The Mechanics Approach to Tanking:

So you’ve read all the tanking guides out there, plugged some numbers around, and you’ve come to the discovery that well, nothing seems definitive. Unlike other classes, no one seems to have the ideal gear set, many great tanks seem to have different opinions on things, and worst of all, it actually seems impossible to effectively min/max the way some DPS classes can.

Welcome to the world of being a protection warrior.

This guide is going to be a bit different. There is no basic introduction, and this guide, unlike others, is not meant to cater to the typical person who just wants the quick answer. What we will be doing, however, is exploring, mathematically and structurally, what it takes to be a good tank, and precisely why the min-maxing approach does not work for us all of the time, and how the min-maxing approach must be done on a boss by boss basis, or a gearset by gearset basis, not on an overall one.

For those of you with a sound fundamental understanding of math, my goal is to help you improve yourself and think about the APPROACH to tanking, as opposed to simply hitting buttons and stacking certain stats.

As a prerequisite to this guide, please read Quigon’s guide which is up on Elitist Jerks. From a standpoint of all the basic formulae and the basic approach to tanking, it is without a doubt the most comprehensive and best written guide you can read.

This guide will be broken up into 4 segments:


I. Raid utility and approach
II. Mitigation and Threat Analysis
III. Protection Warrior DPS
IV. Advanced Theorycrafting Mechanics, a boss by boss approach



I. Raid Utility and Approach

One of the primary reasons tanks are not performing at optimal levels is because they do not fully understand their purpose in every fight. They are each their own entity, and synergizing a raid for tanks is not a priority. Just because you are a tank doesn’t mean you need to be in the same tanking gear for every fight, nor that you will even be tanking on every fight.

Example 1: For pure mitigation, the 8/5/48 build is generally regarded as having the strongest overall mitigation with a viable solo tanking build. 5/5/51 has higher general mitigation, but the lack of imp thunderclap does it in unless someone else can keep it up for them. 11/5/45, 12/5/44, or 12/4/45 can generate higher levels of threat, but usually at the expense of a mitigation talent or three. But most guilds with 3 protection warriors have 3 tanks with variations of the above builds.

While it may seem that having the above builds makes for strong tanking, the fact is, the above builds have no synergy whatsoever. On a fight that requires 3 tanks, 3 warriors with the above builds will never perform as well as having 3 warriors, one with 11/5/45, 12/5/44, or 12/4/45, one with 17/3/41, and one with 8/10/43. Why is that you may ask? The first tank has a build designed for strong threat generation, the second tank can viably DPS, and the third one can ensure that thunderclap and improved demo shout are always up on the target. More mitigation, more threat, and more damage all rolled into one little package of tanking synergy.

Example 2: I see lots of tanks who end up being off tanks on a fight like Mother, who don’t switch any gear to do it. That has always confused me. Personally, off tanking Shahraz, in addition to being a 5 minute break, is also a prime opportunity to throw on all of your avoidance gear enjoy the show. While I typically tank with about 28 dodge, 20 parry, and 520ish defense, I have a set of gear, for that fight only, where I can get my raidbuffed dodge over 35%, my parry over 21, and my defense close to 550, with a stopwatch to pop every 2 minutes. The difference in the amount of damage I take (and need to be healed) vs the other tank is often astounding, averaging in most cases a 1.7 to 1 ratio.

Would I use the same set to tank Gorefiend? Of course not, but that’s the point. It is the very reason why any guide that gives a hard rank or score for tanking gear is by definition false. It automatically assumes a certain role, or that the objective is singular and modal.

The objective of this section is to help you think about, from a role perspective, what specifically you will need to do, on a boss by boss basis, to optimize performance in your specific role. I do not score gear, I do not allow myself to employ tunnel vision in my approach, and in fact, I freely admit that often at times, I believe that the approach to tanking is just as important or more important as the button mashing itself.

Let’s take an example approach, and as the example, I will use a complicated example, Gurtogg Bloodboil, and go through my own approach. Later on, in section 4, it will be explored in more detail mathematically, but simply understanding that the approach is based on the encounter is often more than enough to get an idea of what needs to be done.

Gurtogg Bloodboil:

1. Mitigation:

Q. How hard does the boss hit?
It depends on the number of debuffs present on the tank. For low numbers of debuffs, melee hits for about 4k, crushes for 6-7k, at 10 debuffs, melee hits for 6k, crushes for 9-10k. The debuff can be avoided.

Q. What additional damage is taken?
Every debuff causes a loss of 500 armor and causes 250 nature damage every 2 seconds for 1 minute. The boss has a frontal cleave every 8-10 seconds, hits for normal boss damage, and the cleave CAN refresh the debuff. The boss targets someone in the raid randomly every 15 seconds for a nature breath, doing around 7k damage to everyone in the cone, cannot be avoided, can be resisted.

2. Threat

Q. What are the threat concerns, and is it a burn fight?
It is not a burn fight, however, threat is a concern for the fight, as the boss has a knockback, and will also periodically disorient the tank. The knockback reduces threat by 25%, and the disorient uses normal tanking mechanics (will take a new target, will not switch back unless another target in melee range is 10% over the new target in threat OR a ranged target is 30% over). 2 or 3 tanks need to be able to stay at the top of the threat chart for the entire fight. This requires time spent off tanking as still being capable of building threat, increasing the value of expertise, hit rating and possibly SBV for that purpose. With 8 debuffs, rage is plentiful and can sustain any cycle.

Q. What is the parry risk for the fight?
A. Low, the boss hits are not that hard.

Fight mechanics:

Q. What are the benefits and weaknesses of avoidance in the fight?
In addition to the basic benefits, avoidance will reduce the rate of incoming debuffs. However, the knockback can also be avoided, and standing in too long will result in too many debuffs to be healed through. At 15 or more debuffs, it is impossible for a single healer to effectively heal through the debuff without a significant mana drain. From an off tanking perspective, high avoidance is neither needed or desired.

Q. What can go wrong in the fight, and is any of it under my control?
Four major things can go wrong in this fight.
First, the bloodboils are not properly absorbed, and people start dying from them. There is nothing a tank can do to prevent this.
Second, too many consecutive knockbacks can be avoided, resulting in a mounting stack of debuffs on the current tank target. For this, only a bubble can help, waiting inside the bubble until the next tank has passed you in threat.
Third, the bottom tank who still has a lot of active debuffs takes aggro because of a combination of knockback/disorient on tanks 1 and 2. Once the disorient has worn off, a bubble can help this situation as well, however, the debuffs may have been refreshed in the meantime.
Fourth, the fel rage target can die. If that happens, the current tank target must use some form of cooldown to survive the incoming damage, which will be double the normal damage, and with BB swinging up to 40% faster. Shield wall is generally the best form of survival for this.

Q: What is my specific role in the fight?
When I am main tanking, my job is to build threat until I have a set number of debuffs, say 5 or 6, and then back down and change to survival mode, letting the other tanks catch up on threat, while waiting to get punted (not too high passive avoidance, but enough to prevent quick debuff stacking), hopefully before I have more than 10-12 debuffs. Once punted, while the debuffs are active, I have to build threat quickly to get back to third overall on threat (therefore, threat building stats, like expertise and hit, are critical), but careful not to pass the second tank until my debuffs are going away. Once the debuffs are off of me, I stand on top of the tank to eat the cleaves for some additional rage to keep my threat high. (not too much passive avoidance)

If I am the target of aggro when the fel rage occurs, I stand on the tanking spot like a dumbass the entire time. If I am NOT the aggro target, I stand behind him and keep up TC to counteract the boss’s self haste buff, and keep up demo shout to help with mitigation. If I have a number of debuffs on me (and therefore, essentially an infinite supply of rage, I can also LOLdps during this time. If I have no debuffs, I also use this time to melee him and build rage to use at the start of the next normal phase. Either way, with 3-4 seconds left in the phase, I return to my normal phase position.

