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11/25/08, 4:27 PM
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#1
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Piston Honda
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Feral Survivability Maths
Hopefully this doesn't get me busted for General Idiocy.
Lets get some definitions/acronyms going:
ARM: Your Armor
HP: Your total hit points
MSS: Your chance to be missed
DDG: Your chance to dodge
MIT = .12 + (.88)(ARM)/(ARM+16635): The amount of damage that you will mitigate off of any standard physical hit against a lvl83 boss mob, assuming 3/3 PotP. I.e. 30894 armor -> 65% mitigation from armor + 12% PotP = 69.2%
AVD: DDG+MSS: The % of incoming hits that you will completely avoid. I.e. 3% miss and 40% dodge = 43% avoidance
EFF = AVD+MIT(1-AVD). The general efficiency of each HP you have.
TTL = HP/(1-EFF). The average amount of physical damage you can survive without a heal.
Some history
Pre WotLK/3.0 armor had diminishing returns on armor->MIT, which lead to linear returns on armor->TTL, while AVD had linear returns on agi/defense/dodge->AVD which lead to exponential'ish returns on agi/defense/dodge->TTL. Thus it was demonstratable that the correct method to maximize TTL was to stack AVD. However in practice many had a HP threshold that they determined was sufficient for a given boss, after which they stacked AVD.
WotLK/3.0 has introduced diminishing returns on agility/defense/dodge->AVD such that agility/defense/dodge->TTL is linear much the same as armor->TTL had been linear for some time. This has lead to HP/raw stamina being the king statistic for maximizing TTL.
Current Thoughts
Is TTL the correct statistic to optimize?
Some would answer yes, many would answer no. Correct me if I'm wrong but those who answer no would point to EFF as that statistic to optimize, once a proper threshold has been reached. And it would be the one that I would pick also if I were in a model where I was spending all my time between 1%-99% health. But the truth is that we spend a great amount of time at 100%, and a large amount of healing is lost as overheal.
How to model/account for this?
Napkin Math
Assumptions
30k unmitigated physical damage every 2.5s
Healed to full every 5s
Model Avoidance as Mitigation (i.e. 70% MIT and 40% AVD = .82 MIT)
Base Tank
30k HP
70% MIT
40% AVD
Option A: +1k HP
Option B: +1% AVD
Every 2.5+5x seconds tank A/B takes 5400/5310 damage and is 11.85/11.62 seconds from death.
Every 5+5x seconds tank A/B takes 5400/5310 damage, is healed to full, and is 14.35/14.12 seconds from death.
Every 5s Tank A requires 180 more healing, however whenever healed to full gains 1000 HP over tank B. If the tanks are healed to full over 5s for a 5min fight, Tank A requires 180*60=10,800 more healing than Tank B but gains 60,000 HP that Tank B lost due to overheal.
At every point it appears as if Option A is the better choice. At this gear level/DR is 1k HP a valid comparison to 1% AVD? The model is very rough...
Last edited by Maeltne : 11/26/08 at 12:24 PM.
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11/26/08, 3:47 AM
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#2
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Glass Joe
Night Elf Druid
Die Nachtwache (EU)
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Originally Posted by Maeltne
MSS: Your chance to be missed
DDG: Your chance to dodge
MIT = .12 + (.88)(ARM)/(ARM+16635): The amount of damage that you will mitigate off of any standard physical hit against a lvl83 boss mob, assuming 3/3 PotP. I.e. 30894 armor -> 65% mitigation from armor + 12% PotP = 69.2%
AVD: DDG+MSS: The % of incoming hits that you will completely avoid. I.e. 3% miss and 40% dodge = 43% avoidance
EFF = AVD+MIT(1-AVD). The general efficiency of each HP you have.
TTL = HP/EFF. The average amount of physical damage you can survive without a heal.
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According to these formulae, as avoidance and/or mitigation approach 100%, Eff approaches 100%, and TTL thus approaches HP (from ABOVE)... I assume either you want EFF = 1 - (AVD + MIT(1-AVD)) or TTL = HP / (1-EFF)... or something like that  (The latter seems nicer to me, since it means bigger EFF is good, and leads to bigger TTL)...
