Stamina-Armour Equivalence

Hello Fellow Tanks,

This is a pretty important concept. Here we show how armour and hit points are dependent upon each other in the grand scheme of things, and how they interact with each other. Always remember that you need to balance what you do with your armour and hit points against avoidance. And, of course, this entire thing is meaningless against spells.

We can equate 1 point of stamina to a number of points of armour that will give you equivalence. That is, X points of armour will increase your time to live by the same amount as 1 point of stamina. The caveat here is that this applies only for melee damage; as soon as someone starts slinging spells it all means nothing, making this a mostly academic exercise. First, we note that the AC dynamic is a simple asymptotic function. In beta, mitigation was capped at 75%, and you can prove to yourself that it is still there by going and fighting much lower level opponents in release.(If you could break the 75% mark, you would achieve 98.96% mitigation at 1,000,000AC against a level 70 opponent). Here's the analysis using 10000AC, 10000HP, facing a level 70 opponent.

For the formula to determine mitigation (M) for a given armour rating (A), we begin with: K = K = 467.5L - 22167.5
Where L is the level of the opponent being fought, then:

A
M = -----
A + K


We get 48.6% mitigation against a level 70 opponent with 10000 armour. Since we'll need it later, solving for AC in terms of mitigation gives:

MK
A = -----
1-M



Let's define survivability in terms of how long a given opponent takes to kill you. Assume we have 200 damage per second incoming, unmitigated, melee only. Taking into account 48.6% mitigation, that’s 102.7DPS. Solving for time, the time to live under that damage rate is 97.4 seconds.

Now, let's increase mitigation by 1%. Using the above formula, increasing mitigation from 48.6% to 49.6% means we need 10408AC, a change of 408 from the original AC. At 49.6% mitigation, incoming DPS is reduced to 100.7DPS. The time to live at that damage rate is 99.3 seconds.

The change in time to live between 48.6% and 49.6% mitigation is 1.93 seconds, or 198 damage at 102.7DPS. 19.8 stamina. Therefore, at 10000AC and 10000, 19.8 stamina is equivalent to 408AC, or 1:20.6 stamina-armour equivalence, in terms of survivability under the given damage output.

Solving this for several other AC points while keeping HP constant at 10000 and 15000: AC 10000HP 15000HP
8000AC 1 stamina to 19AC 1 stamina to 12AC
10000AC 1 stamina to 21AC 1 stamina to 14AC
12000AC 1 stamina to 23AC 1 stamina to 15AC
15000AC 1 stamina to 26AC 1 stamina to 17AC
20000AC 1 stamina to 31AC 1 stamina to 20AC
25000AC 1 stamina to 36AC 1 stamina to 24AC
35000AC 1 stamina to 46AC 1 stamina to 30AC


Changing the hit point total while keeping AC constant at 10000 and 15000: HP 10000AC 15000AC
7500HP 1 stamina to 27AC 1 stamina to 34AC
8000HP 1 stamina to 26AC 1 stamina to 32AC
10000HP 1 stamina to 21AC 1 stamina to 26AC
12000HP 1 stamina to 17AC 1 stamina to 21AC
14000HP 1 stamina to 15AC 1 stamina to 18AC
16000HP 1 stamina to 13AC 1 stamina to 16AC
18000HP 1 stamina to 11AC 1 stamina to 14AC
20000HP 1 stamina to 10AC 1 stamina to 13AC


We see that this equivalence is variable on both hit points and armour, but also that increasing hit points increases the value of armour very quickly, while increasing armour increases the value of hit points at a slower rate. Either way, overloading on one over the other drastically increases the value of the lower one.

One of the fundamentals of the calculation above is 48.6% mitigation against a level 70 opponent. Against raid level targets, which will be higher than level 70, your mitigation starts to go down – the effects are shown here: Level 10000AC/10000HP 13000AC/10000HP 10000AC/13000HP 12000AC/12000HP 15000AC/15000HP
Level 70 1 stamina to 20.6AC 1 stamina to 23.6AC 1 stamina to 15.8AC 1 stamina to 18.8AC 1 stamina to 17.0AC
Level 71 1 stamina to 21.0AC 1 stamina to 24.0AC 1 stamina to 16.2AC 1 stamina to 19.2AC 1 stamina to 17.4AC
Level 72 1 stamina to 21.5AC 1 stamina to 24.5AC 1 stamina to 16.5AC 1 stamina to 19.6AC 1 stamina to 17.7AC
Level 73 1 stamina to 22.0AC 1 stamina to 25.0AC 1 stamina to 16.9AC 1 stamina to 20.0AC 1 stamina to 18.0AC
Level 75 1 stamina to 22.9AC 1 stamina to 25.9AC 1 stamina to 17.6AC 1 stamina to 20.7AC 1 stamina to 18.6AC


Finally, we can do some solving to get a general formula for stamina-armour equivalence against a given level opponent:

10(K+A) K+A
1 stamina: ----------------- points of armour or 1HP: ---------- points of armour
H H


Where A is your current armour, H are your current hit points, and K is as defined previously.

A final note is that this formula is not affected by the actual rate of incoming damage per second. As such, it is not affected by avoidance. An avoidance total of 20% from the combined dodge and parry of an individual character does nothing more than reduce the rate of incoming DPS by 20%, on average. While a 20% reduction of incoming DPS is significant (as is the reduction in critical hits that comes with it), it has no bearing on the stamina-armour equivalence.

So, what should you aim for when choosing gear? What we see here is that balance is pretty key to the whole thing. If you stack one at the expense of the other, you are doing yourself more harm than good overall. Having a good balance between AC and stamina tends to focus both for you - when you are taking physical damage. Empirically, the 12000AC/12000HP pair is thrown around as a "good starting point" for Karazhan raiding. We see that this pair tends to be around 1:20. Magical damage is a factor that helps to balance the difference between higher hit points and higher armour. Having very high armour at the expense of hit points might seem to be of benefit against pure melee opponents, but is a definite disadvantage to opponents using magic, and the amount of buffer you have against hard hits and mishap is probably going to be too small - you can't stop every crushing blow. Your mileage will vary.

Any questions please whisper me.

Huntres