Why We Do What We Do:It's finally finished. This atrocity of theory crafting to try and help other people understand the "why" behind stacking EHP. A HUGE thanks to all those that helped me with this, especially Thegreatme, PatrikL, and enricobr
The reason for the gigantic wall of text to follow is to try and get more of the “why” floating around the community. Many people do things such as stacking stam without knowing why they are doing it, other think stacking stam is short sighted. Some think that threat is a huge concern, others contend that it is just in your spec. There are a lot of mantras thrown around that are simply said because people have heard the mantra, but sometimes they never really looked into the WHY.
Another reason why I want to put the WHY out there is to try and give the people reading Tankspot.com a better understanding of game mechanics so that they can understand it as well, not just follow it, and subsequently make their own intelligent gear decisions and advice, thusly making them better tanks. A lot of times people will do something just because they make a HALP! Thread and someone says, “don’t worry avoidance trinkets just use the black heart,” and so they do, but they may not have a full understanding of WHY.
This isn’t to say that people that think opposite me aren’t intelligent or are completely wrong, but rather that maybe they haven’t been exposed to the range of theory craft, or haven’t been in certain situations, or just didn’t know!
A side note when reading this: I would really prefer that if it's a specific contention that you read the entire thread because perhaps the question has already be answered/responded to or send me a PM first. If you have good evidence then I may add your concerns to the thread, but there have been a lot of people that come forth with merely assumptions and don't really have any proof to back up what they say, especially in terms of the EHP vs. Avoidance debate. If you do have data to support your claims than I will be more than willing to listen.
Section 1: Introduction to Effective Health
I’ll start out with the most controversial section first, since it’s also probably the most likely part to be read. There are quite a few tanks out there that will fight tooth and nail about EHP vs. marginal gains in avoidance or threat. Many take a “balanced” approach to tanking. While that is fine in non-progression raids or when you out gear something to the point you might as well gem spirit, for progression tanking it is not optimal, and the following sections will try to show why.
Most subtopics will probably have the math towards the bottom, however with this section I am going to include some terminology and equations at the beginning so that people understand when I throw out forum/WoW jargon.
Section 2: EHP and terminology
First: RNG, which stands for Random Number Generator. This is used to denote anything that is a statistical probability, not a certainty. That is there is a hidden dice roll to determine whether or not you dodge/block/parry/miss or get hit by an attack. This is a random number generator. I’ll discuss this a little more when talking about avoidance and the combat table.
EHP stands for Effective Hit Points. Essentially what this is is converting incoming damage to a raw hit point value. It is a way to relate hit points to damage reduction. The reason is that the number one cause of tank death is running out of hit points, but hit points come in two forms, health and armor. Since armor reduces the damage you take, it acts like hit points in that it keeps you alive and you take less damage, damage that would otherwise need to be healed. So if you convert all incoming damage based on your damage reduction to “raw” hit points, you get how much the boss would hit for if you went from full hit points to zero if none of the damage was mitigated at all. So for a small example if you had 1000 hit points and 50% armor reduction and you were hit for exactly 1000 hit points, the actual hit unmitigated would be 2000 hit points, so a tank with 0 armor reduction and 2000 hit points could take the same equivalent damage as a tank with 1000 hit points and 50% armor reduction.
The variable setup and subsequent equation for EHP is as follows:
Hit Points: This is simply how many hit points you have. If you are evaluating a piece of gear and want the stam conversion then it is:
Health = Stam * 10 * 1.1 * 1.09 * 1.15
The 10 is simply 10 hit points per point of stam
1.1 is the modifier for kings (10% increased stats)
1.09 is for the warrior modifier for hit points (9% increased stam from vitality) and this number changes based on your class. For paladins it is also a 9% modifier, for blood DKs it is 1.03*1.08*1.02(runes) (which is 1.13465), and for druids I’m pretty sure for the number here it is 1.06*1.1*1.02*1.25 (6% from survival of the fittest, 10% from heart of the wild, 2% from imp MotW, and 1.25% from bear form)
1.15 is 15% for the ICC raid buff currently.