Or am I misunderstanding something?
Current Thoughts
Is TTL the correct statistic to optimize?
...
Model Avoidance as Mitigation (i.e. 70% MIT and 40% AVD = .82 MIT)
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This seems a little iffy to me... The problem with avoidance is, of course, that it's not entirely reliable (unless it's at 0 or 100% of course); if you're taking a lot of "small" hits, then modelling avoidance as mitigation is close enough to accurate, but in boss fights you're more likely to be taking (relatively) few really BIG hits, and that's where even a short chain of avoidance "misses" can lead to the nice tank being an ugly red smear...
So in paticular for fights where you're taking big hits, mitigation's reliability makes 1% mitigation seem to me to be more valuable than 1% avoidance... But generating actual numbers for this seems hard to impossible, and surely depends on the boss fight in question (and, as you make clear, the total hit point pool becomes very important). Perhaps the value of 1% avoidance needs to be modelled by taking the ratio between the typical (or maximum?) incoming hit (AFTER mitigation) vs the total hit point pool as an additional parameter?
EDIT: To actually answer your question a little more directly: My impression is, all other things being equal in a sufficiently large statistical period, I'd take mitigation before hit points (same effect but less burden on the healers), and hit points before avoidance (reliability).
Last edited by Maranora : 11/26/08 at 4:14 AM.
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11/26/08, 10:30 AM
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#3
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Piston Honda
Troll Mage
The Venture Co (EU)
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Basically you can work with 2 derived stats:
Worst case TTL
Worst case TTL is calculated purely from your hp and mitigation. For a worst case scenario, anything less than 100% avoidance is useless, it will happen eventually.
The main goal is to survive a classic autoattack+specialmove+double-parryhasted autoattack combo. If the boss has silencing mechanics or other mean tricks, these also factor in. If you are below that threshold, you will find your tank getting insta-gibbed.
Damage reduction
The product of mitigation and avoidance. For Damage reduction, there are 2 goals.
First goal is the make sure that Boss dps < tank incoming HPS. No matter how much HP your tank has, if the boss is hurting him faster than you can heal him, even over a long timeperiod, your tank will die.
Second goal is to make sure the healers have enough mana to last the entire bossfight. The tricky part here is that the length of a fight is determined by the dps.
Stats:
Armor: Works in both cases.
HP: Works primarily for TTL, but higher hp pools also result in less overhealing, which does influence the second goal of Damage reduction, though the more you get, the less useful it becomes.
Dodge: Only serves as a damage reducer. However some bosses feature stacking effects (like a stacking healing taken debuff), where it's essential to not let it build up too much. Only dodge or other forms of avoidance helps you out there.
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11/26/08, 12:19 PM
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#4
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Piston Honda
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Originally Posted by Maranora
... or TTL = HP / (1-EFF)... or something like that 
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This is correct, fixed.
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12/01/08, 1:35 AM
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#5
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Glass Joe
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anyone know the formula for Damage Reduction with Protector of the Pack and the up coming changes to armor like Survival of the Fittest?
i cant seem to find if Proector of the Pack reduces the damage after the damage reduction contributed from armor is factored or if it is part of the 75% damage reduction.
75% - 12% from PotP = 63% new damage reduction cap
OR
75% of XXXXX damage is XXXXX then this is where the 12% from PotP kicks in
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12/01/08, 4:20 AM
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#6
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Meow
Abradix
Tauren Druid
No WoW Account (EU)
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PotP has nothing to do with the 75% armor cap, it's your latter example, aka Damage after armor * 0.88 = damage taken.
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12/01/08, 4:21 AM
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#7
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Piston Honda
Night Elf Druid
Die Todeskrallen (EU)
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Originally Posted by swiftly
anyone know the formula for Damage Reduction with Protector of the Pack and the up coming changes to armor like Survival of the Fittest?
i cant seem to find if Proector of the Pack reduces the damage after the damage reduction contributed from armor is factored or if it is part of the 75% damage reduction.
75% - 12% from PotP = 63% new damage reduction cap
OR
75% of XXXXX damage is XXXXX then this is where the 12% from PotP kicks in
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PotP is after DR from armor (your 2nd example).
