Updated the OP for the latest build, and spent a few hours analyzing Vengeance in detail. It's still somewhat foggy, but here's the best understanding of how Vengeance works that I've got so far:

1. When you first take damage, you immediately gain Vengeance, equal to 5% of the damage taken. From then on, Vengeance 'ticks' every 2 seconds.
2. When it ticks, it checks how much damage you've taken since the last time it ticked, and does either step 3, or step 4:
3. If DamageTaken > 0, new Vengeance is set to: [OldVengeance*0.95 + DamageTaken*0.05]
4. If DamageTaken = 0, new Vengeance is set to: [OldVengeance - MaxVengeance*0.1] (Where MaxVengeance is the highest this stack of Vengeance has ever been)

This has the interesting effect that when you're taking steady/constant X damage per tick (2sec), your Vengeance stack approaches X AP.
This also has a concerning effect that if you're fighting a boss that attacks slower than 2.0 (ie, they're a standard 2.0 attack speed, and you've slowed them with Infected Wounds or similar), then some of the ticks are going to line up between melee attacks, and you're going to suffer that large -10% decay. That's going to significantly lower the average Vengeance AP on any slow-attacking bosses.

EDIT: Oh, another concern: assuming the boss isn't incredibly fast hitting (1sec or faster), every time you dodge/miss, that's a tick of no damage taken, so -10% decay. That means that avoidance will be detrimental to threat by a small amount. (However, remember, avoidance also increases your rage income, so that may be offset somewhat/all)

I moved a conversation from here to the WOTLK Bear thread, so if you're looking for it you will find it there.

This is what I have thus far as well. Thanks to Astrylian for giving me the above calculations. First off my calculation thus far has one major flaw and that is, it doesn't take account for when your max HP changes mid fight. I'm sure there'll be more, but this is based off the information I have so far; and it's been a while since I did this kind of math. T.T

Edit:
Added the calculation for when Vengeance reaches HP cap. It ~should~ be complete now. I've submitted variables and haven't found any errors as of yet. Though please do double check the formula.

Variables

CurrentMaximumHealth = Current HP at time of check
CurrentVengeance = New Vengeance total AP after calculation
OldVengeance = Previous Vengeance total AP at time of calculation
TotalDamageTaken = Amount of damage taken since last check
MaxVengeance = The highest amount of AP you have had since last taking damage

Calculation

If (TotalDamageTaken*0.05) > 0
Then CurrentVengeance = [(OldVengeance*0.95 + TotalDamageTaken*0.05)
Unless ({OldVengeance*0.95} + TotalDamageTaken*0.05) >= (CurrentMaximumHealth*0.1)]
Then If (OldVengeance*0.95) >= (CurrentMaximumHealth*0.1)
Then CurrentVengeance = OldVengeance
Else CurrentVengeance = CurrentMaximumHealth*0.1
Else If (TotalDamageTaken <= 0)
Then Current Vengeance = (OldVengeance - MaxVengeance*0.1]
Else set MaxVengeance = CurrentVengeance

Just a quick question here.

Are these numbers (mainly regarding threat generation) also accurate for WotLK 4.0.1 (lvl 80)? I tried finding something comparable but I was unlucky...

Thank you

I don't think so. I've run some tests, and I found that for instance the calculation of the damage done by Pulverize are not increased by 451 per stack, but by 235 ( more or less 5 ). I tried also to check for informations about these numbers for 4.0 ( and asked in the FAQ ) but without interesting results.

These numbers are obviously for level 85.

Survival Instincts -- Damage reduction changed from 60% to 50%. Cooldown reduced from 5 minutes to 2 minutes. Duration still 12 seconds.

Bear Form -- Stamina bonus lowered from 20% to 10% and Heart of the Wild health bonus from 10% to 6%. Bear health should be close to plate tank health with this change.

More changes said to be in 4.0.3a for bears by Zarhym. Seems they are bringing everyone's "shield wall" to be exactly the same just with different names. The health changes seem a tad excessive with the SD change. Really hope they at least allow lacerate ticks to still proc SD.

While bears are missing parry we have a higher dodge, so the total avoidance tends to be the same. And yes, Savage Defense is and was brutal on the live servers and in the beta. With a little bit of luck you were able to absorb entire bossfights into your SD (or reduced the incoming amage to a value where the healer could keep you alive whith much less effort than needed for other tank). A change was neccessarry - I just hope that item scaling after T11 will still be good enough without additional changes / re-balancing.

