Werner

Nah, we actually had this same argument in an older thread. So this is at least thread three. I'd contribute to yet another thread, but I think y'all have this one covered, and I've been forbidden from continuing to argue on the intarwebs. Well, this particular argument with this particular person, anyway.

Thanks! Yeah, almost unfortunately, I like some of what I see in that (for instance, it didn't occur to me to go with a full Gladiator's Armor set), plus I've had some recent ideas of my own, so it looks like I'm going to lose the first of the two freespecs while I keep playing with ideas. Oh, well. I'm sitting on five veteran respecs, and so far it looks like I'm keeping the vast majority of my IOs, so I should be fine. I'm just so eager to actually play it!

Ah, true. I believe it was being done before ED, then was rare after, and yes, you're famous. Even with inspirations, soloing all those task forces had to be frickin' hard.

I should probably say "without temps or inspirations". Probably was done before ED, and then I'm guessing that only I9 made it possible again, but it took a while for the Scrapper community as a whole to realize it?

Honestly, I don't remember any Scrappers POSTING about soloing AVs until I12, though I certainly could have missed it. Wouldn't surprise me if there was some of it earlier, since it was certainly possible earlier, but I think I12 is when we all suddenly went, "Hey, wait... this is possible! Let's DO this thing!"

I wish! I've actually not done that. It's great that people think I have, though.

How WOULD you go about setting up an uplevel AV to fight? I'd love to try it once I get Alexei's new build nailed down (and with the very rare for sustainable endurance, so who knows when that will be).

WOW. Really? Reverence talks about soloing it with AVs and you think the post must be about YOU and YOUR FEELINGS? When did you become the center of the universe?

You may want to refresh yourself on what the thread is about. The very first sentence in the thread was, "OK...who else was set to AVs and soloed it?" It's the topic of the conversation. It was the topic of the conversation before you badmouthed everyone, and it remains the topic of the conversation still. This thread isn't about you. Perhaps you should take your own advice and let it go.

Edit: Ah, you were probably responding to the post by Claws and Effect. In that case, you probably should have actually responded to that one. Linearly, your post was below Reverence's. Threaded, your post was in response to Reverence's. So it's easy to assume your response was in regards to the post you responded to. Maybe it was, but maybe it wasn't. If it wasn't, I apologize, and you may just want to be more careful about which post you respond to.

Yes. But I honestly get just as much enjoyment out of making builds and playing with game-related mathematical models as I do from playing. Between this and working on my I19 build for Alexei (and doing other things on a Saturday night), I think I've run one mission so far this weekend. Now I'm heading out for dim sum with friends, and then we'll all be hanging out. I'm not sure if I'll get to play at all today. That's fine. I'm a "casual" player. *chuckle*

Shred Monkey explains how mitigation can be used to answer the question:

He says 421 hit points per minute instead of the actual 402 hit points per minute. He also only looks at the smashing/lethal defense. But these are not huge issues, since it's close and since smashing and lethal are the most common damage types. Taking the other damage types into account is doable since I have a chart of their relative amounts in the game as a whole, but that's overly complicated for what I'll be demonstrating. So correcting ONLY the hit points per second:



We can see that the break even point is very low, about 42 DPS of enemy damage. My testing showed that this is a little more than two even level minions of damage output. Chances are excellent that you can and will routinely fight enemies harder than two even level minions at level 50. It climbs to about three minions if we take the other damage types and defense amounts into account, but that hardly affects our line of reasoning.

So basically, if we expect to be fighting more than two or three even level minions, we'll be wanting the defense. Simple.

But then Sailboat said this, which kicked off the whole debate:

Now, why would THAT matter? The graph doesn't depend on initial defense at all, and the graph already answered our question, right?

Well, technically speaking, no it didn't, and it can't. Not on its own. The graph ONLY tells us the break even point. In this particular case, the break even point is so low that our general experience with the game tells us we'll be well above it. Thus, my own answer of, "Very likely." But the graph itself, the math itself does not answer the question. To answer the question mathematically, we need a reasonable estimate for what sort of enemy damage output we'll actually be facing.