If I am the target of aggro and the fel rage tank dies (LOL mages and priests), I am to first use shield wall. If it happens a second time ( *()_*)_(ing healers ), I need a better out than just last stand, preferably something that provides a lot of help with mitigation (meaning Moroes Stopwatch is the extra oh shit button I need).

So what does all of this mean?

Based on my role ON THIS FIGHT, the basic strategy of stacking stam and armor doesn’t really apply. In fact, EH (effective health) doesn’t really play ANY PART in determination of what gear is optimal for the encounter.

I need to be able to build threat quickly in this fight while standing behind him and maintain threat production while standing on top of the tank. While parry-gibbing is a low risk, it is still a risk. Therefore, I want lots of expertise and hit, with maybe some SBV thrown in for good measure.

High passive avoidance is a bad idea, as is too low passive avoidance. Therefore, about 55% passive avoidance is plenty for the fight. (25 dodge, 20 parry, 530 defense). However, there is a clear and present need for extra oh shit buttons. Therefore, trinket wise, Moroes stopwatch can provide that help, as can the Scarab of Displacement from Hydross, or even the commendation of Kael’Thas from the new heroic Magisters Terrace.

So in the end, I need to gear for high threat with extra panic buttons, meaning, I will sacrifice some stamina and armor for more threat building stat aligned gear.

Compare this, for example, to a fight like Azgalor, where survivability is the number 1 issue, and you will see clear differences in up to 4 or 5 pieces of gear (as I would stack more passive avoidance, and potentially 2 panic button trinkets for a bad silence in a rain of fire (I would use the 10 rage I save every 5 seconds from not hitting shield block to assist with making up the threat difference).

Tanks need to ask themselves what stats are important for their particular role in a fight. The answers to these questions becomes obvious in say, resistance fights, but sometimes, the answer is not so obvious, and the pitfall is to think that the same set of gear is equally optimal for everything. As a result, while you may be optimized for some fights, on other fights, you may find yourself not performing very effectively. To provide an analogy: It is entire possible to eat soup with a fork, but you’re going to do a much better job with a spoon.

But the bottom line is: There is no single gear set that is optimal for every fight. You may be able to get away with using it, but you are not doing the raid any favors by doing so.

This brings me to the next topic. How many tanks blindly gem everything with +15 stam? The answer is most. Once again, they are doing this based on either instinct, or reading some scoring report for tanking which scores everything based on a very arbitrary role of main tanking a tank and spank fight. It is important to socket based on what you intend to use the piece for, and what the socket bonus is.

If the piece of gear is part of your avoidance set, chances are you may want to see what the socket bonus is. If the socket bonus provides some avoidance, why not take advantage of it, or at least see if it can? If it is a piece for a burn threat set, by general rule, unless the socket bonus is something ridiculous (+hit, + expertise), chances are that 15 stam gems are the way to go.

Rather than score pieces of gear, ask yourself what role it could help you perform, and judge how much of an upgrade it is IN THAT PERSPECTIVE only. There are several pieces of gear in the game that don’t seem all that great, but in fact, are ideal pieces for a specific type of role.

II. Threat and Mitigation Analysis

The first thing to understanding threat and mitigation is to understand what benefits each stat provides:

I’m specifically not covering the basics (490 def, 102.4% with SB active) because this is not meant to be a beginners guide, and I assume you have them anyway.

For itemization points, here is the equivalencies:
1 Str = 1 Agi = 3.9 SBV = 1 dodge rating = 1 parry rating = 1 defense rating = 1 expertise rating = 1.5 Sta = 1 hit rating = 12 armor = 1 crit rating

Strength: Each point of strength provides 2.42 attack power raidbuffed (vitality and kings). 14 attack power translates into 1 DPS. Every point of strength (on a 1.6 speed weapon), provides an increase of effectively .25 damage on melee hits, and .13 damage on devastates, meaning an increase of roughly .18 DPS at 20% parry (an average of 4.14 melee swings per 6 seconds and 2 devastates, where the extra .34 melee attacks reflect the benefit to YOU from your parries, also assuming 24% of white hits glance, and 10% of attacks are misses). This provides an effective threat bonus of .27 TPS. Strength provides 1 SBV for every 20 points of strength, a value that is so low, its not even worth calculating (.0046 TPS)

Agility: Every point of agility provides 2 armor, .03 crit, and .03 dodge. So from a tanking perspective, this means that every point of Agi provides an increase in threat generated by: [(1 + current crit rate + .03)*(Current TPS)/ (1 + current crit rate)] – (Current TPS). Assuming 12% crit and 1000 TPS, it provides about .26 TPS. However, the extra dodge has a negative effect on threat which we will go into in more detail in the more advanced Theorycrafting section (it turns out to be significant as well). While also providing .03% more avoidance.

Stamina: Every point of stamina provides 11.5 health for non Taurens and 12 health for Taurens.

Hit Rating: Every point of hit rating increases the chance to hit a target by .0633%. While the static marginal rate of return for threat/hit rating is a decreasing one, as the first few points of hit rating actually provide more relative percentage benefit to TPS than the last few, the rate of return is constant due to the increases in scale. The effective hit cap for bosses is 9% (142 hit rating), or 8% (126 hit rating) if a melee Dranei is in the group.

Basic talents provide 6 expertise, meaning at 0 hit rating, the hit chart looks as follows:

Parry: 9.1%
Dodge: 4.1%
Miss: 9%
Glancing: 24%
Hit: 53.8%

Glancing only affects white melee swings, and for the purpose of the delta in TPS, will be ignored. Also, due to the nature of expertise (it is the first stat to cap under any and all circumstances, being the new best tanking stat in the game), I am going to redo the hit chart to reflect that.

Parry: 5.1%
Dodge: .1%
Miss: 9%
Hit/Glancing: 85.8%.

The first point in hit rating provides a TPS increase of:
[(85.863 * 1000)/(85.85)] – 1000 = .73 TPS

The last point in hit rating provides an increase of:
[94.8 *1104]/[94.737] – 1104 = .73 TPS

Where 1104 is the new TPS generated by being one point under the cap, and the reflecting the overall effect of stacking the previous hit rating.

Expertise Rating:
3.924 expertise rating reduce the chances that an attack is dodged or parried by .25%
From the same math as used in calculating hit rating threat, 3.924 expertise provides:

Parry: 5.1%
Dodge: .1%
Miss: 9%
Hit/Glancing: 85.8%.

[86.30*1000]/[85.8] – 1000 = 5.9 TPS, meaning 1 expertise provides about 1.5 TPS

Expertise also provides passive avoidance of the best variety in that it reduces burst damage incoming. It is important to know that once every 60 seconds, regardless of the situation, you will be subject to a crush simply because one swing every 2.4 = 25 swings per minute, while your shield block covers only 24. One 5 second gap per minute is naturally uncovered.

Assuming Weapon Speed = 1.6:
Parry Effect Chart:
12.8% no effect
25.6% chance swing time reduced by .4 seconds
61.6% chance swing time reduced by .7 seconds

Just multiplying that out, each parry results in the boss getting a swing time reduction of about .55 seconds.

Assuming your typical 6 second cycle: (4.14 melee/HS, 2 devastate, 1 revenge, 1 SS), you attack 8.14 times. Over the course of 1 minute, that is 81.4 attacks. At 6 expertise, 7.3 of those attacks will be parried, resulting in an average of 4 extra incoming attacks per minute. At 22 expertise, that number is reduced to 4.1 extra attacks, and 2.3 extra incoming swings per minute. This is positively critical to avoiding burst damage.