The Bear 'rotation' in Cataclysm is significantly more complex than it was in WotLK (a good thing!). Here is my work so far on modeling those rotations:

Optimally, bears should choose their abilities based on a priority list. However, the order of that priority list can change with gear level. There are effectively 10 elements to a bear priority list, which I have labeled a-k for convenience, in no particular order:

a	Demo Debuff
b	FFF Damage
c	[ignored; was Mangle Debuff, but ended up being redundant]
d	Mangle Damage
e	Lacerate Debuff
f	Lacerate Stack
g	Lacerate Damage
h	Pulverize Buff
i	Pulverize Damage
j	Thrash Damage
k	Swipe Damage

Next, I evaluated the potential performance of each ability at a very wide variety of gear levels: from practically naked (1000ap), to entry level raiding (10000ap), to what I'd guess is well past Deathwing gear (100000ap). From that, I was able to see which abilities trumped which other abilities, at the varying gear levels. I extrapolated that into a chart:

	a	b	c	d	e	f	g	h	i	j	k
a	X
b	<	X
c	>	>	X
d	>	>	<	X
e	?	>	<	<	X
f	<	?	<	<	<	X
g	<	?	<	<	<	<	X
h	<	>	<	<	<	<	>	X
i	<	?	<	<	<	<	?	<	X
j	<	>	<	<	?	?	>	?	?	X
k	<	?	<	<	<	?	?	<	<	<	X

Where < means that the ability on top is better than the ability on the left.
And > means that the ability on the left is better than the ability on the top.
And ? means that which ability is better can vary based on gear.

NOTE:Values here are based on damage, threat, and raid utility. Rage cost could potentially be significant, and I hope to redo this with rage cost being weighted as well, but I don't think it will change anything. The primary thing it would change would be to allow FF to beat the things it can already beat, but at earlier gear levels (FFF scales better than Swipe and Lacerate). Regardless, in my experience, you have enough rage, even in entry level gear, to fully fill every GCD; more rage just lets you afford Maul more.

From that chart, I generated a list of possible priority lists. Originally, I found 96 different possible priorities that match the above table. However, any elements in the list after Lacerate Damage or Pulverize Damage end up being irrelevant (since it's always possible to Lacerate Damage, or to Lacerate Stack and then Pulverize Damage). By trimming the lists of anything past those two, and removing the duplicates, I was left with the following 30 possible priority lists:

daefhi	M	D	Lb	Ls	Pb	Pd
daefhjbg	M	D	Lb	Ls	Pb	T	FF	Ld
daefhjbi	M	D	Lb	Ls	Pb	T	FF	Pd
daefhjg	M	D	Lb	Ls	Pb	T	Ld
daefhji	M	D	Lb	Ls	Pb	T	Pd
daefjhbg	M	D	Lb	Ls	T	Pb	FF	Ld
daefjhbi	M	D	Lb	Ls	T	Pb	FF	Pd
daefjhg	M	D	Lb	Ls	T	Pb	Ld
daefjhi	M	D	Lb	Ls	T	Pb	Pd
daejfhbg	M	D	Lb	T	Ls	Pb	FF	Ld
daejfhbi	M	D	Lb	T	Ls	Pb	FF	Pd
daejfhg	M	D	Lb	T	Ls	Pb	Ld
daejfhi	M	D	Lb	T	Ls	Pb	Pd
dajefhbg	M	D	T	Lb	Ls	Pb	FF	Ld
dajefhbi	M	D	T	Lb	Ls	Pb	FF	Pd
dajefhg	M	D	T	Lb	Ls	Pb	Ld
dajefhi	M	D	T	Lb	Ls	Pb	Pd
deafhi	M	Lb	D	Ls	Pb	Pd
deafhjbg	M	Lb	D	Ls	Pb	T	FF	Ld
deafhjbi	M	Lb	D	Ls	Pb	T	FF	Pd
deafhjg	M	Lb	D	Ls	Pb	T	Ld
deafhji	M	Lb	D	Ls	Pb	T	Pd
deafjhbg	M	Lb	D	Ls	T	Pb	FF	Ld
deafjhbi	M	Lb	D	Ls	T	Pb	FF	Pd
deafjhg	M	Lb	D	Ls	T	Pb	Ld
deafjhi	M	Lb	D	Ls	T	Pb	Pd
deajfhbg	M	Lb	D	T	Ls	Pb	FF	Ld
deajfhbi	M	Lb	D	T	Ls	Pb	FF	Pd
deajfhg	M	Lb	D	T	Ls	Pb	Ld
deajfhi	M	Lb	D	T	Ls	Pb	Pd

