If 2% Resistance equals 1% Defense, How much Regen is equal to 1% Defense ?

Keep in mind we're still talking about a sort of tanker mentality with the damage models. Regen has the weird property of rewarding you with nothing when you are at full health but handsomely for a string of dodges following a hit. This makes evaluating regen precarious.

With defense, your chance to dodge is (usually) not affected by how many of the previous attacks landed, or how long ago that occurred. With Regen, that is the biggest part that matters, since damage usually arrives in bursts rather than a steady stream. The reason this is critical to understand is that outside of models, it is rare to let enemies stand around and beat on you. A character with the power to halt or slow enemy attacks following a dangerous hit reaps more benefit from Regen than one who doesn't do that. And Regen also rewards you for running away, giving you rewards up to the point where you're fully healed, or at least healed enough to re-enter combat.

This isn't usually considered in Defense and Resistance models because its simply viewed as time added to the defeat line, which in those models is always eventually reached. With Regen, the line you're reaching toward could as easily be defeat as it is immortality.

That's the long winded way of saying "trust the model only so far."

There are four key variables in determining survivability in the face of damage: bonus max HP, regen bonus, defence, and resistance. And there is a way of reducing the problem of which to focus on to a very simple equation.

For the sake of argument, let us equate survivability with the average amount of incoming damage you can survive indefinitely. Let:

d = incoming damage per second
hmax = base maximum HP
h = current HP
m = bonus HP (as a percentage, so that max HP = hmax(1 + m))
f = defence as a percentage
r = resistance as a percentage
g = bonus regeneration as a percentage

dh/dt = - (0.50 - f) d (1 - r) + (1 + g)(1 + m) hmax c,

d = c' (1 + g)(1 + m)/( (1 - r)(1 - 2f) )

∂d/∂g = d/(1 + g)
∂d/∂m = d/(1 + m)
∂d/∂r = d/(1 - r)
∂d/∂F = d/(1 - F)

(x ∂d/∂g)/(2y ∂d/∂F) = (1 - F)/(1 + g) x/2y

(1 - F) x ≥ (1 + g) 2y.

My personal opinion, and that is all it is really (an opinion), is that the "Immortality Line" is useless for comparing two powersets. Even the model I like; "gone in 60 seconds" has serious limitations, but is more relevant to in-game circumstances.

The way I understand it goes like this.

You regenerate from zero to full in 240sec, regardless of HPs, so your baseline regeneration is 0.42% Health per sec. If you add 10% HPs to your character, you now regenerate at a rate that is still 0.42%. sec, but as a factor of comparison to the original HP value, you have just upped the regen to 1.10 X 0.42% or 0.462%/sec. Your character sheet will still reflect 0.42/sec, but in order to translate that regen back to your original HP totals it needs a larger value for regen to be accurate in the model.

In much the same way, you can convert +HPs to Resist, Heal to Regen, Resistance to +HP etc....

10% bonus regen becomes 1.10 * base regen, and will change the display of your regeneration in game by 10% so you would see 0.462%/sec. If you have 10% bonus HPs AND 10% bonus regen, your ingame display will still show 0.462%/sec, but that is a % of your new HP total, so to get the comparative value in relation to baseline, I would multiply :

0.42/sec * 1.10 * 1.10 = 0.5082 which is approx = +21% regen or +21%HP

I hope this is correct, at least.

Though inherent health now means that everyone's bonus regen starts at 40% unslotted. From a clean slate then, the first 1% defence is worth 2.8% regen if Health is unslotted, or 3.08% is slotted with a single level 50 IO.

EDIT: Just saw Signpost's reply. Sorry for being late to the party

That is an interesting model. I do want to point out why its not quite as cut and dried as it may seem though.

Models tend to break when very high Defense gets involved. Particularly, very high Defense with low Resistance.

The crux of it is that most damage models treat a chance to take damage a percent of the time as the same as taking the same percent of that damage all the time. For example, treating a 5% chance for 1000 damage as the same as taking 5% of 1000 damage from every attack. If you jump into a pile of enemies, you can more or less average things this way. If you're fighting an AV or GM, you cannot. Roll snake eyes one time and you're dust. This is why a huge "it depends" needs to be attached to all of the models we make conflating Defense chances with flat survivability time.

Now, the problem of Regen with high Defense and low Resistance fighting an AV is particularly intriguing. In this situation, you may not end up taking any damage at all for several minutes into the fight, in which case Regen isn't actually contributing. Then, when you get popped, how much Regen contributes depends on whether the next hit happens before you fully heal. If you ever do fully heal, Regen stops contributing again.

Here's where it gets really weird. If you're soft capped but there's a chance the AV could possibly two-shot you, you've hit a point where Resistance becomes unhinged from its standard value. Increasing Resistance to the point where it now takes 3 or 4 back to back hits to kill you could become more important than it normally would, because it closes your vulnerability to hitting a critical fail point before Regen does its work. The duration between how long you get hit becomes critical to know. And unfortunately, its impossible to know, although you can guess at the chances. Most Tankers probably don't have to worry about this, but something like a /Psi Dominator definitely does.

Well Said Tex !

I will have to admit that I don't like the "Tanking" role on teams, so even though I have tanks, they are soloists. I also don't participate in "big game hunting" like some folks do, so fighting AVs and GMs has never been part of my game, unless I am on a team.

As a result, any models I work on will tend toward what survival pictures are present in solo scenarios with lots of manageable enemies. This helps to normalize performance between all three disparate survival factors (Avoid, Resist, Heal) due to typical damage being lots of smaller amounts in a steady, but diminishing, stream.

It's just a personal bias at work here, but it's the only comparative metric that matters to me

Agree entirely, Oedipus_Tex! (I think I've heard of your brother — can I call you Ed?)

The ability to withstand the two (or more) big hits is a definite advantage to resistance and +max hp which are not captured by the simple model.

I was very happy when they put in the no-instadeath scheme, but now it seems like every second heavy hitter does their damage from 'one attack' in multiple tranches or has persistent DoTs, merely to work around it.
Grr, it was put in for a reason!

I love the idea of a Markov model approach for this problem. I can imagine a scenario in which people upload data from Herostats (say) that describe the sorts of fights one gets in to in a variety of contexts (e.g. over the course of a given TF.) These are aggregated, and coupled with survivability stats of a character (derivable in principle from a Mids representation), one could derive the histogram for passive survival in these contexts. Coupled with attack and other power data, could potentially even estimate solo active survivability.

Sounds like a lot of work though!