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Cataclysm Bear Theorycraft

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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)

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

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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 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

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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 :)

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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.

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# Savage Defense is massively overpowered on beta and has been dealt with accordingly. Many of the reports of beta raid bosses two-shotting tanks were because that was how much damage the bosses needed to do in order to challenge Feral tanks. With less damage absorbed, the boss damage can be adjusted downwards. We've reduced the multiplier for attack power on the absorption effect (from 65% to 35%, still modified by mastery) and it no longer procs from periodic critical hits.

Confirmed this is active in beta. I'm trying to confirm scaling with mastery on gear is unaffected, I'll update when I find out if no one else beats me to it.

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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.

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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.

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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:

[table]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[/table]

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:

[table] |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[/table]

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:

[table]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 |[/table]

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:

[table]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[/table]

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:

[table] | | | | | | | | | 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[/table]

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.

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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:

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).

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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.
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.

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