Shield Block Value:
1 itemization point, or 3.9 SBV provides 3.9 additional blocked damage per block (for EH calculation) and also provides additional threat in the form (on a fully sundered boss) of: (3.9*.7) = 2.73 extra damage per shield slam. The additional threat provided by this is based on your current expertise, hit and crit rating. At 0 hit, 22 expertise, and 12% crit, it provides a TPS increase of:

[2.73 * 1.12 * .858 * 1.52]/6 = .66 TPS

At 142 hit and 22 expertise:

[2.73 * 1.12 * .948 * 1.52]/6 = .73 TPS

Therefore, SBV actually scales to your hit and expertise. The more hit and expertise you have, the more threat benefit you gain from SBV. Once you get near the hit cap, SBV becomes relatively interchangeable with hit rating, and for effective health purposes, SBV becomes superior.

Dodge Rating:

Dodge Rating provides approximately .051 avoidance per rating.

Parry Rating:

Parry Rating provides approximately .041 avoidance per rating. Furthermore, parries speed up your attacks and generate rage.

Defense Rating:

Each 2.4 points of defense rating provides 0.12 avoidance in the form of .04 dodge, .04 parry, and .04 miss. Furthermore, it also adds .04 to your chance to block as well.

Crit Rating:

Each point in crit rating provides .04% chance to crit, or roughly .35 TPS

Analysis:

It is important to note that the above threat calculations are based on having applicable raidbuffs (kings, might, sharpening stone, battle shout), and is actually based off of 983.9, not 1000, which is the value of TPS maintained at 6 expertise, 0 hit rating, 12% crit, 1300 AP, with 2.6 HS, 1.54 melee, 2 devastates, 1 SS, and 1 revenge every 6 seconds. The lack of taking extra swings due to your own parries into account is the reason all current TPS spreadsheets are in essence, undercalculating threat, and underestimating the importance of expertise, since they calculate a fewer number of attacks.

If a windfury totem is active, or other buffs are active, most of these values scale multiplicatively. So for example, with a windfury totem active, the base 1000 TPS is really 1100 TPS, so 1 hit rating actually gives .8 TPS instead of .73 TPS, etc..

In terms of burst mitigation and expertise, On average, absent expertise rating beyond that provided by talents, the boss will get one extra swing at the player every 29 seconds. That extra swing is guaranteed to provide one extra attack over that 5 second period. The likelihood that this attack will crush is 15% of the chance that the other two attacks were successful hits, or

(1 – Avoidance)^2 * .15 = .054 at the base level. About 1.84 times every 30 seconds, you’re running a 5% chance of potential catastrophe against a harder hitting boss by stacking nothing but stam (hit, hit, crush in a 5 second gap). Yes, this can be healed through and survived MOST of the time, and you may survive, but congratulations, everyone else’s life is harder because you’re stacking your gear poorly.

At 60% avoidance and 22 expertise, the one extra swing in time is every 64 seconds, and you’re only subject to .61 swings per 30 seconds that fall outside your coverage gap.
(1 - .6)^2 * .15 = .024. So now, instead of a 5.4% chance of catastrophic damage 2.34 times per 30 seconds, it’s a 2.4% chance 1.08 times per 30. it may not look like much, but try asking the guy underwriting life insurance how different those two sets of numbers are. How it affects odds of success over a 5-7 minute fight is absolutely astronomical.

Where tanks fail is in assuming that blindly stacking stamina and armor does the job. It doesn’t. In fact, with expertise now being a factor, stacking just stam, armor, and SBV NEVER does.

The objective is not to avoid damage, or be pure avoidance, or have the big health pool and high SBV, the objective is to avoid burst damage, and avoid spike back to back hit/crush damage.



III. LOLProt DPS

Coming Soon to a theatre near you. (still under construction), but its not a myth.

IV. Theorycrafting FTL

The section is titled for a statement at an old tank class lead I had that who thought theorycrafting was for noobs. Yes, it’s a potshot and I don’t care, because I think theorycrafting has legitimate value.

Initial Value Assumptions:

500 defense = Df0
15% dodge = Dg0
15% parry = Pa0
25% block = BL0
400 block value = BV0
6 expertise = EX0
0 hit rating = HT0
12% crit = CT0
200 Strength = ST0
150 AGI = AG0
550 AP = AP0
15000 Health = H0
17000 Armor = Armor0

Other values:
BP = boss parry rate
BD = boss dodge rate
BB = Boss Block rate
MI = Static Miss Rate of incoming attacks
MO = Miss rate of your attacks

Marginal Values:
Value of increasing each value by 1
dDFrating = +.016Dg0 + .016Pa0 + .016BL0 + .016MI
dDgrating = +.051Dg0
dParating = +.042Pa0
dBL0rating = .128BL0
dExrating = - int(Exrating/3.924)*BP - int(Exrating/3.924)*BD - int(Exrating/3.924)*BD
dST = +2 AP + (ST/20)BV
dAG = .033Dg + .033CT
DSta = + 10.5 Health
DST = + 1.1 ST

Again, using the basis of the following for comparison

1 Itemization point = 1.5 stam = 1 agi = 1 str = 1 crit rating = 1 dodge rating = 1 hit rating = 1 parry rating = 1 block rating = 3.9 block value = 1 expertise rating = 1 defense rating = 12 Armor

Without pages of math, I concluded that the full complement of all BT epics (all level 141/146 items) provides a grand total of 3600 itemization points, including gems. Considering the very base of these numbers consumes roughly 2300 of the itemization points (a good 900 of them in stam alone, 300+ in defense rating, +150 or so across other stats)

Therefore:
67*DSta + DAg + DST + DCT + DDg + DHT + DPa + DBL + .26*DBV + DEx + DDf + .08*Armor = 1100
Subject To
All >= 0
All <= 550 (Simply limiting you from stacking any one stat past this point (its impossible to do anyway, but it provides a force cap to give better relative values)

Remember, using the initial value assumptions, that’s our baseline 0 stats. The wiggle room we have is with where we allocate the other 1400. And more importantly, we can’t put all 1400 in one place either, because there is no gearset that allows it. What instead we are trying to do here is assign relative weighting to each stat, so we can mold our gearsets around getting those primary numbers.

The above subject equation provides us the basis for what stats we can get and how much “purchasing” one of those stats will cost us in itemization points. Remember, if you are wearing lower level pieces (like many people, including myself), do, in order to maximize a certain stat (in my personal case, expertise), you DO effectively lower the total number of itemization points that you have.

The basic subject equation is now based on need for 2 other calculations. First, is the need for high threat generation in the fight. How important is threat, and how much of a burn fight is it? For threat generation purposes, expertise, hit and SBV are critical. Even though SBV catches up (and will eventually pass) hit rating in terms of raw TPS generated, hit rating provides a more steady rate of return, whereas SBV is a hit or miss proposition, where part of the overall threat gen is determined from spike threat generated by a critical hit.

From a mitigation standpoint, expertise, stamina, defense, dodge, and parry become more important. For a very bursty fight, or a fight where short term burst is an issue, you must also consider the need for items that have: “oh shit help me god” on use abilities, which can provide needed short term buffers.

