The Defence Myth

I have a hard time believing otherwise. I don't want to believe someone is that dense.

i wnated stickey but devs no do it halp plz how i get sticked

Or it might be that Bunny realized both of the things going on in the thread are actually correct, just that the method Bunny is using isn't very practical or applicable to the game. This led to him/her going on with the thread and eventually bailing it because they couldn't win the argument. Alternatively they actually think they won, and if that's the case, LOL.

The main thing that keeps me from being certain of that is the regular use of the claim that people disagreeing with Bunny are explicitly wrong. This seemingly isn't just about looking at the same math from a different perspective, it's about claims of erroneous conclusions based on the most common ways of looking at the math.

I doubt there's a sense of victory, since it's clear pretty much no one agrees with Bunny's argument, at least as best as any of us thinks we know what it was. But I do think there may be a certainty of the rightness of their thinking.

Correct or not, who wants something so impractical? Yeesh.

You never know about the tinfoil hat people (and their kin). Maybe they get a kick out of being the only ones to "know the truth".

I don't know, honestly. I just think for some people it is very hard to admit they were wrong, and many of these people just go on with whatever they were crusading about and can't let go of it. In this case Bunny was wrong in claiming that we are wrong.

I'm not worried about Bunny getting it. He thinks he gets it. He actually probably does, but can't figure out how to say it correctly, and ended up arguing sementics for the better part of a week.

But what worries me is that other people who want to know how this stuff works might log into the forum, see a thread with this title, and then get all the wrong information. I'd like to think I was one of those people one day, and when I turned to the forum to discover how the game mechanics worked, I found good data. I learned a ton from this forum and others. This is why it's important we make Bunny look like the fool he is. It's for the integrity of the forum. For what it's worth, I think we did our job here.

OK, I did that. I set DPS to 500, defense to 40% (which should not matter for this purpose), regen to 0 (this is the additional number, not the base), initial DR to 0, and initial regen to 45 hp/s. In the top left box, there should then be no defense, no damage resistance, and no other mitigation other than the base regen of 45 hp/s.

However, this box gives the mitigation as 295 hp/s. That's clearly wrong. Your math, and the resulting conclusion, is suspect.

I believe I understand the discrepancy: base chance to hit. But that's not mitigation, per se... so the math may be right, but just labeled misleadingly.

What I think is that, given no other regeneration buffs, +50% regeneration increases the maximum level of sustainable damage by 50%. That's virtually always what I mean when I talk about "more survivable." It won't increase the amount of time you can survive any random level of damage because obviously in the degenerate case where you are receiving damage large enough to kill you in a second or two, no amount of regeneration within the game (out to the regeneration cap) will be able to help, because there's no time in which for it to act.

This is all spelled out in my Scrapper Comparison thread, which is something that was posted just ahead of I7, which itself is the fourth iteration of those calculations which date back to I2. Regeneration was added to those comparisons circa I3, and this basic principle of how regeneration works relative to time frame of combat has been generally accepted for virtually as long as regeneration has been discussed quantitatively on the forums.

Again, the OP seems to be confused as to what people are saying, and therefore making things up and arguing against strawmen.


Here's the funny part. What I said was:

The interesting question is, is there *ever* a time when +50% regen would be *better* than +5% defense, starting from 40% defense, and make that assertion questionable? Not really, no. At the sustainable damage level, both are statistically even. Above that level, regeneration will be worth less. Below that level you're immortal and can't die, so neither can be said to be worth more than the other (we're talking about averages here; in the stochastic case its more complex, but you only get to reference that if you want to do Markov calculations: only three posters to my knowledge have ever tried, including me).