Added a short version of each ability there, in order, so it's easier to read, without having to reference the top table.
M=Mangle
D=Demo
Lb=Lacerate deBuff
Ls=Lacerate Stack
Ld=Lacerate Damage
T=Thrash
Pb=Pulverize Buff
Pd=Pulverize Damage
FF=Faerie Fire
S=Swipe, but that doesn't matter, since Swipe never ends up before both Lacerate Damage and Pulverize Damage in a priority list

Another way to look at this would be like this:

Mangle Damage	1
Demo Debuff		2	3
Lacerate Debuff		2	3	4
Lacerate Stack				4	5
Thrash Damage			3	4	5	6	7
Pulverize Buff					5	6
Pulverize Damage						6	7	8	9	10
Lacerate Damage							7	8	9	10
FFF Damage							7	8	9	10
Swipe Damage								8	9	10

That's the possible priorities (1 being highest, 10 being lowest) for each element. From that you can see things like... Mangle is always highest priority. Swipe is generally terrible for single targets, and always is obsoleted by some other ability. Thrash is decent, and scales really well.


OK, now we've got a list of possible priority lists that are useful. Next, how to evaluate them for a given character? Well, that's a very difficult question. Up until now, nothing has been Rawr-specific about any of this. And perfectly accurately evaluating these rotations, which include randomness, in a closed form solution is going to be difficult (though not impossible) and time-consuming. So, in the interest of getting things done faster (since Dec7th is rapidly approaching), but still being as accurate as possible, I've taken a different route for now (I fully intend to revisit this later on and write a closed form model for it).

That route is to write a separate (outside of Rawr) simulator, to simulate combat using each of these priority lists, and output a count of the uses of each ability. Simulations are good for certain things, and this seems to be one of them. Here's the results, using a 5min (200 GCDs) fight, and assuming you have the Endless Carnage talent:

									FFF	Mangle	Lacerate	Pulverize	Thrash	Swipe	Demo	LacerTick	PulvUptime	DemoUptime
daefhi	M	D	Lb	Ls	Pb	Pd			1	58.8436	97.2774	31.9086	0	0	10.9704	156.3696	192.7075	197.6928
daefhjbg	M	D	Lb	Ls	Pb	T	FF	Ld	19.4614	58.7596	65.64	16.9618	28.1895	0	10.9877	220.9119	190.8697	197.8402
daefhjbi	M	D	Lb	Ls	Pb	T	FF	Pd	21.5013	58.6964	63.157	20.3334	25.3534	0	10.9585	204.4983	192.6685	197.7428
daefhjg	M	D	Lb	Ls	Pb	T	Ld		1	58.6842	84.2712	16.9674	28.0885	0	10.9887	221.0396	190.9035	197.8544
daefhji	M	D	Lb	Ls	Pb	T	Pd		1	58.9308	78.4456	25.5391	25.1057	0	10.9788	171.4193	192.6978	197.6587
daefjhbg	M	D	Lb	Ls	T	Pb	FF	Ld	17.9856	59.3309	62.9675	16.1606	32.56	0	10.9954	219.6827	184.9858	197.8057
daefjhbi	M	D	Lb	Ls	T	Pb	FF	Pd	21.1176	58.8897	62.8413	20.1688	26.0245	0	10.9581	202.4369	190.9141	197.7312
daefjhg	M	D	Lb	Ls	T	Pb	Ld		1	59.2509	79.9654	16.1931	32.6001	0	10.9905	219.5779	185.0872	197.8003
daefjhi	M	D	Lb	Ls	T	Pb	Pd		1	58.9891	77.7767	25.3382	25.9186	0	10.9774	171.1339	191.6037	197.5764
daejfhbg	M	D	Lb	T	Ls	Pb	FF	Ld	13.9783	59.6674	54.2949	15.5579	45.5161	0	10.9854	192.1749	178.9367	197.8568
daejfhbi	M	D	Lb	T	Ls	Pb	FF	Pd	15.2112	59.5445	53.6593	17.185	43.4418	0	10.9582	182.5582	184.4907	197.591
daejfhg	M	D	Lb	T	Ls	Pb	Ld		1	59.5337	67.269	15.5691	45.6492	0	10.979	192.1328	179.2282	197.8665
daejfhi	M	D	Lb	T	Ls	Pb	Pd		1	59.0001	63.6573	20.6452	44.7084	0	10.989	154.4488	189.2127	197.7778
dajefhbg	M	D	T	Lb	Ls	Pb	FF	Ld	13.4299	59.3452	53.1203	15.7295	47.3852	0	10.9899	185.9652	179.8516	197.8205
dajefhbi	M	D	T	Lb	Ls	Pb	FF	Pd	13.0107	59.0294	52.4955	16.8877	47.5855	0	10.9912	173.4	184.2615	197.8191
dajefhg	M	D	T	Lb	Ls	Pb	Ld		1	59.674	65.2277	15.7602	47.3417	0	10.9964	185.7284	180.0577	197.8615
dajefhi	M	D	T	Lb	Ls	Pb	Pd		1	58.5301	61.7141	20.0208	47.754	0	10.981	144.7811	187.7851	197.7844
deafhi	M	Lb	D	Ls	Pb	Pd			1	59.0332	97.3958	31.9426	0	0	10.6284	156.057	192.6206	195.5974
deafhjbg	M	Lb	D	Ls	Pb	T	FF	Ld	19.2757	58.8973	65.8441	16.9206	28.2736	0	10.7887	220.7523	190.5346	196.4658
deafhjbi	M	Lb	D	Ls	Pb	T	FF	Pd	21.5791	58.6521	63.0164	20.1697	25.7166	0	10.8661	204.2588	192.5849	196.7117
deafhjg	M	Lb	D	Ls	Pb	T	Ld		1	58.8885	84.0619	16.9133	28.3586	0	10.7777	221.0075	190.587	196.4502
deafhji	M	Lb	D	Ls	Pb	T	Pd		1	59.4038	78.3401	25.5036	25.09	0	10.6625	171.417	192.5984	195.6213
deafjhbg	M	Lb	D	Ls	T	Pb	FF	Ld	17.9843	59.2921	63.4859	16.0887	32.3702	0	10.7788	220.2918	184.801	196.2362
deafjhbi	M	Lb	D	Ls	T	Pb	FF	Pd	21.0792	58.9054	62.7931	20.02	26.3509	0	10.8514	204.3759	190.5308	196.5902
deafjhg	M	Lb	D	Ls	T	Pb	Ld		1	59.5849	80.1828	16.1027	32.3329	0	10.7967	220.1486	184.943	196.2476
deafjhi	M	Lb	D	Ls	T	Pb	Pd		1	59.2877	77.7976	25.3004	25.9324	0	10.6819	172.6519	191.201	195.7976
deajfhbg	M	Lb	D	T	Ls	Pb	FF	Ld	13.9706	59.9444	54.385	15.5098	45.4213	0	10.7689	193.893	178.5332	196.0783
deajfhbi	M	Lb	D	T	Ls	Pb	FF	Pd	15.1507	60.0903	53.9836	17.2945	42.8879	0	10.593	182.653	184.2686	195.6078
deajfhg	M	Lb	D	T	Ls	Pb	Ld		1	59.7992	67.3832	15.5023	45.4911	0	10.8242	194.0206	178.5517	196.2188
deajfhi	M	Lb	D	T	Ls	Pb	Pd		1	59.619	63.3546	20.5743	44.6088	0	10.8433	156.6557	188.7979	196.448

