Part 1: Mitigation
Mitigation is whatever reduces the amount of damage you receive from an enemy over a period of time. One thing to note about mitigation is that different types do not truly stack on top of each other; each type of mitigation actually reduces the impact of the next.
I will cover them in the order they actually mitigate damage.
Recharge
-Recharge slows down the recharge speed of enemies attacks effectively reducing the amount of hits you can suffer in any period of time. Recharge suffers of three disadvantages:
<ul type="square">[*]The first wave of hits (the so famous Alpha Strike) is unaffected by it, as all attacks there are already charged up the moment you jump the enemy.
[*]As a debuff, it gets resisted by higher level enemies so it is of lower impact against higher level enemies.
[*]Although it increases the recharge time of an attack, it does not increase the activation time. This means that an attack that takes 2 seconds to hit, and 4 seconds to recharge will only have the 4 seconds increased, not the full 6 seconds, making the benefit a bit more random, yet most attacks have a recharge that is much longer than the animation time making this not extreme.[/list]
The formula to calculate the mitigated damage by this is:
RechargeBenefit = 1-1/(1+Debuff)
ToHit Debuffs and Defense
Defense increases your chance to entirely deflect or avoid an attack.
ToHit Debuffs lowers the chance of the enemy hitting you.
ToHit Debuffs and Defense both act together but they dont stack. Against unbuffed enemies this
does not truly makes a difference and its as if they did stack. Since I7 they affect all enemies equally and 10 Defense really means 20%, since it will give the enemy 20% less chance to hit than normal, I wont get on the reason for this here, all you have to know is 1 = 2 once it comes to defense and ToHit debuffs.
Defense is not entirely reliable, not because it does not work, it does, but because you never know at what point your luck will run out. Its one of the few things in this game that is truthfully random.
The main differences between ToHit debuffs and Defense are:
<ul type="square">[*]ToHit Debuffs being debuff are less effective against higher level enemies[*]ToHit Debuffs affect all of the affected enemies' attacks while Def usually only help against specific types of damage or method of attack.[/list]
As noted on the introduction, this type of protection only works on the attacks that did go through the slow effects of Recharge.
Formula to calculate the mitigated damage by this is:
DefenseBenefit = (ToHitDebuff + Def) * 2 * (1- RechargeBenefit)
Damage Debuffs
Damage debuffs are rather simple: They reduce the damage an enemy can do by a percentage. If an enemy can do 100 and you debuffed his damage by 10% he will now hit for 90.
As all debuffs, this protection suffers a penalty the higher level the enemy is compared to you.
A second disadvantage is that an enemy that is resistant against a type of damage, will also resist that aspect of damage debuff. For example, if you fight a Hellion that is strong against fire, his offensive fire damage will not be lowered as much as his other attacks.
Formula to calculate the mitigated damage by this is:
DmgDebuffBenefit = DmgDebuff * (1-(DefenseBenefit +RechargeBenefit))
Resistance
Very similar to Damage, Resistance lowers the damage an enemy inflicts upon you. The difference is, it is lowering the already lower damage. So, using the above example, if the character has 10% resistance and is already doing 90 damage (since it went down on the example above,) he will now do 81 damage. As you can see, despite them doing the same thing, we cant just sum the two numbers.
A disadvantage of Resistance is that it tends to only cover up certain damage types, while Damage Debuff lowers all incoming attacks.
Formula to calculate the mitigated damage by this is:
ResistBenefit = Resist * (1- (DmgDebuffBenefit + DefenseBenefit +RechargeBenefit))
HP buffs
To understand the true benefit of HP you have to entirely forget about it as a number that changes with level and start to think about it in terms of percentages. All that truly matters is that the little progress bar that indicates health doesnt go from 100% to 0%. Under this logic, having your hp doubled is as good as having a 50% mitigation, as an attack that takes exactly all your health will end doing just 50% of your health. Calculating the mitigation provided by HP buffs however is hard because its just not linear, even if the cap was high enough and there were enough sources to get them, it would take a lot of work to get 90% mitigation purely out of HP buffs. If you are curious, it takes a 900% hp buff to get the 90% mitigation mark.
The biggest advantage of HP buffs is its universal nature, not even un-typed damage can get around HP buffs.
The disadvantage? The mitigation applies not only to damage but also to self heals and outside heals.