So, the statement that I would take +5% defense over +50% regen is still valid, since the time-dependency of regen means +5% defense is always better. The break even point, as I mentioned, is +100% regen without initial regen bonuses, or about +180% if you happened to have slotted Health (more, if you have even more regen bonuses). Right at that mark, its a toss up for me. At the break even point for maximum sustainable damage, on the one hand the +Defense would be always greater than or equal to, so you'd think that the Defense would be better in general. On the other hand, I don't usually die when on my SR scrapper, which means in effect I'm hovering at or just below the maximum survivability mark averaged over time. As long as I have enough health to average out the bursts and the lulls, the regen is just as good and has certain downtime benefits. Its also a lot easier to "ramjet" yourself with lucks than respites.


By the way, this bears repeating: the notion that the maximum survivable damage mark (the "immortality line") is inapplicable to the normal game is not true. On average, everyone who runs missions and doesn't die is at or below this mark on average. Moment by moment they will of course be higher or lower, but as long as you have enough health you can usually average out just fine. Soft-capped scrappers who don't consistently die, in particular, are running right at this line most of the time, bursting higher and then dropping below, so their average health recovery just balances incoming damage after mitigation.

It is not as good a tool to judge survivability when in situations where you don't have enough health to average out, like alpha strike tanking situations. But that's why we have the time-window calculations: to supplement the long-term average calculations for those situations.

In situations like this, convincing the OP is gravy. It happens maybe 25% of the time. The most important thing is making sure misleading lines of thought do not go unchallenged. Individual points of view come and go: not that many people push strange agendas long enough for them to have a long-term effect. In the short term, though, they can unnecessarily complicate the task of figuring out how things work in the game for many players.

I don't really care if the OP thinks I'm just a loon. Next year, it will be some other poster who thinks they've cracked the Da Vinci Code of game mechanics. I'm probably one of the few people who can even remember who most of them were, which is in some respects a delicious irony.


Although, this is a rather longish thread based solely on the mistake that the OP made in not realizing that this equation:

D * (1 - R) * (0.5 - D) <= HR

is just a special case of:

D * (1 - R) * (0.5 - D) <= (HT / T) + HR

for very large T. At least, that is the short-form mathematical issue. If this was a math forum, I should have been able to reply to the OP like this:

D * (1 - R) * (0.5 - D) <= HR is D * (1 - R) * (0.5 - D) <= (HT / T) + HR for low values of T. QED I win.


And since I'm a strong proponent of making sure your equations mean something, this is the english translation of both. The first says this:

Damage Admittance Rate (damage rate reduced by resistance and reduced by defense) is less than or equal to Health Recovery Rate When this is true, you tend to stay alive. When this is false, you're going to die eventually.

The second equations says this:

Damage Admittance must be less than Health Recovery plus total Health divided by the duration of this situation. The truth is that I derived this equation from this one:

T * (D * (1 - R) * (0.5 - D) - HR) <= HT

This one says damage admittance rate minus health recovery times time must be less than total health. Its obvious what this one means: the total net damage you take (damage minus regen) over time must be less than your health bar. If its not, you be dead.

But the other equation says something also, something I think is rather clever. It says when you are taking damage, your regen rate offsets that to keep you alive, and your health bar can also contribute a stream of health during that time period equal to your total health bar divided by the time. If the incoming damage is higher than even this total health rate, you'll die at some point. That's basically what health bar is: its a reservoir of health that can be tapped to temporarily offset more damage than you can heal back immediately. And its finite. But the shorter the period you need it for, the stronger it can be during that shorter period of time.

Its an unusual way to look at the health bar, rather than as a resource to protect that damage eats away: instead its an emergency source of regeneration with finite capacity. But these two points of view of mathematically congruent: they ultimately say the same thing.

Your equations should always mean something. If they don't, you're either a string theorist or an economist, or you're mistaken. Or both.

Don't worry, we still love ya.
And it's things like this that make me love Arcana.

Likewise, when you have no other mitigation, 50 hp/sec is better than 5% DEF under any conceivable situation where the choice is likely to matter. As early as the first thread, Bunny didn't care.

