of the time.
- Blade Warding (one stack, so 200 parry rating) gives 1.64% parry after DR (true for my warrior with 20.94% after DR in a mishmash of gear).
- Mongoose is up 30% of the time (see posts below).
- The 120 agi from Mongoose, when up, gives 1.19% dodge after DR (true for my warrior with 23.76% after DR; source for AGI/dodge conversion).
- The 120 agi from Mongoose, when up, gives 0.53% relative damage mitigation through armor (true at 28k armor before Mongoose).
- I don't avoid death from two consecutive melees because of Mongoose - i.e. the best that Mongoose can do is save me once. If Mongoose saved me twice, that means I didn't get heals for long enough to die twice, so we're probably wiping for another reason (healers dead, etc).
- At the time of the possibly deadly incoming attack, Blood Draining is equally likely to be at 1, 2, ... 5 stacks. In particular:
- I don't go <35% -> full health -> dead before Blood Draining can get up at least one more stack. If I merely go <35% -> dead within ten seconds (without hitting full health), Blood Draining's heal helped me anyway.
All right. With that out of the way, let's figure out how often the three above enchants will save us in the scenario described.
Blade Warding: I have a 45% chance to be hit without it up; with it up (26% of the time), I have a (1.64% / 45%) chance to avoid a hit that would have otherwise landed and killed me. Using the Blade Ward enchant, I therefore have a (0.26)*(0.0164/0.45) = 0.00948 = 0.948% chance to live because of Blade Ward.
Mongoose: I have a 45% chance to be hit without it up; with it up (30% of the time), I have a (1.19% / 45%) chance to avoid a hit that would have otherwise landed and killed me. Even if the hit does land, I can still be saved if the extra armor from Mongoose reduces the damage to a survivable level. A relative reduction of 0.53% will save me 0.53% of the time (if this doesn't seem intuitive, realize that a 50% relative damage reduction would save me 50% of the time, a 100% relative damage reduction would save me 100% of the time, etc.) Using the Mongoose enchant, I therefore have a (0.30)*(0.0119/0.45) = 0.0079 = 0.79% chance to live because of an avoided hit, and a (0.30)*((0.45 - 0.0119)/0.45)*(0.0053) = 0.15% chance to live because of the bonus armor, for a total of 0.94% chance to live because of Mongoose.
Blood Draining: I'm hit and my health goes somewhere below 15k, equally likely to be all values between 1 and 15k. Blood Draining heals me for ~400, ~800, ... or ~2000. We assume each are equally likely. Note that a heal for 800 is twice as likely to save me as a heal for 400; a heal for 1200 is three times as likely, etc. so we can just compute the probability for one of them: a heal for 400 saves me if I was somewhere between 14,601 and 15,000 health, a probability of 400/15,000 = 2.667%
So there you have it. Probability of surviving the otherwise-fatal blow because of the listed enchant, in the scenario and under the assumptions described above:
Blade warding: 0.95% chance
Mongoose: 0.94% chance
Blood draining: 2.667% chance with one stack, multiplicatively greater with more stacks
Let's try modeling harder content. Say the tank has 50k health raidbuffed and incoming hits are for 20k. Our chance to avoid death thanks to our enchant remains the same for Blade Warding and Mongoose, as those don't depend on tank health. (If you're wondering why Mongoose's armor buff doesn't become more important when taking bigger hits, remember we used the relative damage reduction, not absolute.) The chance for Blood Draining, though, will suffer because a) there's a chance you can get hit from >35% to dead without a heal going off, and Blood Draining's heal is relatively weaker to the incoming hits. Assuming uniform health distribution between 1 and 20k, there's a (1 - (17.5k / 20.0k)) = 12.5% chance that Blood Draining never got the chance to heal us before we died. Otherwise, if a heal does go off, there's a (400/17500) = 2.286% chance that it saves us with one stack. The probability to avoid a death is thus (87.5%)*(2.286%) = 2.00%, still beating out Blade Warding and Mongoose.
Blade warding: 0.95% chance
Mongoose: 0.94% chance
Blood draining: 2.00% chance with one stack, multiplicatively greater with more stacks
Note that this ignores some aspects of the relevant enchants, including:
- multiple stacks of Blade Warding
- threat from Blade Warding/Mongoose
- healer mana saved through avoided hits during reactive healing from Blade Warding/Mongoose
- Blade Warding/Mongoose not working on unparryable magic damage
If I had to knock a hole in my own math, I'd say the assumption about health amounts being equally likely between 1 and 15k is probably untrue; I'd guess that tank health over time tends to clump at "full health," "full health minus one boss melee," "full health minus two boss melees," etc. with the second, third, fourth etc. clumps getting fuzzier as small heals + hots + boss RNG factor in. The question then becomes, "How often do bosses kill you with little enough overkill that a Blood Draining heal would have saved you?" (assuming they knock you below 35% first so the heal can go off preemptively; obviously Blood Draining doesn't work retroactively). Another poor assumption is that Blood Draining always has time to get up at least one stack, but I wouldn't know how to model that (you'd have to predict the frequency of otherwise-deadly hits and how frequently healers manage to top you off).
Thoughts? Corrections to my assumptions? Better ways to model the flaws I point out? I keep hearing the tank enchant question being bandied about and would like to settle it (from strictly a tank survival standpoint) once and for all. (I think this is an important question to answer, didn't find much discussion at all on EJ, and didn't find satisfactory discussion on TankSpot, but if a mod feels this issue is old or has been addressed feel free to delete.)
TLDR1: Will Blade Ward, Mongoose, or Blood Draining save you a higher percentage of the time against otherwise deadly hits from progression bosses? Under certain conditions, Blood Draining appears to be significantly favored.
TLDR2: Does anyone have data on the distribution of overkill damage that deadly hits from progression bosses deal?