The formula for this is:
HPBenefit = (1-1/(1+HPBuff)) * (1- (DmgDebuffBenefit + DefenseBenefit + RechargeBenefit + ResistBenefit))
Add it up all up:
Now that all has been accounted for we want to see our total mitigation. This simply means summing it all up:
Mitigation = DmgDebuffBenefit + DefenseBenefit + RechargeBenefit + ResistBenefit + HPBenefit
Part 2: Healing
For an enemy or group of enemies to kill you within a limited amount of time, he must do your entire HP worth of damage plus the entire HP that you can regenerate within the amount of time.
Example, if a hero has 100 points of hp, and he regenerates at the standard regeneration rate of 25% of his hp in a minute, and the enemy must be able to kill the hero in exactly one minute, he must do 125 points of damage during that time, or in other words, about 2.084 points of damage per second.
That is the reason why a long fight favors a build that is based on healing, because you have more HP that must be removed to successfully kill you. And that is the same reason too that alpha strikes almost ignore regeneration and self heals, the damage per second of such a wave of attacks is so high that you never get the chance to heal up. This is the why you got to keep time into the formula, because I bet in house, the devs actually balance all enemies around how long they should take to kill X or Y build.
While talking about self-preservation healing means just two things: self heals and regeneration.
Regeneration
Regeneration is simple; its a multiplication of your base regeneration factor. We regenerate at 5% every 12 seconds, having 100% regeneration rate means we cut those 12 seconds to 6.
We calculate our regeneration per second like this:
Regeneration = 0.05*(1+Regen/12)
Self Heals
First off all self heals must be calculated to acquire how much healing per second they can provide, then we sum all those self heals together (in the case of more than one)
To calculate the Heal Per Second of a power use this formula:
HPS = PercentageHealed / (Recharge + Activation )
Once you got the HPS of all your attacks summed up you have to apply the resistance to healing you acquired from any HP buffs:
FinalHPS = HPS * (1-1/(1+HPBuff))
Add it up all up:
To get our final maximum recovery per second we just sum them all.
HPRecovery = Regeneration + FinalHPS
Part 3: Adding them up
Now that we know how much mitigation we have, and how much health we can heal back per second, how do these affect me together?
There is one rule: an enemy must inflict upon you the amount of not mitigated damage * your healing per second divided by the time available to kill you.
Mathematically:
D = 1 Mitigation * HPRecovery / Time
Where D is the amount of damage per second needed to kill you in a given amount of time.
Part 4: Cross AT comparisons
We now know how much percentage of your health must be inflicted per second to kill you, but how can you compare how much more survivable are you than a tanker? Or how much more survivable is a specific tanker than a brute?
To compare your set against another you first have to equalize the health difference. You do this by multiplying the result of your whole formula by the appropriate value.
You can use this table:
<font class="small">Code:[/color]<hr /><pre>Tanker 1.0000
Brute 0.8000
Scrapper 0.7143
Blaster 0.6429
Kheldian 0.5714
Corruptor 0.5714
Controller 0.5714
Defender 0.5429
Stalker 0.5429
Dominator 0.5429
Mastermind 0.4286</pre><hr />
Once you equalize the value now you want to get a relative score. To do this you need to do this you run the entire formula but with zero buffs. In short the true formula is always:
D * HPM / (1+0.05/12*Seconds) / Seconds)
Where H is your ATs HP modifier according to the chart mentioned before.
This score will tell you how much better are you at surviving the specific damage type than a naked, unbuffed tanker.
Circeus helped me with the easiest way to describe this value:
If someone has a rating vs. a damage type of 15 it takes 15 times more damage of that type to bring down the character than a Pure-Meatbag (no powers) Tanker.
1.0 would mean you just got as good as a naked tanker.
0.8 means you are a naked brute.
For reliable tanking against only the specific type of damage you should get to the 9.0 to 10 mark, in my opinion.
15 is enough to tank for an average 8 man group without constant babysitting by a defender.
Anything under 7 should have trouble even tanking for 4 man teams without a babysitting on the part of a defender-type.
your witchcraft is too dangerous to use GOD hates the darkarts
good guide! 
[ QUOTE ]
Part 3: Adding them up
Now that we know how much mitigation we have, and how much health we can heal back per second, how do these affect me together?
