Catastrophic Defense Failure: thinking out loud

This is a split from the BoTZ thread. Because I have a belief and I want to see if the math supports it. I will list all the assumptions I can think of in my modeling, and if any of them are dramatically wrong I'm sure someone will mention it.

The claim is, essentially, that "any defense without debuff resistance is useless" and I think that's entirely specious. Any defense without debuff resistance will sometimes fail catastrophically. I agree with that. But the question should be asked: how often does that happen, and how fast?

First, it has to be an enemy with defense debuff- Cimerrorans and Council are the most common level 50 enemies I can think of with DefDebuff. Am I missing something obvious? Probably. Malta, maybe.

Let's consider two melee builds here. Both have mez protection. One is Generic Resistance + IO Defense and the other is SR. Both are exactly at 45% Defense. One has the SR "bag of goodies" and the other has 66.7% resistance to incoming damage (most attacks with def debuff are lethal) and one significant heal (Dull Pain, Healing Flames, Dark Consumption, whatever) for 50% HP (3D).

Let us approximate enemy attacks as follows: Eight enemies with 1.6 accuracy modifiers firing in perfectly synchronized waves every four seconds. All attacks have a 10% Defense Debuff that lasts 9 seconds. (That allows doublestacking, unless something interferes.) Damage for the attack is some variable "D". We will say the player has 6D hit points. I don't know how good a model this is; feel free to suggest a better one.

Let us also assume fairly bad luck on the player's part; after all, players go through hundreds of spawns, and the fights with good luck are irrelevant for our purposes. And let us pretend the players have just given all their insps to a worthy cause.

Round 1: Both targets are at 45% Defense, with a (1.6 * .05) 8% chance of getting hit by each attack. As the 8 attacks are perfectly synchronized, there's a (.92^8) or roughly 51% chance that the entire first volley misses.
If none of the eight attacks hit, round 2 is just like round 1.
We will assume one of them hits.
SR is at 91% chance to be missed by each of the next volley and has taken D hit points of damage.
Generic Resist (GR) is at 82% to be missed by each of the next volley and has taken .333 D .

Round 2: SR gets hit by one attack 53% of the time. Generic Resist (GR) gets hit by about (.18 * 8) 1.44 attacks. Let us assume each, again, gets unlucky. Over time, it's the unlucky spawns that determine how you do. SR now has been debuffed by 2% and GR has been debuffed by 30%- it now has 20% defense. SR has been hit for 2D damage (two hits) and GR has been hit by 3 attacks totalling D damage.

Round 3: SR gets hit by one attack 57% of the time. GR has 20% effective defense,for (1.6* .3) 5 hits.
Rounding up, SR has been hit three times for 3D and GR has been hit eight times for 2.666D.

For the next round, "Round 1" debuffs expire. SR is still at 43% defense, GR is at -20% defense (7 debuffs remaining.)

Round 4: SR gets hit by one attack 57% of the time. GR gets hit by all 8 attacks. GR is now getting hit by everyone, forever: enemies are at capped "To hit". SR is getting close to needing their built-in resistance. SR has been hit four times for 4D (out of 6) and GR has been hit sixteen times for 5.333 D. GR uses their heal, lowering damage to 2.333 D.

Round 5: SR gets hit by one attack 57% of the time; at WORST they're at 5D and now have about 30% damage resistance. GR goes straight back up to 5.0D (2.33 existing, plus eight attacks at .333 each).

Round 6: SR is hoping some badguy drops a green soon. GR is dead.

So that took 20 seconds (counting the alpha), with what I think are very aggressive assumptions about enemy capabilities and some bad luck.

It does not include any active mitigation by the players- no enemies taken down, knocked back, stunned, acc debuffed, or held.

In this near-worst-case scenario, it took 48 very accurate attacks to produce catastrophic failure in supplemental Defense. The length of fight is highly variable depending on team vs.solo; most teams I play on are mopping up by second 10.

Am I overlooking anything major in this model? The things that seem weakest to me are the lumped attacks and the homogenous assumptions (no "two-hit" outliers, for instance.)

Don't forget Longbow - I believe their assault rifle attacks have -Defense. I'm pretty sure they've gotten to my brute a number of times (not helped by the -Resistance from the Nullifiers, either).

Good point. I've dived into a big batch of them on a Invuln brute and seen both my S/L res AND my S/L Def go well into the red... one of those "a second is a really long time" moments.

Are there still any ugly Thorns at level 50? or do you outlevel most of the really nasty things, the way you do with DE?

Malta don't appear to have much in the way of defence debuff.
I've been running a Malta arc on my L50 SD/SS Tank without issue (+0/x8) - apart from the odd incident of being hit by an unseen Sapper.
That was until last nighr anyway when the mission included Nemesis.
Ran into a mixed room of Malta/Nemesis and used my usual attack chain of Foot Stomp, Shield Charge, Fireball.
I checked my health after about 10 seconds and it was at about 50% and my defense was collapsing rapidly, I popped a couple of greens and oranges, a few seconds later the my defence was in the red as was my health. I died soon after thinking WTF!

My DDR varies between 95% and 70% dependant on stacking.

From what I saw both the Malta and Nemesis had Vengance and tore straight fthough my defense, Nemesis must have quite abit of Defense Debuff.

Arachnos have mental scramble, which is defense debuff, and I believe the poison ray of bane spiders also has poison debuff.

