When I was looking to make a tank to support my priest in taking down old raid content for reputation and rare mounts, my goal was to find the tank that could do the most damage while being basically invincible. Block tanking was extremely powerful for old content, but focusing gear on maximizing block rating meant doing less damage. A Death Knight could do lots of damage while healing herself for 15% of her health between 4 and 5 times every 20 seconds with Death Strike. That meant every point of stamina on the Death Knight was 0.3 healing per second, which meant that with a couple thousand stamina I wouldn't have to worry about much of anything being able to kill me.
Before Death Knights, bears were the masters of self healing with Improved Leader of the Pack giving them a mere 6% health at most every 6 seconds. A far cry from the 3% per second given by death strike.
I've been analyzing self-healing done by various tanks to figure out which class to level as my old content raiding partner for my priest, and I've come up with the following.
A Blood Death Knight gets 23.6% more stamina from talents and abilities. It would be 29.7% in a raiding situation, but for two-boxing they won't get the blessing of kings/mark of the wild buff. The Death Knight should get about 0.141 Death Strikes per second1. Against low level content they will heal for 10% of the Death Knight's maximum health plus a shield for half of that. In addition, from experimentation, each point of stamina gives approximately 0.032 extra health per second from blood worms. This totals to 0.294 health per second per stamina on gear.
A Warrior has self-healing in the form of Blood Craze and Enraged Regeneration. Warriors get 20.75% extra stamina without blessing of kings/mark of the wild. Blood Craze should have an uptime of around 29.5%2 and will heal for 1.91% of the warrior's health per second thanks to Field Dressing. That gives around 0.56% of health per second or 0.068 healing per stamina of gear. Every three minutes a warrior can activate Enraged Regeneration3 to regain 38.16% of total health. That translates to an additional 0.026 healing per stamina on gear for a total of 0.14 health per second per stamina on gear.
Bears get mark of the wild and have a total of 51.6% extra stamina from buffs and abilities. Frenzied Regeneration is very similar to Enraged Regeneration. Bears don't get Field Dressing, but they do get a huge amount more stamina, so it comes out to 0.0252 healing per second per stamina on gear. Assuming bears are using abilities on the GCD, they should get a Leader of the Pack trigger every 9.89 seconds4 for 8% maximum health. In total, bears heal for 0.147 per second per stamina on gear.
Lastly paladins. Paladins don't get any healing based on their total health or stamina, Ardent Defender excepted. Their self healing is instead based on strength. Word of Glory gets around 11.5% of attack power and 19.5% of spell power to its healing effect per holy power used. Since paladins will have 5% extra strength from Blessing of Kings and get 60% of their strength to spell power, this means Word of Glory has a coefficient of around 36% on strength on gear per holy power. Talented this in increased by 79.8%. Since you generate one holy power every 3 seconds and retain it 30% of the time that you use Word of Glory, Word of Glory heals for 0.312 per second per strength on gear. If you choose to use Seal of Insight, that accounts for another 0.13 healing per second per strength on gear5 for a total of 0.442. Since strength is 1.5 times as expensive as stamina from an item point perspective, we'll divide this by 1.5 for comparison purposes and get 0.295.
Of course there are more factors to consider. A druids and warriors do not give up any damage to self-heal while paladins give up a lot of damage and death knights give up a little. For low level content the paladin's damage penalty from self-healing will likely be made up for by the fact that the self-healing is very controllable - that is, you'll only use it when you need it - and because a lower-level content paladin tank will be geared for damage rather than tanking because their self-healing relies on strength rather than stamina. Also, paladins are the only tank class that have base numbers attached to their self healing. With Protector of the Innocent, even a one point Word of Glory will have a base heal of around 7.5k, which even in top end gear should push paladin self-healing way above other classes.
In raiding content, a paladin tank will presumably not be able to heal themselves as much if they want to hold threat. Death Knights, however, give up very little to Death Strike as often as they can. Keeping up diseases will cost a death strike every 33 seconds, reducing Death knight self healing per stamina on gear to 0.238, but I doubt that it will be necessary to use the Blood Runes generated through Death Strikes for Heart Strikes in order to maintain aggro.
There are clearly two tiers of self-healing. Paladins and Death Knights occupy the upper tier while warriors and druids are on the lower tier. Of course in raids paladins probably can't self-heal as much and Death Knights don't have blocking or Savage Defense, so these things may even out in some ways.