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12/01/08, 6:38 PM
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#8
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Von Kaiser
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Is the mitigation from PotP included in the mitigation figure in the character sheet?
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12/01/08, 6:48 PM
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#9
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Great Tiger
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Is the mitigation from PotP included in the mitigation figure in the character sheet?
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No.
And the character sheet is basing its mitigation on a lvl 80 mob, not a lvl 83.
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12/02/08, 11:00 AM
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#10
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Glass Joe
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Originally Posted by swiftly
anyone know the formula for Damage Reduction with Protector of the Pack and the up coming changes to armor like Survival of the Fittest?
i cant seem to find if Proector of the Pack reduces the damage after the damage reduction contributed from armor is factored or if it is part of the 75% damage reduction.
75% - 12% from PotP = 63% new damage reduction cap
OR
75% of XXXXX damage is XXXXX then this is where the 12% from PotP kicks in
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Some one correct me if im wrong but the 12% from PotP isn't additive.
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"Druids, they are so stupid they can tank better than warriors, out damage rogues, and nuke as well as mages. On top of that they can turn into a mutated seal."
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12/02/08, 12:29 PM
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#11
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Piston Honda
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The mitigation you get from armor + PotP is clearly defined in the OP.
MIT = .12 + (.88)(ARM)/(ARM+16635): The amount of damage that you will mitigate off of any standard physical hit against a lvl83 boss mob, assuming 3/3 PotP. I.e. 30894 armor -> 65% mitigation from armor + 12% PotP = 69.2%
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12/03/08, 4:01 PM
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#12
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Von Kaiser
Night Elf Druid
The Forgotten Coast
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Originally Posted by Maeltne
Every 5s Tank A requires 180 more healing, however whenever healed to full gains 1000 HP over tank B. If the tanks are healed to full over 5s for a 5min fight, Tank A requires 180*60=10,800 more healing than Tank B but gains 60,000 HP that Tank B lost due to overheal.
At every point it appears as if Option A is the better choice. At this gear level/DR is 1k HP a valid comparison to 1% AVD? The model is very rough...
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It looks as if, at this level of gear 1% AVD requires about the same number of item points as 1k HP. AVD+MIT equivalent of 1% AVD in expected TTL at this level of gear requires 37.17 agi, while 1k hp requires 57.1 sta, which is equivalent to 38.1 agi in terms of item budget. So you are skewed slightly toward stam, but it's very close.
The big problem I see with your analysis is that you assume that in healing tank A to full, healers will always overheal by at least a full 1000 hp. Is that an accurate assumption? I would guess that there would be many situations in which tank A would be overhealed by something less than 1000hp in which case tank B requires another heal, which might result in *more* rather than less overheal. Realistically, healers are going to put out the healing required to make tanks full, no matter their hit points and will try to minimize overhealing to the extent they can do so safely. A bigger HP pool makes overhealing easier to judge, but I don't think it's anything like this big a difference. I'd guess that healer's efficiency is linear in total HP. The %overheal saved from having a bigger pool is probably similar to the %HP gain.
So the +1k HP is 3.33% to the HP pool, which means overheal will go down at most 3.33%. Overhealing is typically around 25-30% of healing, so the efficiency gain is going to be somewhere around 1%, but 1% avoidance in this scenario is actually a 1.67% efficiency gain. So the 1k HP is worth about 60% as much as the 1% avoidance to the healers (assuming you are far enough past worst case TTL that healers care mostly about efficiency).
That's actually a fairly significant portion. I've been thinking in terms of stam giving no gain to healer efficiency, but as you say here, that's really not right (although I think your model is overstating things dramatically). As such, the point where you stop stacking stam is probably a bit higher than I might otherwise have thought.
But it does not appear to me that we will stack stam always and forever, only as long as TTL is still worth something to us, in fact, only as long as it's still about 1/2 as important as total healer efficiency.