To illustrate this, consider the state equation matrix that is tanking:

21000 raid buffed health
Assuming HPS

State 1 Initial: 21000 health
State 1 post initial = return to state 1 health
State 2 = {A0 min (State 1 health +2.4 HPS, 21000)
1- A0 min (State 1 health +2.4 HPS, 21000) - Boss Damage + BV
}
State 3(A0) {A0 min (State 1 health +4.8 HPS, 20000)
1- A0 min (State 1 health +4.8 HPS, 21000) - Boss Damage + BV
}
State 3(BL) {A0 min (State 1 health +4.8 HPS, 21000) – Boss Damage + BV
1- A0 min (State 1 health +4.8 HPS, 21000) – 2 * Boss Damage + 2 *BV
}
State 4 (no 3 swings)
{ 1 Return to State 1 + .2 HPS}
State 4 (chance of cycle having 3 swings)
Subset 1:
(A0 * A0) ) {A0 min (State 1 health +4.8 HPS, 20000)
1- A0 min (State 1 health +4.8 HPS, 21000) – Boss Damage + BV
}
Subset 2:
2* (A0 * (1 –A0)
) {A0 min (State 1 health +4.8 HPS, 21000) – Boss Damage + BV
1- A0 min (State 1 health +4.8 HPS, 21000) * Boss Damage + 2 *BV
}
Subset 3
(1 – A0)^2
{A0 min (State 1 health +4.8 HPS, 21000) - 2 * Boss Damage + 2 *BV)
BL min (State 1 health +4.8 HPS, 21000) – 3 * Boss Damage + 3 * BV
Max(0, 102.4 – A0 – BL - 15) min (State 1 health +4.8 HPS, 21000) - 3 * Boss Damage + 2 *BV
Max(0, 102.4 – A0 – BL) min (State 1 health +4.8 HPS, 21000) - 3.5 * Boss Damage + 2 * BV + 4.1 HPS
}
If health = 0 then, end
Else, return to state 1 + .2 HPS

Boss Damage in this state is the mitigated damage taken based on armor, I simply didn’t write it in because I didn’t feel like typing it out and clustering it with something that is already obvious if you’ve been following along so far anyway.

Your chance of the cycle of having 3 swings is simple. Divide the base number of 3 swing cycles per 30 by 6. That is the chance of any given cycle putting you into one of the subsets of State 4. Subset 3 is basically known as the catastrophic state, because that is the state at which you are in danger of taking more damage per that 5 seconds than you are normally getting healed for, meaning either
a) you just died, congratulations
or
b) you are going back into state 1 with significantly less than full health, so either catch up time/Loch/etc. is needed before you are relatively safe again.

Assuming you are receiving in the ballpark of 4500 HPS (2.5 direct healers)
Plug in the numbers. For a boss hitting for 8k per hit, 500 block value, and plug into the 4x4 matrix, and knock yourself out. 20,000 health with 22 expertise, 60% avoidance is SAFER (less likely to reach health = 0) than 25,000 health, 6 expertise, 45% avoidance. In fact, at 6 expertise and 45% avoidance, you would need almost 27,800 health to get to that same level of relative safety, due to the sheer number of times spent over 7 minutes in subset 3 of State 4.

Take the above matrix and subject it to the following:

Min P(health = 0, (21000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25% + .128BL)
Max: 1000 + .21Agi + .27 Str + 1.5 Ex + .73 HT + .17BL - .31Dg - .12Pa - .24Df +.35CT - .00003 Armor - .005 BL
Subject to:
+.67 DSta + DAg + DST + DCT + DDg + DHT + DPa + DBL + .26DBV + DEx + DDf + .08Armor = 1100
All >= 0
EX <= 43
Hit <= 142
All <= 550

What this shows is that mitigation tanking has positively nothing to do with how hard the boss hits when he connects, or how deep the health pool is past a certain amount, but rather, how much time are you going to spend in the catastrophic state (subset 3 of state 4) over a 5-6 minute fight, how many times will you be in that subset, and how often will you be in that subset in 2 consecutive 5 second cycles?

The reality is that tanking is nothing but 5 second cycles over and over again, with chances each time that something bad will happen. Limiting that chance is far more important than having an extra 1k armor and 1k health. People can talk all they want about health and armor and EH being static amounts, but avoidance/expertise just playing with chance, but the math shows otherwise. It is precisely reduction of that chance that helps to ensure success, while the total health pool and armor are actually absolutely meaningless unless they are ridiculously and unacheivably high numbers. This is not to say stamina and armor are bad, but rather than expertise dominates them even from a mitigation standpoint.

Actually doing the math will bring you to a borderline comical conclusion in terms of pure mitigation. The leather belt from Vashj provides almost as much mitigation (due to helping reduce spike damage), as the Girdle of Stability from BB. The difference being the damage reduction from the Vashj belt is all spike and burst damage, while the Girdle of Stability provides a constant reduction.

The next step on the chart is to provide dominance reduction:

Expertise dominates hit, crit, strength, SBV, and agility for Threat generation, AND provides the highest reduction in P (health = 0). Therefore, Expertise caps first at all times. This reduces the equation to:

Min P(health = 0, (21000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25% + .128BL)
Max: 1000 + .21Agi + .27 Str + .73 HT + .17BL - .31Dg - .12Pa - .24Df +.35CT - .00003 Armor - .005 BL
Subject to:
+.67 DSta + DAg + DST + DCT + DDg + DHT + DPa + DBL + .26DBV + DDf + .08Armor = 955
All >= 0
Hit <= 142
All <= 550

Expertise = 43 (145 rating)

Now we need to provide reduction for dominated stats. From the threat side, it is clear that strength and crit are completely dominated by SBV and Hit. Therefore, 0 them out.
Furthermore, we find that armor is dominated by every other stat. 0 that one out too.


Min P(health = 0, (21000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25% + .128BL)
Max: 1321 + .21Agi + .73 HT + .17BL - .31Dg - .12Pa - .24Df - .005 BL
Subject to:
+.67 DSta + DAg + DDg + DHT + DPa + DBL + .26DBV + DDf = 955
All >= 0
Hit <= 142
All <= 550

Expertise = 43 (145 rating)

What we find next is that due to scaling density and a sort of economy of scale, hit rating caps next. This conclusion is jumped to for the following reasons:

Avoidance for this calculation is soft capped at 70% passive, at which point, around 400 points would remain for stamina, hit rating, and SBV). Hit takes precedence over SBV initially, and stamina provides little initial return since it provides very small marginal rate of return in P(H=0). Furthermore, SBV also dominates stam for reasons of scaling, up to a certain point, as it provides 26% return in effective health as well as threat scaling up to around 80 itemization points.

Min P(health = 0, (21000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25% + .128BL)
Max: 1334.6 + .21Agi + .17BL - .31Dg - .12Pa - .24Df - .005 BL
Subject to:
+.67 DSta + DAg + DDg + DHT + DPa + DBL + .26DBV + DDf = 733
All >= 0
All <= 550

Hit = 142
Expertise = 43 (145 rating)
BV = 80


What does this mean?
Basically, in a nutshell, that under just about any and all circumstances, you will want 142 hit rating, 145 expertise rating, and 430 SBV for any kind of bossfight. Most of the remainder of the stat point allocation will go towards avoidance stats and more SBV, depending on the desirability of threat or avoidance for the fight. For a mathematical answer, just find the determinant of the 6x6 matrix with the top 4 rows being the state equations and delta probabilities of P(H=0) by stat, and the bottom 2 rows being the maximization statement variables, and the bottom row being the subject equation variables. Multiply that by the X by 1 matrix of (Probability of State 1, 2, 3, 4, 0, 733), (using the determinant is simpler than calculating forward by plugging in boss damage).

When you get your resultant 6 variable equation, you can either try to solve it mathematically (which will be a pain in the ass), or you can solve it by testing endpoints (test out each variable at 733) to give you an idea of relative benefit.