But there are circumstances in raiding where this self-healing capacity may end up being dramatically overpowered. Most importantly, self-healing creates an extremely different dynamic in 10 and 25 player raids.
To look at self-healing in perspective, a Flash Heal has a healing coefficient of around 64.3%. For a Holy priest talents and specialization would increase this to 85%. With a 1.5 second cast time, this means Flash Heal heals for 0.625 per itemized point of intellect. Dividing by 1.5 to normalize with stamina, that's 0.458 accounting for criticals. And that's spamming Flash Heal, not using a sensible rotation. Using the atonement spreadsheet I already made to get an estimate of the benefit of one intellect on gear for a Discipline priest healing, it came out 0.388 per intellect on gear, or 0.259 when normalized with stamina.
If a tank is off-tanking an add that is supposed to be tanked rather than killed and uses a full self-healing rotation, then the difference between using a Death Knight versus a Warrior scales with stamina at about 60% of the rate that a healer scales with Intellect. Since healers get more of their base effect from spells than Death Knights do from base health and stamina, the difference would probably be in the 40%-50% of a healer actually healing. In 25 player, that would mean getting to bring 6.4 or 7.4 healers instead of 6 or 7; essentially a 6-7% bonus to your raid's healing. In 10 player it would instead be a 13% to 20% bonus to raid healing, since the number of healer shrinks but the number of tanks tanking the add stays the same. And this is assuming the Death Strikes always heal for 10% of the Death Knight's health. With the new rune system, the Death Strike can be timed to coincide with a fire breath or other similar attack. If the dragon breaths for 40% of the Death Knight's health - less scary than you think and plausible for an add - then a Death Strike after such a breath weapon would heal for at between 17.5% and 25% of the Death Knight's health, depending on whether other attacks landed near the same time. This could increase overall Death Knight healing per stamina on gear against dragon type bosses or other bosses that do a large hit every 12-ish seconds, to 0.392 even if only half the Death Strikes can come after breath weapons. Compared with warriors that scales as though there were a full extra healer in the raid.
I'm not convinced that Death Knights are the best tanks on account of their self healing. Without blocking they are going to take more damage, and normally they won't be able to realize their full self-healing abilities. But self-healing is a tricky thing to watch for in terms of tank balance. For certain fight mechanics, it can become extremely overpowered and make one kind of tank much, much better than the others. While I have lots of confidence in the play ability of my guild members, I doubt we would have ended up in the top 100 in the world for kills on a hard mode if Blood Death Knights had not been so overpowered on Vezax. If this particular feature of Death Knights does not make them overpowered all of the time, it almost certainly will some of the time, and I think guilds that have a Death Knight in their stable of tanks are going to have a noticeable advantage in working towards first kills over guilds that don't.
1. Thanks to Improved Blood Presence rune regeneration is increased by 20% which gives 0.12 Death Strikes per second from runes. With 30 runic power generated from rune based abilities every eight and a third seconds the Death Knight is generating 3.6 runic power per second. At one boss attack every 2 seconds and a 3.5 weapon speed the Death Knight would generate about 1.95 runic power per second from Scent of Blood. That gives one Death Coil every 7.1 seconds. 45% of Death Coils generate an extra rune and one extra Death Strike results from every 3 extra runes on average. That's one extra Death Strike per 48.1 seconds or 0.021 extra Death Strikes per second.
2. Since this is on taking damage rather than getting hit I use the more liberal estimate of one hit every 1.5 seconds. Blood Craze has a 10% chance to proc and lasts 5 seconds, so the chance to proc will be 1 - (1-10%) ^ FLOOR(5/1.5) * [1 - 10% * (5/1.5 - FLOOR(5/1.5))].
3. We simply ignore the need to be enraged since the warrior can just time enrage abilities properly.
4. Bear attack speed is 2.0. An extra attack every GCD means one attack every 1.167 seconds. Assuming a roughly 30% chance to crit that will give a proc every 3.89 seconds, plus the 6 second cooldown.
5. The coefficient on Seal of Insight is 15% for both attack power and spell power and it is increased by 6% twice for Divinity. It procs 15 times a minute, but this should be increased by around 13.3% from Reckoning based on an incoming attack every 2 seconds. It will probably be difficult to avoid having some haste, which will increase this further.
Note: Edited to correct the 1.41 Death Strikes per second error Ziggyny pointed out in comments.