Tamral

Just to give you an idea of how wide the variance is for bosses, here are the recommended gearing levels for every boss I have come across, from SSC to TK.

The following are used to create the boundaries:
I’m not including the effects of incoming crits, simply because if you’re not stacking 490 defense already, you’re too stupid to understand any of this anyway. If you’re stacking INT or Spirit and want to see those in the calculations, please direct your concerns to barrens chat in your local realm.

Initial Assumptions

500 defense = Df0
15% dodge = Dg0
15% parry = Pa0
25% block = BL0
300 block value = BV0
6 expertise = EX0
0 hit rating = HT0
10% 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

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 = 3.7 block value = 1 expertise rating = 1 defense rating = 12 Armor

Without doing 46 pages of math, I concluded that the full complement of all BT epics (all level 141 items) provides a grand total of 3400 itemization points. 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 + .28DBV + DEx + DDf + .08Armor = 1100
S.T
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)

That’s the simple part.

Now it gets a bit more complex, so we’re going to summarize some of the data together (and yes, I realize I am combining dodge and parry together under the avoidance hat, and anyone with a brain realizes that parry is better in equal quantities, but it makes the math actually doable)

First, we need to provide proper caps where applicable;
Ex <= 43
HT <= 142

Avoidance = A0 = Pa + Dg – 1.2 + 10 + (DF-500)/25
Boss Damage = Boss Damage * .9 * ( 1 – (Armor/(11960+Armor))

Character hit chart:
{
A0 0
BL Boss Damage - BV
Max(0, 102.4 – A0 – BL - 15) Boss Damage
Max(0, 102.4 – A0 – BL) Boss Damage * 1.5
}

At first glance you may think it best to limit the expected damage, but that is not necessarily the case. We’ll get into that later:

First, we need to measure every stat relative to Avoidance, and Threat where applicable, because we are going to turn the entire equation into a second order exact equation, and second, we want to control the determinant (we want to be able to spit different ideal stats out by supplying the boss stats, not determine what boss our gear is ideal for (because the answer to that will always be an endpoint of 0 damage per swing, infinite time between swings, etc.)

The base values above, as per any normal threat spreadsheet, will be able to give a base of around 900 TPS based on 200 ms lag, using a SS, Rev, Dev, Dev cycle, with 2 heroic strikes per 4. So, using the same kind of calculator, we get marginal values of:

1 Agi = .033 A0 - .008 TPS (Agi leads to a relative decrease in threat because .05% crit provides less threat than .033 dodge removes)
1 Str = 0 A0 + .2TPS
1 Ex = 0A0 + 1.7 TPS
1 HT = 0A0 + .7 TPS
3.8 BV = 0A0 + .6 TPS
1 Dg = .051A0 - .31TPS
1 Pa = .042A0 - .12TPS
1 CT = 0A0 + .44TPS
1 Df = .047A0 - .24TPS
12 Armor = 0A0 - .00045TPS
1BL = 0A0 - .0000081*BV TPS (being it I don’t want to have to use Fourier to estimate this BS, I’m going to revolve this around a static number)
Therefore
1BL = 0A0 - .005 TPS (revolving around 600 Block Value, because this number is so damn small it means next to nothing anyway)

TPS0 = 800 (the value any tank who has l2played can maintain)
A0 = 39.2 (15 dodge, 15 parry, 500 defense)

Now, going back to the damage formula.

First, we need to find the probability within a 30 second cycle that the tank will be subject to a crushing blow.
2 attacks per 5 are off the table

Now, we must determine how many free/extra swings the boss will have.

Using a simple estimation of 1.6 weapon speed, and the fact that parries can occur at any time within a boss swing cycle (2.4 seconds)
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.

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.

30 seconds = approximately 38 swings.
38 * BP = number of parries.

At the base level, this number is around 3.4 parries per 30 seconds, which results in the boss getting one extra attack per 37 seconds (1.9 reduction in swing time) total over the course of 30 seconds. However, this is misleading. The reality is that the extra attacks are not evenly spread out, and it actually results, in on average, 1.41 swings per 30 seconds that are potentially a third in a 5 second gap.

On average, absent expertise rating beyond that provided by talents, the boss will get one extra swing at the player every 37 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 – A0)^2 * .15 = .054 at the base level. About 1.41 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 72 seconds, and you’re only subject to .5 swings per 30 that fall outside your coverage gap.
(1 - .6)^2 * .15 = .024. So now, instead of a 5% chance of catastrophe 1.9 times per 30 seconds, it’s a 2.4% chance 1 time 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 7 minute fight is absolutely astronomical.