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12/03/08, 5:08 PM
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#13
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Glass Joe
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Okay, so I'm trying to learn all this stuff but it seems like a lot of theory and not a lot of game application. For example, we've talked a lot about Worst Case TTL but what exactly, with the current raids, is a Druids HP/Mit goal here? It seems that Armor>HP so let's just kinda forget about it and assume that we're going to take it when we can get it anyway. How much HP do we want before we say we have enough and we want to start stacking more dodge? I'm at 32k unbuffed and it makes bosses like Maexxna and Patchwerk a breeze but am I causing my healers more trouble than they should have by sacrificing a few % of dodge to get there?
Also, let's say I'm consistently running with the same healers and they don't have problems with mana is this something to think about? It seems that if this is the case, I can then not worry as much about EFF and instead focus on the worst case TTL. Granted, at some point in progression problems will probably arise but I could gear differently for different runs. For example, focus on EFF for a 25 man run and just worry about an effective worst case TTL for a 10 man where the healing is easier. If I'm misunderstanding something please let me know, I'm not a pro theorycrafter just yet.
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12/05/08, 7:06 PM
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#14
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Glass Joe
Tauren Druid
Kor'gall (EU)
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From my experience raiding in patch 3.0.3 is that stamina is the way to go.
Last raid I had around 44k health raid buffed and 85% damage reduction against a level 83 boss. With that amount of health healers know that they do not need to heal me to full. However I also feel that 44k is a bit much.
But who are we kidding? It is not like there are many choices in gear for tanking druids. Its all basically the same. All we can choose is what gems to put in the gear. And many of those sockets will be used to reach the hit rating and expertise rating needed.
Avoidance does not speak very well for your survivability. Even with very high avoidance you can be unlucky and get hit 5 times in a row. It is a nice way to save some healing mana but your first priority should be to survive the encounter.
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12/05/08, 7:12 PM
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#15
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Great Tiger
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And many of those sockets will be used to reach the hit rating and expertise rating needed.
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What hit and expertise rating is needed for tanking? I'm not asking what the specific numbers are to reach the caps; I know those. I'm saying why does a feral need hit rating? Why do you need to cap expertise? Threat is so not an issue it's not funny.
As to avoidance - yes, you can be unlucky and get hit multiple times despite having high avoidance. But when you can be hit 5 times in a row and still have 10k health, chances are you don't need that much health.
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12/05/08, 9:49 PM
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#16
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Piston Honda
Night Elf Druid
Azjol-Nerub
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I don't know how important I'd consider hit/expertise, but I want at least two things:
1) Initial pickup and threat move as guaranteed to land as possible
2) Multi-mob tanking pickup (a la M'uru) to be as painless as possible.
Obviously, the amount of hit/expertise desired may vary on those fights, but those are the things I'd be concerned about.
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12/05/08, 9:53 PM
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#17
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Glass Joe
Tauren Druid
The Venture Co
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threat output stands out on 25man patchwerk.. i felt that expertise/hit is very necessary for threat output to keep up with pally and warrior
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12/05/08, 11:53 PM
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#18
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Glass Joe
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Originally Posted by effekt125
threat output stands out on 25man patchwerk.. i felt that expertise/hit is very necessary for threat output to keep up with pally and warrior
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I'm not so sure I agree. With a Warrior MT on Patchwerk and me main OT I was hit with Salvation so that I could keep DPSing and not pull aggro. I had to stop using Lacerate and even literally sit there just meleeing him because my threat was so high. The warrior and I were so high above all the DPS as well it was ridiculous. We could have AFK'd half way through the fight and I'm confident no one would have pulled off us. And I haven't gemmed for hit or expertise at all. All I have is what's on my gear. I would say that expertise is nice for the parry protection but really, is hit necessary? The only trouble I have with threat is in 5 mans when the DPS are literally going all out. Otherwise, I've never seen problems.
I don't know what your DPS'rs are doing for damage but we probably average 3k with our top 5 or so guys doing 3500+. At least, I'm pretty sure. Some of them might be a little higher.
Last edited by Balroth : 12/06/08 at 12:10 AM.
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12/06/08, 12:34 AM
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#19
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Glass Joe
Tauren Druid
The Venture Co
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i dont know what type of gear you guys have but..
in 25man u use 3 tanks and its not that i cant outhreat the dps beccause i can. i have hatefuls along with a warrior and we push threat to stay in the top 3 behind the prot pally tanking him. i generally have to use berserk at the beginning to keep up with them at the start.
