Effective Health - The holy grail of tanking?

Go to any tank-related forum and open a thread on gear-choices and the first thing you'll notice is that everyone always talks about Effective Health (or EH). It's great, it makes you live longer, be the star of the raid, get epics and possibly create world peace. However, the concept as it is used by 99% of the posters on these forums is wrong. They assume circumstances that simply do not happen in actual raids.

What is EH?
EH is a measure for the amount of damage you take before you die in a worst-case scenario. The worst-case scenario being: You don't avoid any hits, you don't get healing, you don't get shields and you don't use any cooldowns.

This means that there are 2 main contributions to effective health: HP and garantueed damage reduction. HP is straightforward, get 10% more of it and you'll live 10% longer when there's no healing. By garantueed damage reduction, people generally mean armor. It reduces the physical damage you take and since this is the majority of the damage, having more of it will make you live longer.

Health comes from stamina. Each point of stamina gives you 10 HP. However, various talents and buffs increase the stamina you get from gear. A Feral Druid gets 25% more stamina from being in Dire Bear Form, 10% from Heart of the Wild, 6% from Survival of the Fittest, 2% from Imp. Mark of the Wild and finally 10% from Blessing of Kings. Since these bonuses stack multiplicatively, the Druid ends up with 16.35 HP from 1 point of stamina on gear. Plate tanks have less of these talents, so they gain less from 1 point of stamina, but their gear tends to have more stamina, so it evens out somewhat.

For armor, the following formula holds for L83 opponents (which means: raid-bosses):
DR = Armor / (Armor + 16635)
Fill in 30000 and you get DR = 0.643, so a 64.3% damage reduction from armor.

If you have 60K HP and 65% damage reduction from armor (30894 armor), your EH is 171429. This means that a mob has to do 171429 damage before armor-reduction to kill you. Adding 1 stamina gives you 16.35 HP and this translates into an increase of your EH by 46.71. On the other hand, adding 10 points of armor increases your damage reduction by 0.00736%, which changes your EH to 171465, an increase of 36. So at these stats, 1 point of stamina gives you more EH than 10 points of armor (note that 1 point of armor is equal to 6.7 points of armor in terms of itemization-budget).

With just the built-in Windows (or in my case: Linux) calculator, you can redo these numbers for your particular situation.

So where does it go wrong?
The above calculation makes sense in the absence of any form of healing, shielding or cooldown-usage. And since the goal of EH maximalization is to gear for the worst possible case, this sounds reasonable right? Well, no. Sure, no healing at all is the worst possible case, but in any realistic raiding environment, there will be heals landing on you all the time, even if the main tank healers are focused elsewhere.

In my raid, there's always at least one Resto Druid who has a whole array of HoTs on me. There generally are HoTs from Priests or Shamans ticking and there's often some form of shielding as well: Sacred Shield from Paladins, Power Word: Shield from Priests, but most of all my own Savage Defense shield which is up for the vast majority of the attacks that land. Since bosses don't one-shot you, but instead need several swings to kill you, the HoTs plus any incoming splash or direct heals will heal you. And direct heals will land, since my healers know that a tank needs healing and will be casting their heals. And I don't know of any 25man encounter that takes all healers out of the game for a little whle at the same time.

Suppose a boss takes 5 seconds to deliver a series of burst attacks that could kill me. In this time-frame it's not unlikely to have 20K worth of heals and absorbs in total. Going back to the numbers-example I mentioned above, this means that my "effective" health would be 80K, not 60K, since in the no-healing scenario, I would have the same survivability with 80K HP as I would in the scenario where I have 60K HP and 20K healing/absorbs coming in. At 80K effective HP, the EH benefit you get from 10 points or armor increases from 36 to 47.88. That's a massive difference.

If you weigh in the costs of both stats in terms of itemization budget, stamina still wins out, but the gap is alot smaller now. And these are just some randomly picked example values. In most boss-fights where tank-death is an issue, you can generally identify the moments that are the most dangerous and use your cooldowns during these moments. Take Festergut for example, once he hits 3 stacks of Inhale Blight, he starts to hit like a truck. During the largest part of this phase, I have Survival Instincts active, this increases my HP by 30% (even more for people who glyphed it) and thereby gives the EH-contribution of armor a massive boost.

On the other hand, bosses that use magical damage as their main tank-killer don't care all that much about armor. On Sindragosa, that Frost Breath when you're at high stacks of Mystic Buffet will play a much bigger role in your death than the melee swing that follows it. In these cases, your EH is purely determined by your stamina (and to some extent your frost resistance).

Conclusion
EH is seen as the holy grail and a straightforward way of calculating the value of stamina compared to that of armor exists and is used regularly. However, which factors actually contribute to your EH depend greatly on the encounter. The naive EH formula assumes a 100% physical damage encounter, which is not always the case. And even in fights where all the (dangerous, bursty) damage is affected by armor, the fact that you're never in the "worst-case-scenario" assumed by the naive EH-computation means that your actual EH is not so easy to express as a number. On top of that, using cooldowns during the dangerous phases again shifts the balanace of stats compared to the non-cooldown phases.

So take EH arguments with a grain of salt: They're often based on some sort of idealized environment that will never occur in the actual game. Think about the encounter when you select your gear and only play the numbers game once you factor in the specifics of the boss and how you plan on reacting to them.