Assuming starting values:

20000 raid buffed health
Assuming HPS

State 1 Initial: 20000 health
State 1 post initial = return to state 1 health
State 2 = {A0 min (State 1 health +2.4 HPS, 20000)
1- A0 min (State 1 health +2.4 HPS, 20000) - Boss Damage + BV
}
State 3(A0) {A0 min (State 1 health +4.8 HPS, 20000)
1- A0 min (State 1 health +4.8 HPS, 20000) - Boss Damage + BV
}
State 3(BL) {A0 min (State 1 health +4.8 HPS, 20000) – Boss Damage + BV
1- A0 min (State 1 health +4.8 HPS, 20000) – 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, 20000) – Boss Damage + BV
}
Subset 2:
2* (A0 * (1 –A0)
) {A0 min (State 1 health +4.8 HPS, 20000) – Boss Damage + BV
1- A0 min (State 1 health +4.8 HPS, 20000) * Boss Damage + 2 *BV
}
Subset 3
(1 – A0)^2
{A0 min (State 1 health +4.8 HPS, 20000) - 2 * Boss Damage + 2 *BV)
BL min (State 1 health +4.8 HPS, 20000) – 3 * Boss Damage + 3 * BV
Max(0, 102.4 – A0 – BL - 15) min (State 1 health +4.8 HPS, 20000) - 3 * Boss Damage + 2 *BV
Max(0, 102.4 – A0 – BL) min (State 1 health +4.8 HPS, 20000) - 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, gag
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 (3.5 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, (20000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25% + .128BL)
Max: 800 - .008Agi + .2 Str + 1.7 Ex + .7 HT + .16BL - .31Dg - .12Pa +.44CT - .00003 Armor - .005 BL
Subject to:
+.67 DSta + DAg + DST + DCT + DDg + DHT + DPa + DBL + .28DBV + DEx + DDf + .08Armor = 1100
All >= 0
EX <= 43
Hit <= 142
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)

Ok, looking over this, we get the following:
A 4 State matrix with not enough static equations to solve (it is a ridiculous partial that isn’t even worth looking at). BUT… well at first glance, we can eliminate several of our variables.

Under any circumstances, the following relative dominances can be made:
Expertise dominates hit and crit. Since 3.8BL is the same as 1 crit rating in itemization, BL dominates crit. Therefore, under all circumstances, crit = 0.
Strength is dominated by everything. It is quite possibly the most worthless stat out there for a protection warrior. It is dominated by everything. Therefore, STR = 0.
None of these stats provide any avoidance, the relative gains in these stats therefore can be measured in a linear fashion against one another.

Until we can plug in boss damage, we don’t know about the relative values of anything that provide both avoidance and threat results. Furthermore, itemization points spent in armor past the basic level of 17000 is such a waste it defies belief. If you get a +armor enchant or kit, go shoot yourself now, because it’s beyond idiotic. You’ll get 18k or so armor anyway just from the items themselves, but the relative value of armor in itemization is literally nothing compared to everything else.

Put relatively, the gains from 100 Stam vs 1200 Armor is the difference between 1050 health, vs, (at 17k armor), a 1.5% decrease in damage taken (60.2% vs 58.7%), or about 350 less per hit. Since the objective here is to limit any possibilities of 3 consecutive hits, a stat that does not pay back dividends until AFTER that happens is pointless. Oh, and the State matrix tells us something else. BL doesn’t even matter until you’re in the oh shit state anyway. It doesn’t otherwise do much of anything. Therefore, byebye.

So at this point, knowing only that armor, str, crit, and BL are equal to 0, we have to actually now solve this matrix. Still seems impossible… BUT, we can write relative formulas as well. Especially since we did that cool thing before writing out avoidance, right? Not to mention, a quick rewrite to make all this shit a bit easier on the eyes:

Min P(health = 0, (20000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25%)
Max: 800 - .008Agi + 1.7 Ex + .7 HT + .16BL - .31Dg - .12Pa S
Subject to:
+.67 DSta + DAg + DDg + DHT + DPa + .28DBV + DEx + DDf = 1100
All >= 0
EX <= 43
Hit <= 142
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)

Still we are a bit short on equations, and this is still a clusterfuck of a partial to even attempt. But, we’ve got some abbreviations here. First off, because the minimization equation dominates here, and because I know something else you don’t know…… No really, from before since we know that Expertise dominates hit and block value, and that hit dominates block value….
Rewrite it to be:

Min P(health = 0, (20000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25%)
Max: 800 - .008Agi + 1.7 Ex - .31Dg - .12Pa S
Subject to:
+.67 DSta + DAg + DDg + DPa + DEx + DDf = 1100
All >= 0
EX <= 43
Hit <= 142
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)

AHA! A 4 State matrix, 2 subject equations, and known endpoints! We can now solve this. To make a long long long long story short: Expertise caps first in every circumstance from Boss damage =0 to 99999 and any other parameter you set. It then allows us to rewrite the equation as follows:

Min P(health = 0, (20000 + sta * 1.15, 39.2% + .033Agi + .051Dg + .042Pa + .047Df , 25%)
Max: 800 - .008Agi + 1.7*43 + .7*HT + .16BL - .31Dg - .12Pa S
Subject to:
+.67 DSta + DAg + DHT + DDg + DPa + DDf = 1057
All >= 0

EX = 43

Hit <= 142
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)

First, solve the relative partials from above with everything else constant to get your variance rates. The reason you are doing this is because you’re not creating the ideal gear set, you’re creating the a means to measure the relative values of increasing stats BY BOSS (I can’t stress the need for different sets for each boss enough here)
Ok, now, you’re supplied multiplier row in the end matrix (6 x 6) x (1 x 6) is (Boss Damage, 2.4, 10.6, 26.2, 0, (your weapon speed).

The lighter the boss hits, the higher the value for things like Block Value (and Block rating, even though I zeroed it out). Stam has an exponentially decreasing rate of return. For example, against a boss hitting for 10,000 a pop, stam has a very high rate of return until about 22,800 HP. For a boss hitting for 9000 a pop, the point at which it gets overtaken is closer to 20600. These are raidbuffed numbers by the way.

So, going off of the original BASE numbers, here is what the ideal scenarios look like by boss (other than Resistance Fights), and they are estimated to the nearest 1/10.

Again, this is what my spreadsheet spits out, and I take into account a lot more than just whats up above, including specific threat dumps, additional attacks, silences, fights where threat is not an issue (karathress) and DoTs. I have not done leo or vashj simply because the number of factors going in is too high)

Lurker: 55% avoidance , 43 expertise, 142 hit, 17000 armor, 850 block value, 16,400 health.
Morogrim: 61% avoidance, 43 expertise, 0 hit, 17000 armor, 350 block value, 17,600 health (I inserted the quakes as an extra physical attack per 30, and decreased his swing timer to 1.9 to reflect his additional attacks)
Karathress: 61% avoidance, 43 expertise, 142 hit, 17000 armor, 350 block, 16,100 health.
Leo, Vashj: Cannot be done, I’m not even going to bother with the math.
A’lar: 52% avoidance, 43 expertise, 142 hit, 17000 armor, 970 Block, 16,600 health
VR: 49% avoidance, 43 expertise, 142 hit, 17000 armor, 990 block, 81 crit, 15,000 health.
Solarian: who cares
KT: 58% avoidance, 43 expertise, 0 hit, 17000 armor, 350 block, 18,400 health
Rage: 61% avoidance, 43 expertise, 142 hit, 17000 armor, 350 block, 16,100 health

I’m not going to go on simply because of the amount of time it took me to create the spreadsheet, and at least as of now, I consider it a general disservice to just spit out numbers in an unqualified manner (because I’m not posting the spreadsheet for a reason, especially since it is somewhat incomplete). I’ll be happy to entertain individuals who want to discuss it and are legitimately interested in helping to tune it.

The main mission here is hopefully 4 lessons:

1) If you are using only one set of gear as your “best” gear for tanking everything, then you should think again, because every situation is different, and sometimes, the gains and losses can be incredible.

2) That stickied “fortifications” post on the warrior forums on the official forums is not only outdated, it’s a piece of shit and a waste of space, and needs to be taken down. That strategy is not only dated, it’s stupid in BC.

3) Hopefully it helps people come up with their own systems of determining whether or not gear is an upgrade not as a whole, but within certain sets. I HATE seeing quality items get DE’d simply because it doesn’t have enough stam, or because it has too much avoidance, or “I’ve already capped this stat”, etc. The fact is, there is not enough plate in the game as is to make ANY of the ideal typesets, let alone all of them.

4) It qualifies what I mean by many warriors right now trying to eat soup with a fork. There are situations gear wise you could run into, where no matter how good a player you are, it won’t matter. You’re leaving too much up to luck and chance, and you’re not giving yourself or your raid a fair shot at the encounter.