3k dps isnt that crazy, we have people pushing 5k dps. but my point is that other tanks can put out much more tps than we do. the dps dont even come close as the fight goes on, but the fact that the others putting out so much more tps made me realize how important expertise/hit can be, in terms of putting out tps
though as things currently are, a dps cant DREAM of pulling agro off anything. i simple dont want to even see a POSSIBILITY of me falling too far behind the other 2 tanks on patchwerk
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12/06/08, 6:01 AM
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#20
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Glass Joe
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Originally Posted by effekt125
i dont know what type of gear you guys have but..
in 25man u use 3 tanks and its not that i cant outhreat the dps beccause i can. i have hatefuls along with a warrior and we push threat to stay in the top 3 behind the prot pally tanking him. i generally have to use berserk at the beginning to keep up with them at the start.
3k dps isnt that crazy, we have people pushing 5k dps. but my point is that other tanks can put out much more tps than we do. the dps dont even come close as the fight goes on, but the fact that the others putting out so much more tps made me realize how important expertise/hit can be, in terms of putting out tps
though as things currently are, a dps cant DREAM of pulling agro off anything. i simple dont want to even see a POSSIBILITY of me falling too far behind the other 2 tanks on patchwerk
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We did the same set up this week. I did see the pally have quite a bit of threat as MT but I really didn't have trouble keeping up even with the Hunter MDing to him. Warrior was way behind on threat. My gear isn't spectacular. Good enough to MT Naxx 25. Don't look at armory, it's a ghetto mess, I'm not sure what I was on before I logged off. I think I have like, 21 hit and 35 expertise in my tanking gear. I'm not really sure if that's high or low but I have never had problems keeping up with other tanks. When we do Loatheb we try to keep all the tanks at the top of threat and I haven't seen any problems there either.
Basically, I would say that in my experience, DKs have the worst threat generation, then Warriors, then I'm not sure between Druids and Paladins because I only see them in Naxx really where they can push more threat than usual because of the Undead.
It is possible that you have far better geared tanks than my guild has. Or at least, ones with more +hit but honestly, from talking to other tanks as well, everyone seems to think that threat generation is a joke now and I have not talked to anyone that's considering losing survivability stats for increased TPS.
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12/06/08, 3:06 PM
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#21
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Soda Popinski
Night Elf Druid
Frostmourne
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Originally Posted by Raqtor
85% damage reduction against a level 83 boss.
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Avoidance does not speak very well for your survivability. Even with very high avoidance you can be unlucky and get hit 5 times in a row. It is a nice way to save some healing mana but your first priority should be to survive the encounter.
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You said yourself you felt you had too much hp. Nothing in Naxxramas and Malygos honestly needs a pool bigger than 35-38k raid buffed. Past that, the less healing you require on average the more leeway you have for, say, pushing more DPS into the raid.
To illustrate the point, I've got a gearset that puts me at 50.3k raid buffed for a very very specific tanking role. (Which isn't much, someone has 54k for the same encounter) I wouldn't be caught dead using it for anything other than that. My avoidance is ass, my threat is worse, and when you're trying to do stuff like push DPS (i.e. TPS) or shave off the number of healers, the stam buffer which never, ever gets utilized is pretty much a waste of item budget.
Yes, stam scales a little too well at the moment due to the 1.5 base bear multiplier, At this point in the expansion however it's literally the embodiment too much of a good thing.
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#elitistjerks
<^clicker> nice job trying to troll but you're a fucking idiot because i wasn't responding to you
<^clicker> this is the channel for serious discussion of important world of warcraft issues i believe youre looking for /b/ get lost scrub
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<^clicker> do you act like this all the time
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12/07/08, 6:40 AM
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#22
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Piston Honda
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Maybe the DPSers in your guilds just aren't well versed in the new rotations for max DPS, but I can tell you from experience that several of the DPS in my guild are really starting to have threat issues. Our top Mage, especially, has to get several Hand of Salvs on certain fights because he's catching up to our MT (both of whom are in very nearly full 25-man gear). And you also have to consider certain gimmick fights like Malygos, where the DPS can get a huge boost in damage in a double-spark bloodlusted burn, and your tank doesn't get anything except Tricks and MDs.