First, I'll address your conclusion: If it's possible to have "enough" threat without reaching the values in your conclusion, then your conclusion is wrong-- you won't want to maximize hit rating. Same with SBV. And those fights tend to be... a significant portion of them and not "just about any and all circumstances". I can't follow your probability math, but you're simply weighing threat too highly if it's more important than survival/mitigation/time-to-live.

Second, the statement that:
"The reality is that tanking is nothing but 5 second cycles over and over again, with chances each time that something bad will happen."

Is kind of wrong. The reality is that while you're working from a cycle, the boss is also working from a cycle that doesn't match your own. In addition, special attacks are on separate timers, which would be accurately treated as different cycles. You're oversimplifying, which is what you accuse people of doing in their other math. At a minimum bad form, but not counting intersections of cycles will hurt you.

Finally, while you might be filling in a state diagram of one tanking class here, at most you're taking into account 1/3rd of the entire picture (and a lot of other players); if you think you've covered boss mechanics enough, you've covered 2/3rds. But from a healing perspective, while you might see 4500 sustained healing, you'd also see higher spike healing (swiftmends, PW:Ses PoMs, upranked heals and so on) in tank spike situations in 5-second periods. In these cases, a high HP pool will be more beneficial-- simply, your bad spots may be more frequent, but they won't be as "bad".

You may want to change the title to mention Warriors, since the content of the post is very Warrior-specific.

Love the work, but would you mind providing the "Dummy's Guide to..." version? I stopped my math career after Calc 2.

Correct in your statement about boss ability timers not being in sync with the 5 second cycle, but in the end, it also is within a rotation of 5 second cycles. Boss does something every 30 seconds? 5 standard cycles, 1 out of standard cycle. It makes the math more complex to get relative probabilities of recovery after the boss ability cycle, but in essence, stays within the 5 second model.

As for threat being weighted too highly, it is because by maximization of itemization, it fills gaps that stam and avoidance wouldnt otherwise cover without going past the point of relative benefit.

Second, time to live calculations show that after a certain point, more and more stam really does very little. The relative benefit of avoidance at a certain level of stamina far outweighs more stamina.

Bigger hits downplay the importance of block value, and blind stam stacking, simply because avoidance provides more direct returns.

Not to mention threat stats (hit & expertise) keep your main hand generating rage during avoidance streaks, so you can keep up base line threat, while maintaining shouts, shield block and other defensive goodies, like spell reflect on Gaithos.
It's decreasing the probability of a combination of avoidance on you and the mob, which can reverse catastrophically.

Forcing anyone to do both Demo and TC is just cruel. 17% resist rates on 2 spells with 30s durations is nasty. Have your MT do TC since he won't have to stance dance for it.

It is not much of a guide to be honest, you're saying wear gear appropriate for the encounter. This is true, and you learn it as early as karazhan. The bloodboil example is way to specific. One suggestion I would make is linking the talent specs to wow talents or wowhead.

He's saying "wear appropriate gear for the encounter" and giving us a step-by-step process to follow when considering what gear to wear for encounters. He uses Bloodboil as an example because it is complicated enough to cover every step in the process. As a non-tank, I found the OP's post extremely interesting, because it proves mathematically that the common thought-process of "Max HP for every fight" is not so accurate as once thought. The class mechanics forum was not meant to be a place where complete newbies come to find simple "how-to" guides for every class and spec (though some of those can be found), and I would not expect someone new to tanking or theorycrafting in general to truly appreciate a post like this.

To the OP, thanks for this information. I've reposted it to my guild forums and the other theorycrafters in my guild enjoyed the read just as much as I did.

False or tenuous assumptions your calculation celebrating avoidance makes:
- spike healing doesn't exist (swiftmend, PoM, PW:S, LoH, etc.)
- all boss specials can be avoided like autoattacks (see: magic damage, AOEs, DoTs, etc)
- boss specials don't interrupt your 5-second pattern (stuns, fears, etc)
- threat up to the arbitrary point you picked is still worthwhile (see any fight where DPS is interrupted but tank isn't)
- avoidance is the same to all mobs (see Sunwell anti-avoidance mechanic)
- every "swing" is the same (special attack swing timers don't get affected by expertise)
- emergency buttons are of the same worth regardless of other stats
- emergency buttons don't occur in the cycle

Simply: your argument for avoidance above stamina is that your state tables actually represent incoming damage and healing. They don't. They adequately simulate boss auto-attacks in T6 and below, and to a degree boss attacks that behave like auto-attacks, and 3 resto druids that forgot where their swiftmend button is.

Good theorycraft is valid. But you really need to account for most of the points above before you even begin to claim you're right.

As a Tankadin, I read more deeply into the mechanics of tanking shortly after moving past 5-mans and trying out Karazhan and above, and I quickly ditched the "max STA" concept in favor of something more balanced towards block value and armor.

However, from what I can get from your post, expertise and hit rating are far more important than even those two other stats? Do you recommend gemming with [Rigid Dawnstone] on yellow slots and [Glinting Noble Topaz] on red slots until I'm capped?

Also, do your computations account for the lesser amount of potential parries a Paladin gets? Our only Parried attack is our autoattack, whereas a Warrior can have as much twice that amount (1.50 speed weapon plus an ability every GCD).

Although no expert on protection Paladins, I would think that the class differences are such as to negate a lot of Tamral's conclusions. For example, the value of expertise and hit will be significantly lower than for warriors, as Holy Shield has 4 charges per 5 seconds vs a warrior's 2, a non-trivial amount of Paladin threat comes from blocks/consecration (neither of which benefit from hit), and as you note, there are no additional special attacks (discounting Reckoning) that increase the chance of a parry gib.

Edit: Which is not to say that expertise/hit are useless; they could be (and probably are) extremely valuable, but you would need a new set of calculations tailored to Paladin tanking to deduce this.

Ignoring glancing blows is, I think, a huge mistake if you're planning on bringing up precise numbers in order to theorycraft properly. Just to list some of the effect glancing blows will have: reduced Str/Agility/ArP/AP/Crit/Expertise/Hit/Rage Generation efficiency compared to SBV. Lower Rage Gen will hurt both TPS and can even potentially hurt mitigation should a bad avoidance streak occur (out of rage for Shield Block/Tclap/Demo). Further effects of the glancing blow mechanic on TPS (and as I've stated, mitigation) mechanics is that Warriors will also see a decrease in overall usage of Heroic Strike for extra threat and less glancing blows: the Heroic Strike can't glance but not having the rage to Heroic Strike incurs the chance of having the white hit being a glancing blow.



Fully sundered or Sunder + CoR + FF; low or high armored target? The difference is quite large.



You'll probably want to include calculation for how many extra swings (or TPS) each Parry Rating adds. You'll also want to calculate how much of an increase in damage taken (and TPS from extra damage) the extra attacks you will get in regards to parry haste for the boss (if this isn't clear: Warrior parrying means the boss parries more).



While easy to derive, you may want to include (or re-type) this small section with 1 defense rating in mind, like the other stats you list, instead of 2.4.



How would lacking some of those buffs change the weight of each stat that you can add? While this is more spreadsheet material, it's still important to come up with the proper values each lacking, or additional buff will bring for a Warrior. Best example of this is that as a tank, I rarely get Battle Shout from other Warriors, but I get to use my own Drums of Speed. Sometimes I even have the luxury of being in a Hunter group for GoA + Str + Flametongue + 3 * FI. How do all of those buffs affect threat? For example, having Flametongue will change the value of weapon speed, and it will be further changed by % based buffs and debuffs (Imp. Scorch and CoE).

The point I'm trying to get across is that taking a fixed TPS value with fixed buffs to derive other calculations on is not a very valid course of action to truly pin point actual values for each stat.