FFF=Count of FFF usages
Mangle=Count of Mangle usages
Lacerate=Count of Lacerate usages
Pulverize=Count of Pulverize+3 usages
Thrash=Count of Thrash usages
Swipe=Count of Swipe usages
Demo=Count of Demoralizing usages
LacerTick=Count of Lacerate Ticks, times the number of stacks at the time of the tick
PulvUptime=Count of GCDs that Pulverize was up for
DemUptime=Count of GCDs that Demoralizing was up for


For Rawr4's initial Cataclysm release, Rawr.Bear will include those numbers, just hard-coded in the code, for each of the 30 possible priority lists that it evaluates for each character. From those numbers, we can evaluate the rotation in terms of threat and damage for a given character.

..whew, that was a lot of tables.

Hey Astrylian, been a while!

I have been trying to figure out where the crossover for FFF /swipe/lacerate is for my move suggester/debuff addon. Using the scales in the OP, I have put together a little spreadsheet which seems to indicate that lacerate pulls ahead of swipe around 7k-15k depending on talents and debuffs. FFF doesn't seem to overtake Lacerate till 2 or 3 times that (again, depending on debuffs and talents). I'm not sure I have the stacking correct for the damage multipliers and I am assuming the spell damage debuffs apply to FFF (since it seems to be using the spell crit multiplier). I don't know how much AP we are talking about beyond t11, but it seems like a lot before FFF becomes a threat bonus over Lacerate (though it does do more damage per hit much sooner).

agreed. although another item to consider with filler (especially if you have multiple mobs) is that lacerate has its base threat, damage, and rage cost, but also procs, at 30% per tick, free mangle and allows for the high threat/damage of mangle with no rage cost as well as frees up more rage to dump into maul. If you are spreading the lacerate love around on multiple target you can mangle/maul more often. We will need to run these numbers once Rawr 4 is up.