Also, I may be wrong because I didn't do naxx at 60, but don't Patchwerk's melee hits (and hatefuls) give bonus threat to their victims? That's why you see your tanks so far ahead of the DPS on that fight, I'd imagine. There's a significantly smaller gap between tank and DPS threat values on every other fight these days, from my experience.
TL;DR version: Threat is most certainly not a non-issue like it was at 70 post 3.0, so hit and expertise are quite valuable tanking stats.
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12/07/08, 6:58 AM
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#23
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Soda Popinski
Night Elf Druid
Frostmourne
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Don't forget good old 'DPS' stats in addition to hit/expertise.  With the removal of bonus armor there are a lot more ways to gear now, and if you're not dying, you'll want to push your TPS, and to a lesser extent, tank DPS.
Also yes, Patchwerk does give bonus threat, so it's not an ideal gauge for TPS rotations.
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#elitistjerks
<^clicker> nice job trying to troll but you're a fucking idiot because i wasn't responding to you
<^clicker> this is the channel for serious discussion of important world of warcraft issues i believe youre looking for /b/ get lost scrub
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<^clicker> do you act like this all the time
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12/08/08, 12:54 PM
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#24
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Glass Joe
Tauren Druid
Kor'gall (EU)
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Originally Posted by kalbear
What hit and expertise rating is needed for tanking? I'm not asking what the specific numbers are to reach the caps; I know those. I'm saying why does a feral need hit rating? Why do you need to cap expertise? Threat is so not an issue it's not funny.
As to avoidance - yes, you can be unlucky and get hit multiple times despite having high avoidance. But when you can be hit 5 times in a row and still have 10k health, chances are you don't need that much health.
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You do need enough so that your growl does work every time in the tank rotation. I do not know how much is actually needed but I can tell you what I was told. My fellow tank tells me that Taunt/Growl has less chance of not working than other physical attacks and therefore it is plenty with 5% against a level 83/boss.
Originally Posted by Falk
You said yourself you felt you had too much hp. Nothing in Naxxramas and Malygos honestly needs a pool bigger than 35-38k raid buffed. Past that, the less healing you require on average the more leeway you have for, say, pushing more DPS into the raid.
To illustrate the point, I've got a gearset that puts me at 50.3k raid buffed for a very very specific tanking role. (Which isn't much, someone has 54k for the same encounter) I wouldn't be caught dead using it for anything other than that. My avoidance is ass, my threat is worse, and when you're trying to do stuff like push DPS (i.e. TPS) or shave off the number of healers, the stam buffer which never, ever gets utilized is pretty much a waste of item budget.
Yes, stam scales a little too well at the moment due to the 1.5 base bear multiplier, At this point in the expansion however it's literally the embodiment too much of a good thing.
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All true on paper. However in the real world healers over heal quite a lot. Most fights we have over 30% over healing done to the tank. With a health pool of 40k healers do not need to heal you to full health thereby eliminating almost all the over healing. If the gear existed that would allow you to go for avoidance I still don't think it would be more mana effective.
Then there is the true test of a tank, Sartharion+Drakes. The 25% health debuff reduces your 40k to 30k and the double fire damage actually makes death possible.
Yes dodge is delicious and I am working hard to try and improve my 42% dodge. I just feel that it is nice to have a 40k health pool. And I can recommend making sure tanks have the health and armor to survive burst damage before they start going all out avoidance.
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12/08/08, 2:31 PM
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#25
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Glass Joe
Night Elf Druid
Silvermoon
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Originally Posted by Raqtor
You do need enough so that your growl does work every time in the tank rotation. I do not know how much is actually needed but I can tell you what I was told. My fellow tank tells me that Taunt/Growl has less chance of not working than other physical attacks and therefore it is plenty with 5% against a level 83/boss.
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Growl is a spell and has 17% chance to miss against a level 83/boss. Glyph of growl reduces this by 8%, leaving you with 9% to miss with growl. If you add in your 5% chance to hit from hit rating, you still have a 4% chance for Growl to miss.
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