What about bosses that can't crush? Also I don't think you're valuing HoTs properly for those situations, especially since HoTs drastically increase the effects of stamina in those burst damage situations. In a 5 second gap, with 3 Trees and 1 Priest, you'd get 15 Lifebloom ticks, 3 Rejuv/Regrowths ticks and 1 Renew. While in theory you just look at all that healing as pure HPS, it still acts a lot differently than having 2.5 healers (the number you used) spamming heals on the tank. Again, you can't just put up numbers and undervalue stats - stam in this case - based on one of the many different types of healing you can receive. Not to factor in overhealing.

Let's say Teron hits the tank for 8k 8k 12k in 5 seconds. Worst case scenario: 2 heals landing during the 5 second window for a total of 12k healing. You're 16k in the hole, the value of stamina now becomes this: how much stamina do you need to either survive another hit (unlikely, which is what you assume) or to survive another hit with all the "OH SHIT!" happening in the raid, which is what is more likely to happen in a raid. You can't realistically assume that no one will react to spike damage occurring over 4-5 seconds.




You probably want to reword this section a little bit. The acronyms aren't very clearly labeled: DST/dST, DSta and all that. They have no real meaning to someone unless you make some sort of reference. I mean that some of them are obvious, some aren't.


Again with acronyms (dAG/DAg/DDf). Also does your 3600 itemization point number include trinkets? Are you saying that a Warrior in full BT/Hyjal gear will have 2300 itemization points and will then have the rest of his points (is it 1300 or 1400 and where does your 1100 come from, really?) to allocate based on gems? Are enchants counted in?



You'll need to weight in expertise on fights where boss parry-haste is a non issue, especially hold true for Brutallus, who I'm fairly certain will become the new Patchwerk of theorycrafting.



Please be clearer with acronyms (A0/BL?). How would someone go about properly adding new matrixes based on particular fights (IE: instant boss swings).



How much of a difference will armor make in worst case scenario? Such as the difference between Hardened Heart and Illidan shield, wearing armor rings/trinkets, wearing lower iLvL gear, Ironshield pots, armor procs, Ancestral Spirit + Inspiration, etc. How will it affect the value of stam, how will it affect the value of stam with a more HoT based HPS Vs. a more direct healing HPS approach?



What does your Min P mean exactly? And this isn't a general comment, but I don't see how this particular calculation can derive that mitigation affects the damage a hit does. Are you saying that armor, which is mitigation, will not change how hard theboss hits when he connects?



In *THEORY*, if the 5 second cycle can't kill you because of incoming heals, then having avoidance does absolutely nothing to help your survival (excluding overhealing and overall damage taken during the course of a boss fight) during a 5 second cycle, right? Because then, all you need is more HPS to cover the maximum potential damage intake during a 5 second cycle to start the next 5 second cycle at full life.
And what about when the 5 second cycle becomes meaningless due to boss mechanics (such as no crushings, instant casts or whatnot).




What about when you attack a boss from behind, either from the boss turning for a casted ability or because you aren't main tanking the boss at the exact moment?


What about a matrix where the Warrior is literally forced to take unavoidable damage, be it physical or magical? Or what if you need to construct a matrix where the Warrior will have to take a specific amount of HPS regardless of avoidance/expertise parry-haste reduction? This is more for Brutallus, obviously.



Again not too sure I understand. You're basically saying that until a boss hits hard enough, SBV is better than stam in terms of survivability?



And to finish off, the big problem with your conclusion is that it doesn't take into account a lot of variables which are either very important, or very hard to quantify (such as HoT healing vs direct healing). But saying that for threat, a Warrior will want those exact stat seems silly, since having those stats would generate more threat than needed in most cases.


To add other things you'll need to cover: unreachable stats (item not dropping, making a certain stat ceiling unreachable, how do stats weight in without the theoretical best of each stat?), ArP affects on threat, full rage bar and lack of avoidance streak in regards to rage expenditure (how much does a bad string of non-avoidance affect threat), expertise value Vs. other stats on bosses who have their parry-haste mechanic turned off, being able to gem for other than +15stam due to gem availability (using non epic gems Vs. abundant 15 stam gems for starting guilds).

Wouldn't it be reletively simple (not to mention accurate) to model all of this directly in a computer simulation? That would allow ease of modelling HOTs, swiftmend, PW:S, as well as instant attacks from bosses.

Healing could be set up for a specific class composition, and assumptions made about HOT uptime, heal cancelling, when to use a swiftmend or shield, as well as reaction times for healers and tank trinket/cooldown use in "oh shit" situations.
The program could simulate several hours of combat, resetting every time you "die." It could then output statistical data based on whatever features you wanted to look at, max burst dps over any 5s period, number of times per death you fell below 15%HP, expected TTL etc, and also provide all the combat data in a delimitted format for graphical representation in excel or whatever.

I'm not a very good programmer, but I'm certain someone here is.

Unfortunately no, because while it is easy to program for the variances in what is computer controlled (whether or not you get hit, damage range of the hit, unavoidable special damage), it is impossible to accurately program the random levels of heals you will get. If you want to assume perfect healing, I suppose you could with simple variation of the healing received parameter, but how to accurately take into account healing spikes and reactiveness of healers to every situation is not a realistic possibility.

You are absolutely correct. And the TPS raw number includes the chance for glancing blows, and is balanced to reflect that. Where I ignore glancing blows is that the increase within a certain stat as a delta of that. The reason it can be ignored is not because it isn't significant, but rather because 24% of all white hits are glancing blows regardless, and the number cannot be changed. If I increase my strength by 1, the increase in threat generated is independant of that static number so long as the increase in the stat by 1 does not change the percentage of heroic strikes vs melee. While that is a general truth for small deltas, you are correct that hit capping and expertise capping would provide sufficient additional incoming rage to incresae that ratio. A small change (stat increase by 1), I assume would not. It is a point I leave up to debate.


An excellent point. Currently, everything in the calculation bases off of a fully sundered target with 30% armor reduction. This number would indeed change otherwise. This would affect TPS calculations, but it would in a scaling, multiplicative manner. It would not change relative gains of one stat versus another, but it would provide diminishing returns on threat based stats earlier within the maximization and minization equation.


On a boss that has 1 parryable attack every 2.4 seconds, 20% parry provides an extra .34 swings to you every 5 seconds. it is a relatively linear calculation relative to your parry rate. 10% parry would provide .17 swings. If the boss is swinging more often, the relationship is not fully linear, but can be quite accurately estimated in an inversely linear fashion unless the attack speed is faster than 1.7.

I do. Df rating is the delta from one additional defense, which provides .05 Avoidance. It is part of the calculations.

While there is a standard "AP value" assigned to flametongue in most threat spreadsheets, it is an estimated AP conversion that ends up being inaccurate due to the fact that it does not scale properly. That being said, Knowing the gains from 1 AP, or 1 crit, you can calculate the effects of each buff by converting them into what stats or buffs they provide. For example, a non imp Battle Shout is 306 AP. 2.42 AP (1 str) is around .26 TPS. Therefore

306/TPS value = 2.42/.26, meaning the TPS value of 306 AP is around 32 TPS.

Unlike some damage coefficients, which are multiplicative, threat is much more of a linear calculation, one of the things, based on the numbers, I was hoping people could extrapolate. While the relationship is not 100% linear, it is relatively close to linear. For example, doing a full out calculation finds that at 0 hit, 0 crit, and 0 expertise, 1 point of strength provides .2328 TPS. At 43 expertise and 142 hit, and 25% crit , 1 strength provides .319 threat. While that seems like a reasonably large jump, the RELATIVE value of strength remains largely unchanged. While hit rating provides static returns (thus is dominated by SBV at higher hit and expertise numbers), the relative value of strength, as compared to the other threat generating stats, remains largely unchanged. That is the point of creating the mathematical relationships between the stats, and measuring it as a partial deterministic matrix. In terms of the usefulness of the stats, some stats always dominate others.