Armor: The reduction from armor is given by the following equation
First we need a value “K” which is a static number based on blizzard calculations. The use of it will be more evident in the total armor equation. The equation for K is as follows:
K = (467.5 * L) - 22167.5
In this equation L is the level of the mob you are fighting. Therefore at level 80 a boss (level 83) would yield an L value of 83. Subsequently solving this equation we can get the constant we are looking for:
K = (467.5 * 83) - 22167.5
K = 16635
This is going to be the constant value we use in the armor calculation. Remember the constants 467.5 and 22167.5 come from blizzard set standards, at least as far as I can tell it does and it yields proper numbers so I assume it is correct.
After this we can solve for the total armor reduction equation:
Where M is the mitigation percent in decimal form and A is the armor value you have on your toon. So for an example if you have 35000 armor the equation yields:
Therefore at 35000 armor the percent reduction against a level 83 mob is 67.78%
A side not here, there is an innate diminishing return to the value of M. As A approaches ∞ it because significantly greater than K, but since K is still a part of it technically never reaches A/A or 1, so as A is really big, each increase in A is a smaller increase in total mitigation. To further illustrate I’ll give an example in 5,000 armor increments:
As you can see by the 5,000 step increase in armor, the change in reduction gets smaller as you approach 75%. Now 75% is the actual cap, so the “Armor Cap” is 49905 armor.
These values lead us to the final EHP calculation which in its simplest form is:
However the denominator of this equation is a little tricky because you see the damage reduction values are not “Additive” they are “Multiplicative.” If it were additive then if you had 67% reduction from armor and 10% reduction from inspiration and 3% reduction from blessing if sanc you would add those up and have 80% damage reduction. However, this is not so, instead the damage is multiplicative meaning that each modifier gets multiplied by the last. Therefore for every reduction effect you add (1-%reduction) to the bottom. Essentially all classes have a set number of reduction effects when raid buffed: reduction from armor, some talent or presence, 10% from inspiration effects, and the 3% reduction on buffs like blessing of sanctuary or vigilance. If there are any other modifiers, you simply multiply them to the end of the denominator in the same (1-%reduction) form.
Therefore the EHP calculation for a warrior raid buffed would be:
Therefore the effective hit points of a prot warrior with 50,000 health and 35,000 armor fully raid buffed is 195,918. Meaning that if a boss was to hit the tank unmitigated and you turned the tanks mitigation into hit points, the tank could take 195,917 damage without dying.
Now for some more terminology:
I think one of the biggest misconceptions is “mitigation” versus “avoidance.” Mitigation is defined as a reduction in damage when hit. Therefore armor mitigates a hit because it still lands, but hits for less. Block is another form of mitigation in that when you do block the attack lands, but usually for just a decreased amount. However, since unless you have a warrior with shield block up or a paladin manages to get to 102.4% dodge+block+miss+parry (or warrior in an unhittable set), block still is somewhat RNG based since it is a % chance. I guess I’d call it probable mitigation, not guaranteed mitigation.
Avoidance is simply completely avoiding an attack and subsequently taking no damage from it. Thusly things on the avoidance category include dodge, miss, and parry.
Since we’ve already talked about armor reduction, I guess I’ll briefly cover magical resist. Now, when gearing for a max EHP fight, armor doesn’t mitigate magic or bleed damage. Nothing can really mitigate bleed damage except for base reductions like inspiration. However magic damage can be mitigated by resistance. Basically it comes down to calculating EHP for a fight is divided into two halves, the physical half and the magical half. You calculate PEH or Physical Effective Health by the formula above, then you do the same thing for MEH or Magical Effective Health using the above formula only instead of %reduction from armor you use %reduction from resistance. You then multiply each by the %damage intake (so if there is 40% physical and 60% magical damage then you calculate .4*PEH+.6+MEH = TEH or Total Effective Health). However the percentages you use may vary depending on fight mechanics. For example if melee damage isn’t a huge factor, but the magical damage is very bursty but relativisticly infrequent (like Sindragosa) then you may choose to use a full to dead calculation instead of a total damage over the course of the fight in which case say you have 50k health, a boss does a magical attack for 40k and then the rest of what could kill you would be physical, then you’d have .2*PEH + .8%MEH = THE instead of the overall damage intake which might be closer to the aforementioned 40%/60% split.
For more on this Total Effective Health I highly recommend reading TheckHD’s thread on maintankadin.com: http://maintankadin.failsafedesign.c...rb_v=viewtopic