So might the enemy damage output we're facing depend on whether this is the first 16% of defense or the last 16% of defense? Of course. We will be facing a lot more enemy damage output if we're soft capped, because we can, and because to do otherwise would be extremely boring and never call our survivability into question. Now, it won't affect our decision about which build is better in this specific case in practice, since these look like Willpower defensive values and Willpower is a solid secondary that should be able to fight more than three minions at level 50 almost no matter how badly you gimp your build. But for demonstration purposes, and since we've been ignoring damage resistance all along for simplicity, we'll say we have no damage resistance, and we'll say the original build only heals 16.7 HP/S, so the proposed defensive build will heal 10 HP/S.

Knowing whether this is the first 16% defense or the last 16% of defense then lets us estimate what sort of enemies will actually challenge us. It's overly simplistic, but we can use the immortality line for this estimate:

• At 16% defense and healing 10 HP/S, we can survive 29 HP/S of enemy damage output. This is BELOW the break even point. So the regeneration is better.
• At 45% defense and healing 10 HP/S, we can survive 200 HP/S of enemy damage output. This is ABOVE the break even point. So the defense is better.
• And at 26% defense and healing 10 HP/S, we can survive 42 HP/S of enemy damage output. This is AT the break even point, which will soon become relevant, so is included even though it isn't one of the alternatives that Sailboat suggested.

We can show this in graphical form, of course. Here I've placed vertical lines (immortality lines) for each of these levels of enemy damage output. One line is below the break even point, one is above the break even point, one is at the break even point.



So initial defense COULD matter here. So COULD initial damage resistance. So COULD initial regeneration. Basically, the level of all forms of damage mitigation and damage recovery COULD affect which side of the break even point we'll find ourselves at when we're actually facing challenging enemies. And that's the damage level of interest - the one that is challenging. Not trivial, not suicidal, but challenging.

And that's what the survivability calculation does. It tells us which side of the break even point we're at with the proposed build change, a question that mere reference to the mitigation graph leaves unanswered (since it doesn't tell you what damage output to use). It does go about it a bit differently, though. What it does is calculate the level of enemy damage output that would challenge the original build as well. For the three defense builds we've plotted in the chart, we can calculate the damage level that would challenge the ORIGINAL builds:

• At 0% defense and healing 16.7 HP/S, we can survive 33 HP/S of enemy damage output.
• At 29% defense and healing 16.7 HP/S, we can survive 79 HP/S of enemy damage output.
• At 10% defense and healing 16.7 HP/S, we can survive 42 HP/S of enemy damage output.

Let's plot these lines as well, this time in green.



The graph is getting a little crowded, and there's probably a better way to graphically show what's going on, but I'll explain. If you're to the right of the break even point, the defense build immortality line (black) will be higher than the regen build immortality line (green). If you're to the left of the break even point, the defense build immortality line will be lower than the regen build immortality line. And if you're AT the break even point, both builds will have the same immortality line (black and green dashed line).

So what we can see is that doing ONLY the survivability calculation for the builds under consideration tells us which side of the break even point we're on when we're facing a challenging but not suicidal level of enemy damage. It tells us which side of the break even point we're at when our mitigation actually matters. And it does so without ever calculating the break even point.

Again, mitigation and survivability are two sides of the same coin. But only survivability can actually answer the original question in a MATHEMATICAL way, since only survivability mathematically tells you whether you're going to be over or under the break even point when your survivability is being challenged.

And again, in THIS case, for THIS example, it's been obvious to all involved that we're "very likely" going to be over the break even point. But that this is obvious doesn't mean that the mitigation calculation of the break even point actually provided the complete answer. And most questions along these lines are much less obvious than this one, involving more subtle trade offs. If the break even point were, say, two bosses, two lieutenants and four minions, we'd never know whether we'd be above or below this break even point without additional information about the builds in question.

Exactly, they're two sides of the same coin, or as I've been saying, step 1 and step 2. It's just important to not get stuck on step 1, or to see only one side of the coin.

At best, this is an argument against using the immortality line as the way of calculating the damage, and instead using something like 60 second survival line. I'm personally not interesting in what I can survive for 60 seconds, but rather what I can survive indefinitely, but JUST. As I mentioned earlier, though, for lower levels of mitigation and lower difficulty levels, something like the 60 second survival line might be better.

On the opposite side, I agree that the majority of time you are not taking an immortality line worth of damage. The majority of time, you are not in much danger. The only point where the question of which is better becomes interesting is at the point where the decision may save your life. The point where you're actually facing a challenge to your survivability. I really don't know why anyone would care how MUCH their green bar is pegged at full when facing easy enemies. If it's full, it's full.