This has been pointed out before, and you are correct. Mathematically modelling spikes in healing due to HoTs WILL be part of my follow up. As for them drastically increasing the effects of stamina, in a previous point I did a rotational model 12 cycles deep in which accounted for high variances in healing. At no point in those variances did stamina increase value. In fact, the higher the level of variance, the more value was given to raw avoidance, and at the highest levels of variances in pure ANOVA testing, avoidance was actually scaling up in threshhold value above 70%. While the model did not include internal cycle balancing, based on just plugging around numbers, the stamina approach was still seen as having a much higher P(health=0).

This is not a valid mathematical point. The higher expertise rating you have, the less you will be subject to this, however, from a pure stamina vs avoidance aspect, let's cover this. Let's assume for whatever reason, that expertise on both sides is equal, and this scenario of 3 swings in 5 seconds happens 100 times during the fight.

At 50% avoidance, 87.5% of the time, only two or less of those swings will land, meaning 12.5 times, you will be in the above situation. 6.2 of those times, the next hit will land as well. meaning, you will be pressed for some very reactive healing. 1 of those times you will be able to last stand, and another 1 will have a shield wall active, meaning 4.2 times you are hit again with no outs other than reactive spike healing, because 2.1 of those times, the next strike will also be a hit, when you have little to no health to recover to.

At 65% avoidance, 95.8% of the time, only two or less of those swings will land, meaning 4.2 times, you will be in the above situation. 1.5 of those times you will be hit for a 4th consecutive time. A last stand can cover 1, and a shield wall can cover another situation, and other times will require reactive healing.

You cannot simply make assumptions about the effectiveness of the avoidance unless you fully calculate the effects.

Rereading it, it is a bit easier for me to follow since I did it, but you're absolutely correct, I will revise it accordingly.

My typo. 3400 itemization points, of which 1100 are at least partially customizable. Roughly 2300 of the itemization points are in stam and armor, no matter what you do, and in truth, even with itemization choices otherwise, you will not have FULL control over the 1100, but you do have some control based on which gearing choices/gems/enchants you go with


I'd love a combat log of him. We're currently working on Kalecgos, and only about 50% through. I would love to be able to get a combat log or three, or even twenty, so I can look at the data in an actual setting.


Min (P) is shorthand for Min(P(health=0), which is the minimization of death equation. Solving the minization and maximization problems as a FUNCTION of the matrix values allows me to solve the problem as a deterministic matrix as opposed to a probabalistic one, which would be a much larger pain in the ass to set up.

As for armor, I discredit armor as a valued stat for a number of reasons. The basic gearing of T6 level gear gives you 18000, and along with an ironshield potion, defensive stance, and a healing armor buff, brings you to a level of reduction at which point stam becomes a much more relatively beneficial stat.

On a boss like Azgalor, the benefits of 2500 additional armor is effectively a reduction in damage intake per swing of around 400 with all buffs active, and 650 naked. For the same itemization points, you could have had about 200 stamina, or 2100 more health. Even with no buffs, you would have to be hit in succession 3.5 times with no spikes in incoming healing, or no topping off before it paid dividends, so the reality is that armor, while it provides a consistent percentage in reducing incoming damage, at a certain point, because it is NOT a linear curve, but rather a decaying one in static damage reduction, becomes wasteful.

As for the 5 second cycle, you misunderstand the concept. The fight is a series of 5 second cycles, with the only change being how much health you have entering and exiting each cycle. Avoidance greatly increases the number of cycles entered during which health was at full value.



Once you have 2.5 times the amount of health as the boss can do damage in a single swing, SBV in general becomes a stronger stat than stamina.

As for the unavoidable damage, again, this is easy to do. If the fixed damage is constant (1000 DPS), it can be plugged directly into the state equation. If the boss has an ability, such as Sathrovarr's corrupting strike, used every 20 seconds, then run 4 time-state matrixes in succession, during the 4th of which you include the hit from corrupting strike as a special state5 and state6(during which you can not block, only dodge/parry/be missed and are subject to crushing blows)

In Sathrovarr's case, due to how hard he hits, I won't lie. Stamina becomes more valuable. 12000 damage + chance of 2crushing (for which avoidance cannot help) does increase the value of stamina up to 25,700 health (the point of diminishing returns) for that fight specifically.


I was afraid people would take this approach to the mechanics guide. It is not the purpose. This is a mathematical approach to gearing from which you will still have to make your own decisions, however, the purpose of this was to provide warriors with a means to analyze the differences between stats, measure their relative worth, and maximize their gearset by encounter under the very assumption that optimal gearing is likely to be impossible.

For example ok, XYZ bossfight
XYZ boss has the following abilities
XYZ does this and that, etc.. therefore I want to stack the following stats to give myself the best chance to tank him.
Given what gear I have, that means I will be using these pieces.

Hope that helps.

While not written out, the actual model does include this variance, in a completely linear fashion. If the boss raw damage is 15,000 - 20,000, it is taken into account.


The model assumes full coverage of the armor buff, but does allow for variances in this, such as the buff falling off for intermediate cycles. This is modelled via a seperate mechanic. As for pally lay on hands, that is not a part of this, and this will HAVE to be corrected. Thanks for pointing it out.

My previous post addresses this. However, don't make the mistake of assuming just because 15k + 45% is safer in those circumstances, that it is also superior for the entire fight. 15k + 45% may be relatively safer during those cycles, however, overall for the fight, you may find that much of the time, you enter the unavoidable damage cycle with significantly less than 15k health going in. Remember, the majority of the advantage in avoidance tanking lies in the strength that it will ENTER most successive cycles at max health, whereas that is the case less often with EH builds. Consider the corrollary to your point.

say I enter the unavoidable state of the cycle as avoidance at 21k (max) health 95% of the time, and with less 5% of the time. So 95% of the time its 10k and 60% avoidance, and 5% of the time, I have only 2-3k left and 60% avoidance.
You enter the unavoidable state of the cycle with 25k health 75% of the time and with less 25%. 75% of the time you are 15k and 45%, and 25% you are anywhere from 3-9k and 45%. Which one seems safer now? I don't know, to be honest.

As for maximization of threat, you are absolutely correct, and while the whole problem statement assumes maximization is desirable, dropping some threat for survivability is certainly both valid and desired. In that case, your own discretion in reading the results is key. Remember, I am not advocating that avoidance is best at all times, nor am I saying gearing a specific way is worthwhile at all times. However, those avoidance pieces or threat pieces that are rotting because a tank already has a T6 instance piece in that slot is part of the reason for this guide. Almost every piece has its use.

Regarding periodic and special damage, that can certainly be incorporated. Remember, the 5 second cycle theory still holds true. It can be multiple iterations with something nasty in one cycle per 6, but it is still a rotation based on the 5 second cycle.

As for the brutallus and shahraz info, I honestly did not take that into account, and it would actually be difficult to account for, given it is built into the formulae. I will see how easy/difficult that is to incorporate.

But, let's take a specific boss into account, and a good example would be Sathrovarr.