I believe he understands the math. He's shown on the Tanker forum that he knows how to make a good build. But he's also shown a desire to throw numbers around like an eighth-grade student flush from his first algebra class and determined to prove the adult world wrong. The rest of us aren't wrong, and his way of looking at mitigation is far from new. It's not like it's some great revelation.

Whether his arguments were made in good faith or not, all he's managed to do here (over and over again) is to provide the exceptions that prove the rule. Not a single one of the counter-examples he's so contemptuously supplied is instructive in any kind of gameplay-relevant way. And as was noted earlier, his model breaks in hilarious ways when we plug in 100% mitigation.

And so the theory built on cherry picking finds itself cherry picked to death. C'est la vie.

Originally Posted by Iggy_Kamakaze Nice build

Well, if it was 5% base defense, it might matter if you were tanking more than four Hamidons. Unfortunately, you can't really get base defense anymore, and the devs took Hamidon away from me back in I14 beta.

Well, layering as a principle is not a bad idea, but often people are comparing a layered defensive combination that is extremely strong against a single layer one that is actually weaker, which isn't a straight up even comparison.

For example, 35% defense and 40% resistance and 20hp/sec regen (which would be somewhere north of +300% regen on a mastermind) is numerically stronger than softcap plus slotted health.

Technically speaking, all defenses are at least a little layered. Even pure soft-capped defense has base regeneration underneath. Its just that base regen and soft-cap even on a scrapper is not all that spectacular. Slotted Health makes a big difference, regen bonuses make an even bigger difference, and aid self makes a huge difference inside of soft-capping.

What situation you're going to be in matters as well. Tankers cannot rely solely on defense, because an unlucky damage spike will simply kill them. They need resistance an/or +health to provide that buffer against bursts. I'd probably take 40% defense and perma-dull pain over 45% defense and just the heal of Dull Pain with no +health, even though numerically the 45% defense is stronger. I'd supplement with inspirations if necessary.

Its the qualitative differences between the mitigation types that start to become important once you start talking about really big numbers. Defense doesn't just deflect damage, it also allows you to avoid secondary effects like debuffs. Resistance slows damage down rather than showing spikes which can provide more time to react to a bad situation. Regeneration typically provides better downtime recovery after a bad situation, assuming you survive. Once you have enough numerical strength to deal with what you want to deal with, these secondary issues start to become more important.

Here's the tricky question: what's better: 40% defense, or 30% defense and 50% resistance? Same numerical damage mitigation, but either all defense or split up and layered. On the one hand, the latter is much stronger against alpha volleys and damage spikes. On the other hand, the former will be avoiding twice as many secondary effects as the latter. This is not an easy decision to make, and I think a case can be made both ways.


Here's my defensive story of the week. I've been working on a new repec for my MA/SR. Its taking some ideas of my own and a twist or two from some suggested builds I received a couple of months ago in another thread. Its not completed yet (most of the purples and all the PvP recipes not acquired yet) but its finally slotted enough to be playable (I started completely from scratch: I wanted to be able to compare this new build to the older build, so I did not deslot anything from the old build which made this take a little longer). Its just short of soft-cap, but I can test soft-cap with inspirations. I quickly ramped up to 0x8 and the build works quite well so far (even better with the first Incarnate power slotted).

The third mission I tested with just happened to have KoA in it. Very humbling. I don't think I have to describe what +0x8 KoA does to SR scrappers whose primary protection is defense and whose backup plan is aid self to the scrapper forum. I could finish the mission without reseting by running around like the Energizer Bunny on crack, but it reminded me why Tankers aren't getting SR anytime soon.

This. The soft cap is great, but on its own, you're still going down against anything difficult. Also, some builds can do very well without it, like Scrapper Regen. And yeah, for regular play, I consider one purple from soft cap to be very, very good.

On the other hand, I think there may simply be a myth of this defense myth. I can't remember anyone seriously suggesting that you soft cap and then you're done. You don't hear about layering much anymore, but I think it may be because that lesson sunk in long ago. I would hope, anyway.