On the subject of your math: It seems oversimplifying things a bit, but I don't think much would be gained to go on an all out statistical analysis. Your assumptions seem about spot on.

I've got anecdotal evidence that supports your findings: I have a dark armor / fire melee tank at the S/L softcap. Like your example, I have no defense debuff resistance and no extra mitigation in my secondary. With tough, I have about 70% resistance to S/L. Every 25 seconds I can fill my health bar. Without munching a tiny purple the Cimerorans will kill me. With a single tiny purple inspiration, I don't get hit by defense debuffs often enough for them to stack.

Further, I'd like to say that until I got that softcap, I couldn't take the Cimerorans at all without team buffs. Nothing in the game without +tohit or -defense gives me any pause. So, without defense debuff resistance, is the softcap useless? Hell no.

1st:

The SR is capped to all 3 positions.

2nd:
Just what did you give up on your generic resist to get all three positions ?

Just at a rough calculation if you slot both defense uniques, take combat jumping, weave, and maneuvers, You need 27% more defense in 3 positons

A guassians in build up will give you 2.5 percent in all three positions bringing you down to 24.5% def still needed in all three positions.

You still have 2 power pools, 54 slots, and 16 picks, you can probably manage it but you are going to be foregoing things that the sr doesn't have to.


3:
If the Generic resist is not capped to all three positions. The attacks coming from the uncapped vectors dramatically accelerate defense failure.

That analysis really only applies to Scrappers, Brutes, and Tanks. Even moderate defense on a high-resist character provides a significant boost in mitigation, and even if the defense collapses somewhat you still have resists. Layered protection is the best mitigation, which is why Stone Armor and IOed Invulnerability are so good.

Try running that analysis again assuming either zero or around 30% resist since that is what most softcapped squishies run. Also assume more than 8 enemies since the main reason to softcap a squishy is to handle large spawns (like +2/x8). So figure one hit on average per round of attacks against a non-debuffing enemy, and 4-5 hits allowable before faceplanting. That gives enough time to wipe out most of the spawn (the minions) before they can hit often. Now look at defense debuffing foes... figure 1 hit the first round, 2 the second, and death on the third. That allows a lot less time to wipe out the spawn, and more importantly the odds of being mezzed goes up significantly as you get debuffed, and with a non-held +2 boss around mez = faceplant in many cases. Even if the minions are wiped by round 2, with only 25% defense or so the boss's third attack is much more likely to land (especially if there are multiple bosses). Bosses only have to hit a squishy a couple times to kill them.

Granted, squishies fighting +2/x8/bosses spawns are usually pushing the absolute limits of survivability, but that's where you see the so-called "catastrophic defense failure" occur. With the exception of a handful of enemies like Longbow and their 40% or so defense debuffs, softcapped defense generally doesn't get completely negated. But if you're pushing so close to the edge that losing 5% defense triples your odds of faceplanting and losing 15% all but guarantees it...

First of all, I don't think anyone is claiming that defense without defense debuff resistance is 'useless'. I believe the argument is that it's not nearly as good, which is especially true when you start running into def debuffers, lol.

Secondly, I know you love calculators, but simply take a level 50 SR toon into an itf, then take a softcapped def toon with little to no def debuff resistance. The difference will be obvious and glaring. I remember back when I was unfamiliar with def debuff resists, and I took my freshly softcapped DA scrapper to the wall, where he was repeatedly abused, lol.

Cloak of Darkness does not appear to suppress.

Malta have decent +ToHit don't they? I guess you could consider that a defense debuff

EDIT2: Removed the first section because I think there was a mistake. Need to go through it again.

And while I was at it I tried to compare the basic survivability of both contestants. The worst that can happen to the GR is to be debuffed to zero defense while the best that can happen to the SR to not be debuffed at all.

We then have GR with 66.7% resistance and a 50% heal which is up every 40s (unslotted Healing Flames – Dark Regeneration would be 30s and DP 360s but comes with +HP which is a bit more complicated than a simple heal) and no defense, and SR with 45% defense. And lets assume SR and GR both have a regeneration rate of 0.42%/s (this is the basic value if you have no powers or anything that improves regeneration). Our attackers have an accuracy modifier of 1.6 (a +2 boss would have 1.56).

The formula for damage is dps*(buffs)*(0.5-def)*(1-res)*time.
We want to know how much damage we can survive so the formula for the SR is
dps*1.6*(0.5-0.45)*(1-0) = 0.42%/s
<=> dps = 0.42%/(1.6*0.05*1)s = 5.25%/s

For the GR it is
dps*1.6*(0.5-0)*(1-0.667)*40s = 0.42%/s*40s+50%
<=> dps = 66.8%/(1.6*0.5*0.333*40s) = 66.8%/10.656s = 6.27%/s

This means GR + heal has better survivability even if he starts with zero defense. In other words the GR do not have to worry about defense debuff if his heal is good enough.
EDIT: Hmm... forgot to factor in SR scaling resists and rereadig the OP it seems to be more an all or nothing situation. Guess basic survivabilitly doesn't mean that much when you get hit so hard and often.

Hope all this makes sense.

Achieveing the 'softcap' is far from useless. Most enemies only debuff Defense when they hit, and if you can have purples on hand to pop to keep yourself above the magic 45% number, you can avoid the infamous cascading defense failure.