The state equations are as follows:


HP = 21000
D = L(4809, 1163) - defines the hits as varying between 4809 + or - 1163 damage, linearly scaled.
A = 60.86%
Pr (passive reduction of crushes) = 2.68% (this implies that passive miss + block + dodge + parry is 2.68% above 87.4, although this will not affect stun states)
EX = 27
#A (number of player attacks) = 6.42, this is a baseless assumption for this calculation that I would spend 30% of the effective 6 second ability cycle (4.14 hits, 4 abilities) using only 3 abilities (putting up TC, demo, rage starved). This is bases entirely on historic data for myself.
#P(number of expected parries per cycle) = .247 (=6.42*3.85% (my effective parry rate assuming 10.6 boss parry and 27 expertise)
Effective modified Boss Swing time (from 2.4) = 2.27 = 2.4 - (.247)(.55)
P(S=3) probability of 3 swings in the cycle- 20.2%
P(S=2) probability of 2 swings in the cycle - 79.8%
The above probability are based on 2 swings in 4.54, with .46/2.27 of the cycles falling outside the standard coverage gap.
P(n, var) = linear
Pr(n, var, dT) = Min ( 4.7-dT, (21000/(current health) - 1) )
dT initial = 0, max = 4,
if Pr(heal > 2.5) dT = dT + 1
if Pr(heal > 1) dT = dT - 1
Varying healing between 0 and 4500 *4.7 = 21000 on a to be defined probability chart, in which I will assume the healers are perfect, and will heal more when health is low at all times, but as the dT function above defines, cannot exceed a value of 2.5 times normal healing for more than 2 time states, and has recovery involved (in other words, under no circumstances will HPS > 15000 be allowed to be kept up for more than 4 seconds, after which elevated HPS (more than 1.7 times normal healing amount) of those levels will not be able to be established again for 6-8 seconds.

So let's do 1 minute worth of state matrices

SET 1
(.798)
T = 0
[ 21000 .6086 0]
[ 21000 .3914 -4809 + P(1109, -1 < xi < 1) - SBV(519)]
T=1
[ 21000 .6086 0]
[ (21000 - 4809 + P(1109, -1 < xi < 1) - SBV) .6086 21000] if you dodge the second attack, you will be at full prior to the next time-state, given reactive heals to the first hit and incoming normal heals)
[ (21000 - 4809 + P(1109, -1 < xi < 1) - SBV) .3914 - 4809 + P(1109, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)]
End State

The only difference in the standard time-state matrix is that due to variances in healing, 2 consecutive hits, due to varied amounts of healing received, you may not be at full. Therefore, healing will be normalized to assume that 2 consecutive blocked hits will automatically be healed through via a normalization of P(r) by an overgoverning:
Sum(yi) = 0, Sum(yi + y(i+1)) >= - 1.09, or enough to heal 2 blocked attacks that hit for the full amount (4809 + 1109 - 519).

Therefore:
- 2(4809 + P(1109, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)]) = 21000

SET 2
(.202) (whether the first or second attack was parry hasted makes no difference)
T = 0
[ 21000 .6086 0]
[ 21000 .3914 -4809 + P(1109, -1 < xi < 1) - SBV]
T=1
[ 21000 .6086 0]
[ (21000 - 4809 + P(1109, -1 < xi < 1) - SBV) .6086 21000]
[ (21000 - 4809 + P(1109, -1 < xi < 1) - SBV) .3914 - 4809 + P(1109, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)]
T=2
[ 21000 .6086 0]
[ (21000 - 4809 + P(1109, -1 < xi < 1) - SBV) .6086 21000]
[ (21000 - 4809 + P(1109, -1 < xi < 1) - SBV) .3914 - 4809 + P(1109, -1 < xi < 1) + 1.85 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)]
(.85)
[(21000 - 2(4809 + P(1109, -1 < xi < 1) - SBV)) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)] .3914 - 4809 + P(1109, -1 < xi < 1) + 1.85 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)]
(.15) (crush)
[(21000 - 2(4809 + P(1109, -1 < xi < 1) - SBV)) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)] .3914 - 8683 + P(2106, -1 < xi < 1) + 1.85 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)]

based on this, during normal (no special attacks incoming), you will be in Set 1 of the time-state 79.8% of the time, and Set 2 20.2% of the time.

Now, let's deal with the special attack cycle.

the stun lasts for 2 seconds, and because you cannot be parried or attack during that time, and assuming TC is active, 3/2.4 = 1.25 is the expected number of attacks. 75% of the time, you will be stunned for 1 attack, and 25%, 2

.75
T = 0
[ 21000 .6086 0]
[ 21000 .3914 -4809 + P(1109, -1 < xi < 1) - SBV]
T = 1
[ 21000 1 9500(500, -1 < xi <1)]
[ 21000 -4809 + P(1109, -1 < xi < 1) + (4500 + Pr(4500, -1, yi < 4.7) 1 9500(-1 < xi <1)]
T = 2
[21000 - 9500(500, -1 < xi <1) .3461 2.4*(3500 + Pr(4500, -1, yi < 4.7) ] 3500 instead of 4500 to reflect the fact that the 1k dot is active, and the .3461 reflects dodges and misses only
[21000 - 9500(500, -1 < xi <1) .3539 4809 + P(1109, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)] not crushed or blocked
[21000 - 9500(500, -1 < xi <1) .15 8683 + P(2106, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)] crushed

.25
T = 0
[ 21000 .6086 0]
[ 21000 .3914 -4809 + P(1109, -1 < xi < 1) - SBV]
T = 1
[ 21000 1 9500(500, -1 < xi <1)]
[ 21000 -4809 + P(1109, -1 < xi < 1) + (4500 + Pr(4500, -1, yi < 4.7) 1 9500(-1 < xi <1)]
T = 2
[21000 - 9500(500, -1 < xi <1) .3461 2.4*(3500 + Pr(4500, -1, yi < 4.7) ] 3500 instead of 4500 to reflect the fact that the 1k dot is active, and the .3461 reflects dodges and misses only
[21000 - 9500(500, -1 < xi <1) .3539 4809 + P(1109, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)] not crushed or blocked
[21000 - 9500(500, -1 < xi <1) .15 8683 + P(2106, -1 < xi < 1) + 2.4 * (4500 + Pr(4500, -1, yi < 4.7) - SBV)] crushed
T = 3
(i'm not writing out the iterations because I'm lazy and there's 6 of em with independant probabilities)
[Entering Health .3461 +healing amount received]
[Entering Health .3539 hit + healing]
[Entering Health .15 crush + healing]

Ok, so now, let's work it through.

Assuming the ability is used every 25 seconds, calculating 50 seconds of combat yields:

8 normal states with a 79.8% chance of Set 1 and a 20.2% chance of set 2.
2 special states with a 75% chance of Set 1 and a 25% chance of set 2.

The common mistake is to average them together, because that would be incorrect. Combat is a series of 5 second cycles, but not the average result of them. So what you are instead solving, is a DETERMINISTIC matrix with probabilities built into the starting state, rather than calculate the endless series of probabilities of each state.

So just taking the first 10 cycles, the problem statement would be the above state matrices solved using probability and depth. To find relative gains in value, it is simple, you simply solve it as a function of accrual of deltas:

[ 21000 + 11.5*dStamina .3914 +d Avoidance (4809 + P(1109, -1 < xi < 1))dArmor(yes, armor changes are a multiplicative function, but the formula is known) ]

Now when you solve the matrix, instead of getting steady state probabilities, you will get probabilities as a function of the stats. Apply it into the itemization constraints, and you will be able to allocate freely.

Note that the specific constraint of all<=550 eliminates any ability to "solve" the equation, but rather just take the determinant of the resultant probability function matrix, and you will have relative values. not all circumstances will have real determinants either, as many times it will result in some imaginary numbers, specifically in armor, as the matrix itself will not know you can dump armor for other stats, which it very often attempts to do for the minimization equation.