Why do tanks die?
I've made posts like this before, so apologies if it's a bit repetitive. I've also been playing around with it for a while. Apologies also therefore if it doesn't make much sense.
Bear in mind that most tank healers run at 30%+ overhealing. Generally, if your 10 man raid has three healers then someone will be spam healing you the whole time. If you have two healers they have to work a little harder, but very broadly the chances of a big heal (or a series of hots) hitting you every two seconds is very very high.
Once you hit a certain stamina hurdle (eg, the ability to survive one hit from a boss, plus some random magic damage that is flying around), and your healers reach a reasonable gear level for the instance, then extra stats are there just to stop you dying to something that goes wrong with your healing.
Let's be clear - when everything is going well and you clear the stamina hurdle, improvements to your gear do not matter. You could have zero avoidance - it would not matter to the healers who will be healing you whether or not you are taking damage since they are spam healing you. Adding 1,000 health will not affect anything at all (you will simply be healed up to a slightly higher benchmark each time), whereas adding armour or block will simply increase overhealing.
When one of your healers is doing other stuff however (running from a light bomb, healing the raid, being dead), they can't heal you and so you may get little or no healing for a period of time while your healing team resolve their problem and resume healing you again. You need therefore to be able to survive that "healing drought". The issue here is that boss damage is spiky - you might take zero damage for two or three seconds, then 20k from a bit meaty hit. Because boss damage is not a continuous function, increasing health or armour can make a huge difference or no difference at all. Similarly, a defensive cooldown can save your life, or make no difference at all.
Example - You have 20,000 health fully buffed. The boss hits you for 15,000 every three seconds. Suddenly your healer gets silenced. Boss hits you for 15,000 leaving you with 5,000 health left. Your remaining healers have 3 seconds to heal you for 10,001 or you will die to the next boss hit. If you get no healing then neither Last Stand or Shield Wall will save you on their own, although both together will save you even if you get zero healing in the next three seconds. Your healers would then have another three seconds to heal you up to 15k (or a bit less with shield wall up). So if you do nothing and don't get healing you will die in 3 seconds (subject to avoidance). Use of both defensive cooldowns will keep you alive for another three seconds. After that you are toast. You might get lucky with avoidance, and we can all remember occasions where that has saved us (I remember a parry on 500 health tanking Thorim once). Avoidance means you have a chance, but not the certainty, of living longer.
Suppose you have 29,000 buffed health instead - note that here you will STILL die in 3 seconds from the boss's next swing unless you are healed. Your extra 9k of health does nothing to prolong your life unless you get healed. It means that the healers only need to heal you for 1,001 to save you, but if you are not getting healed for any reason then the extra stamina is not helpful in this situation. In the latter case however last stand or shield wall will save you (you don't need to use both) for a further 3 seconds.
Suppose now that you have 30,001 health. All of a sudden you will survive for 6 seconds even if you get no healing. The extra 101 stamina make a big difference to in this particular situation.
So what does stamina offer then? It means that you might survive an extra hit from the boss, either because you have the raw health to do so, or because you are getting SOME healing during your healing drought.
The damage reduction offered by armour is a less effective version of stamina in terms of increasing your expected life time during a healing drought.
Avoidance gives you a random chance of surviving the healing drought. Sometimes you will live and sometimes you will not.
The answer that most people give to stam/armour/avoidance is that they prefer stamina. It's obvious that a stamina stacking tank is geared. You can admire their massive green bar (steady there...). If you stack avoidance or armour however, it's not obvious to someone who is not a tank ("He's got 30% dodge, 30k armour and 30k health" "He's undergeared, kick him!"). Ultimately however all three attributes have their place.
Avoidance - Provides the best damage reduction over the course of a fight so ideal if your healers are in the position where they either can't keep up with the boss's damage output, or there is a lot of raid damage.
Stamina - Great for reliably taking big hits. Provides zero mitigation so you will take a lot of damage, but you shouldn't get one or two shot. Gives the best chance of surviving a healing drought.
Armour - A compromise between stamina and avoidance. Better during a healing drought than avoidance, but worse than stamina. Provides good mitigation throughout the fight, unlike stamina, and so has some of the benefits of avoidance listed above.