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# Feral Survivability Maths

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### #1 Maeltne

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Posted 25 November 2008 - 08:27 PM

Hopefully this doesn't get me busted for General Idiocy.

Lets get some definitions/acronyms going:

```[B]ARM[/B]: Your Armor
[B]MSS[/B]: Your chance to be missed

[B]MIT[/B] = .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%
[B]AVD[/B]: DDG+MSS: The % of incoming hits that you will completely avoid.  I.e. 3% miss and 40% dodge = 43% avoidance

[B]EFF[/B] = AVD+MIT(1-AVD). The general efficiency of each HP you have.
[B]TTL [/B]= 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...

### #2 Maranora

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Posted 26 November 2008 - 07:47 AM

```[B]MSS[/B]: Your chance to be missed

[B]MIT[/B] = .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%
[B]AVD[/B]: DDG+MSS: The % of incoming hits that you will completely avoid.  I.e. 3% miss and 40% dodge = 43% avoidance

[B]EFF[/B] = AVD+MIT(1-AVD). The general efficiency of each HP you have.
[B]TTL [/B]= HP/EFF.  The average amount of physical damage you can survive without a heal.
```

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)

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).

### #3 Grubsnik

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Posted 26 November 2008 - 02:30 PM

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.

### #4 Maeltne

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Posted 26 November 2008 - 04:19 PM

... or TTL = HP / (1-EFF)... or something like that

This is correct, fixed.

### #5 swiftly

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Posted 01 December 2008 - 05:35 AM

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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Posted 01 December 2008 - 08:20 AM

PotP has nothing to do with the 75% armor cap, it's your latter example, aka Damage after armor * 0.88 = damage taken.

### #7 charriu

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Posted 01 December 2008 - 08:21 AM

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

PotP is after DR from armor (your 2nd example).

### #8 Oiysters

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Posted 01 December 2008 - 10:38 PM

Is the mitigation from PotP included in the mitigation figure in the character sheet?

### #9 kalbear

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Posted 01 December 2008 - 10:48 PM

Is the mitigation from PotP included in the mitigation figure in the character sheet?

No.

And the character sheet is basing its mitigation on a lvl 80 mob, not a lvl 83.

### #10 Guest_Acearan_*

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Posted 02 December 2008 - 03:00 PM

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

Some one correct me if im wrong but the 12% from PotP isn't additive.

### #11 Maeltne

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Posted 02 December 2008 - 04:29 PM

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%

### #12 mesullivan

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Posted 03 December 2008 - 08:01 PM

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...

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.

### #13 Balroth

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Posted 03 December 2008 - 09:08 PM

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.

### #14 Raqtor

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Posted 05 December 2008 - 11:06 PM

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.

### #15 kalbear

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Posted 05 December 2008 - 11:12 PM

And many of those sockets will be used to reach the hit rating and expertise rating needed.

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.

### #16 Silverstorm

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Posted 06 December 2008 - 01:49 AM

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.

### #17 effekt125

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Posted 06 December 2008 - 01:53 AM

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

### #18 Balroth

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Posted 06 December 2008 - 03:53 AM

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

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.

### #19 effekt125

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Posted 06 December 2008 - 04:34 AM

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

### #20 Balroth

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Posted 06 December 2008 - 10:01 AM

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

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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