Ardent Defender as an Effective Health Bonus

This is a modified version of an old post of mine from maintankadin, but it's one of my favourite bits of theorycrafting, so I thought it merited a post here. For those of you who aren't paladins, Ardent Defender (AD) is a talent that reduces all damage we take by 30% when our health is below 35%. Effective Health (EH) is our heath adjusted for armor bonuses, and was created as a way of considering worst case scenarios and how many hits we could take before we died a horrible, bloody death when we fail to avoid a single attack. This post was designed to see how much of an equivalent to EH we are given by Ardent Defender in various worst-case scenarios.

1-2) For any mob that can kill us in one or two hits, it is useless.

3) For any mob that can kill us in three hits, the third hit would be affected by AD. So, in order to kill us:

x+x+0.7x=100%

2.7x=100%

x=37%

That means that, in order to kill us in three hits, a mob would need to do 37% damage to us on each hit.

This translates into: 37%*3=111%

So, for a mob that can kill us in three hits, AD is like a 11% EH bonus.

4) For a mob that can kill us in four hits, the fourth hit would be affected by AD:

x+x+x+0.7x=100%

3.7x=100%

x=27%

27%*4=108%

5) For a mob that can kill us in five hits: x+x+x+x+0.7x=100%

4.7x=100%

x=21.3%

21.3*5=106.5%

Note that 21.3%*3 is very close to 65% (it's 63.9%), so if one of the first hits is a little larger, the last two hits will both be affected by AD:

x+x+x+0.7x+0.7x=100%

4.4x=100% x=22.7%

22.7%*5=113.5%

6) For a mob that can kill us in six hits, though, the last two hits will definitely be affected by AD: x+x+x+x+0.7x+0.7x=100%

5.4x=100%

x=18.5%

18.5%*6=111%

So, assuming we get hit by a mob for about the same amount (not exactly a fair assumption, but true in many situations), the bonus EH from AD is:

2 hits: 0%

3 hits: 11%

4 hits: 8%

5 hits: 6.5%/13.5%

6 hits: 11%

Strictly speaking, of course, this isn't an EH bonus in the same way that Block Value isn't EH. However, in a "worst case scenario", we can consider what would happen if we never avoided an attack, which is the purpose of calculating EH in the first place. Therefore, one can think of AD as being an EH bonus in the same way one can consider BV an EH bonus. In a worst case scenario, it adds to our survivability like effective health. Like BV, the amount of bonus scales with the number of hits we take before we die (though the bonus is a curve rather than a straight line).

Ardent Defender is one reason why we are such resilient tanks right now. For a long time, our lower hit points and then our lower damage reduction were justified by appaling to Ardent Defender. For mobs that couldn't kill us in two hits, this was true, but for those that could, it was useless. Now, however, we've been given the health and damage reduction but kept Ardent Defender. This had the effect of making us really hard to kill.