There is one rule: an enemy must inflict upon you the amount of not mitigated damage * your healing per second divided by the time available to kill you.
Mathematically:
D = 1 &#8211; Mitigation * HPRecovery / Time
Where D is the amount of damage per second needed to kill you in a given amount of time.
[/ QUOTE ]
Because you do things a lot differently, I might be misinterpreting, but I think this is wrong. I think you meant to write something like:
D * (1 - M) = HPRecovery
This is steady state.
And to kill:
D * (1 - M) * time = HPRecovery * time + 1
ergo:
D = (HPRecovery * time + 1) / (1 - M) / time
or
D = (HPRecovery + 1/time) / (1 - M)
The units don't work out in the version you posted, which tipped me off to a problem. But perhaps somewhere in your calculations the units get scrambled. I'm not 100% sure.
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Darnit I cant edit this now...
The formula (as it is on my MS Word document) is be this:
(1+(HPRecovery*Time)) /Time/(1-Mitigation)
I dont know what part in the process of posting I ended copy/pasting the wrong formula there...
I actually like that last one you posted better, its more simplified than mine.
Could you explain how you came to your formula for relative survivability and how it relates to tanking capacity?
I'm unable to comprehend conceptually how you arrived at this formula.
At part 3 you end up with what many call the immortality line, this is how much % of your hp must be output in dps for you to die in that amount of time.
To compare ATs i do three things:
Step 1
Is to equate hp bars. The if the above holds true for a tanker, it cant hold true for a brute even if he had the same amount of mitigation, because their HP bar is different, for this I "weaken" it by multiplying it by the base HP. in the case of a brute that would mean multiplying it by .8
Step 2:
Run everything again with zero mitigation. No resist, no defense, no nothing. Once you get the result you will have in your hands how much a tanker that is naked can survive.
On my Part 4 post, (1+0.05/12*Seconds) / Seconds) is simply the shortened version of calculating a naked tanker without any sort of mitigation.
Step 3
Dividing the first number by the second will yield you the survivability score.
[ QUOTE ]
At part 3 you end up with what many call the immortality line, this is how much % of your hp must be output in dps for you to die in that amount of time.
[/ QUOTE ]
Actually, I coined the term "immortality line" back in I4 to represent the maximum average sustainable amount of damage that could be sustained indefinitely. I.e. M * DamagePerSecond = HealthRegenPerSecond. I called the maximum damage value that could be withstood for a specific period of time the "survivability line" for that time period.
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Ah well, then i got to find a diferent nitche name for Step 3, or i can call it perpetually Step3! 
I used the term "appreciable damage" for net damage sustained over time back when invul tankers didn't actually accumulate damage faster than their base regen, hence it didn't "appreciate".
Not many people liked that term save Invul and Regen.
Ahh... now I see where you compensate for the armors... sorry. I'm sleep deprived.
Now for the kicker... doesn't mez have a LOT to do with survivability of melee classes (Burn, Cloak of Fear, Oppressive Gloom) or is the variability on that mean you didn't want to include it else it would disrupt the precision?
Crowd control (mez effects and the such) "are beyond the scope of this guide"
Reason are a few:
1) Its hard to quantify
2) It actually would require me to get into the full Controller/Dominator balance world, and thats a huge segment of the game on itself.
3) The only set that actually uses many of these status effect on their defensive set is Dark Armor, and they are very expensive on endurance (or even drain your own health), so i decided not to dedicate much time to them YET. As for burn "panic" effect, I call it more a penalty than a tool.
Someday i may get deep into this, but not until Im done with pure front assault survival AND then defenders (Im not much into them but how balanced is their influence on other ATs survival is vital to know)
Introduction:
There are 3 things that stand between death and you.
1) Crowd Control
2) Mitigation
3) Healing
Each of these are sub divided in different methods
Crowd Control
1) Hold
2) Sleep
3) Immobilization
4) Knock back/Vomit
5) Fear
6) Confusion
Mitigation
1) Self Buffs
--a. Resistance
--b. Defense
--c. HP Buffs
2) Enemy Debuffs
--a. Damage Debuff
--b. Accuracy Debuff
--c. Recharge Debuffs
Healing:
1)Regeneration
2)Self Heals
3)External Heals
In this guide I will discuss self-preservation of the melee sets. This means I wont be touching Crowd Control.