The defense and resistance alone are about 91% damage mitigation (already better than soft-cap's 90% mitigation) vs smash/lethal. The debuffs are trickier because they can be affected by resistances and combat modifiers (i.e. the purple patch).

At full strength, incoming damage would be reduced to the floor which is 10% damage, and the tohit debuffs would essentially soft-cap you. 99.4% damage mitigation, somewhere around perma-unstoppable + invincibility + dull pain circa I1. 800% regen is about what an SO slotted Regen can generate in total health recovery with slotted FH, slotted Integration, and slotted reconstruction.

Not counting bodyguard, net incoming damage that can be mitigated by that build (before debuffs and defenses) is about 4400 dps. And I'm not sure its possible to experience 4400 dps at even con due to the aggro cap.

Of course, this is the theoretical max. The seeker drones have to hit, and they can't hit everything, and triage beacons don't follow you around, and the debuffs would degrade attacking higher level critters or critters with resistance. Just counting defense, resistance, and regen, the sustainable damage associated with that level of damage mitigation is about 300 dps. Its close to the aggro cap of even level minions (at level 50) in melee range.

Its possible people say it in-game, although people say all sorts of silly things in-game. On the forums, especially on the Scrapper forums, I haven't heard that assertion made credibly in years.

I find my fire tanker does well almost no intrinsic defense, because purples drop often. So its not so much that I don't have defense, but rather that I don't build for defense. A high resistance high heal build can do very well by supplementing with inspirations in normal play. I find I actually have a harder time supplementing with inspirations with my SR, because its much easier to stack purples than to constantly pop greens.

In fact, the great irony of SR is that until I7 defense used to suck, and after I9 defense became so plentiful it almost doesn't matter how much you start off with. People are range-capping blasters now.

All I know is I've seen every version of the high defense build, from perma-elude to invention based soft-capping and everything in between. Soft-capping is great relative to the strength of conventional SO builds, and its night and day for squishies. But on its own its actually not all that fantastic without additional support when it comes to high performance melee. Softcapping an Invuln is fantastic. Softcapping a Willpower is amazing. Softcapping SR is kissing your sister.

If I didn't refuse to change my sig because I have a grandfathered one too big to be allowed on the new forum, this would so be my new sig.

For "Regen", you add either Siphon Life or Aid Self. For resistance, you stack Tough with the scaling resistances. Not much, you say?

I think people underestimate just how much mitigation the scaling damage resistance can provide. I was doing survivability tests at different levels of defense on my DM/SR about a week ago, and I could hang out with frequent blinking red with an average of maybe 40% resistance for ten minutes or more and the spawn might never put me down. They weren't smashing/lethal, but if they were, add Tough on top of that. You may not see that much resistance very often, but you may also find your Super Reflexes ridiculously hard to kill in normal spawns even if you THINK you're about to go down. For that matter, it sometimes works out that way in really nasty spawns. That's pretty much what happened when I took on Manticore Automaton as an AV and near the aggro cap of Nemesis.

OK, yes, a soft-capped Dark Melee/Invuln and a number of other combinations can be even better. But Super Reflexes is no slouch. (Edit: Plus easy 95% defense debuff resistance. Tasty.)

No slouch, no - But it is not the same thing. It just doesn't get as much total benefit from IOs in those extreme builds.


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Aid Self is great but due to the interrupt it is weakest when you need it the most (something getting through your defense) - its no Dull Pain, and definitely no Rise to the Challenge.

Tough is pretty good but 17% + scaling is not the same ball park as what Invul or WP gets

But unless the baddies debuff defense, WP or Invul can get pretty much "the same thing" as an SR and more goodies besides.

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But sure - against the right(most) groups - a softcapped /SR is basically insanely powerful defensively.

hmmmmm
400%+ regen, 1950+ HP on top of 38% Aid Self every 7 seconds with 20% S/L Resists seems pretty good to me