Also, in a very real sense, in the sense of what you can actually survive in the game, this method DOES determine which protects me from more damage. It tells me exactly how much damage it will protect me from WHEN MY SURVIVABILITY IS AT STAKE. Much more than that number, and you're going down, and all you can do is affect how fast. Less than that number, and you're just caring about how much your green bar is pegged. Neither of these scenarios seems particularly interesting to me personally since the fights that interest me are long and difficult, though the "how fast I go down" scenario should be of interest to the "kill or be killed" crowd, in which case they might want to use 60 second survivability instead of the immortality line.

And the answer doesn't lie merely in finding where defense pulls ahead of regen. That's the first part of the answer, and the second part is deciding if you're before or after that break even point, which is a question of how much damage you'll be facing when your survivability is actually on the line.

And this is what I think is so amusing. In terms of what you can actually SURVIVE in the game with that mitigation, based on the original table #2:

0-25%: +1 boss
40-45%: +5 bosses

In a fundamental and obvious sense, going from 40-45% is five times better. In fact, in a fundamental and obvious sense, going from 40-45% protects you from five times as much damage - the damage output of five bosses instead of one. The exact opposite of what you are saying.

Now, I WILL argue against such a simplistic conclusion. It may be fundamental and obvious, but it could be considered a bit misleading. I think it's best to instead view survivability increases in percentage terms, and both of these are double the survivability, or +100%. But I wouldn't go so far as to say that the more extreme view, that surviving 5 bosses is fundamentally and obviously five times better than surviving 1 boss, is actually wrong.

But to conclude the exact opposite, that mitigation is all that really matters, and therefore surviving one more boss is five times BETTER than surviving five more bosses? The mind boggles.

Indeed, which is why it's so valuable to actually establish the value of this variable in an objective way. You can then replace it with other variables which can simply be looked up.

No, the second is not 5x better at saving your life. For either change to be able to save your life, you MUST be approaching the immortality line of damage. For the first person, that number is MUCH higher than for the second person. Smaller percentage of a higher number. Works out the same.

Of course the answer depends on the damage faced, but that doesn't mean that damage must be a variable in the calculation, a very significant point.

Your method gets as far as showing that the answer is dependent on the damage faced. So far so good. From there, the standard survivability model moves on to step two, providing a way to objectively determine that damage value from more fundamental quantities, and thus to actually SOLVE the original problem instead of just saying "it depends on the damage" or plucking a damage figure out of thin air.

Except that I have. I answered it using a survivability analysis four posts up from the post with the graph, and this being the second time that I've mentioned it. In fact, you've already quoted the more recent post where I said where to find that post.

You'll be certain that my answer is wrong, or flawed because I made up variable values (as you must with DPS, though at least mine are easily gathered from Mids'), but you might want to at least stop repeating that I haven't provided an answer at all. Or not. Say whatever you want.

Strange, many of us use this exceptionally difficult metric all the time. Maybe it's easy for me because I can't do maths. No need to draw graphs. Just do a couple quick survivability calculations regarding the two options, one with the regen, one with the defense. Yes, doing this well this requires some numbers that Mids' will give you. Making the right decision based purely on mitigation requires you make a very good guess for what damage output the build will be facing. Either way you need additional variables, but mine are easily supplied. Yours is not, or at least not accurately. It is of course easy to just make one up, "I'll be facing 100 DPS!" Good luck guessing accurately on that one, though.

Right, there's nothing wrong with the math Bunny highlighted. To quote the conclusion, "So if you have 50% resistance, if 8% of enemy damage output > the regen amount, you should take the defense."

Unfortunately, that isn't an answer - it's a decision procedure.

To apply that procedure, you need to plug in a value for the variable - enemy damage output. This is unknown. Yes, we could create a graph of enemy damage output and compare our horizontal line of regeneration vs. our upward sloping line of mitigation from defense. Yes, line. Mitigation of a given increment of defense vs. damage output is indeed linear. I'm not arguing that. You do have a point where the two lines cross. Above this point, choose the defense. Below this point, choose the regeneration. But again, all we've done is graphed the decision procedure. We STILL need to choose a number for enemy damage output. Only then can we actually know which is better.

You could choose this number randomly, which is where my magic 8 ball comment comes in. You could choose it based on past experience with the character, but this will be iffy at best unless you run a lot of herostats and the new builds being considered are very close to the current one.

But we don't need to do any of that, because we have a very good way of choosing it - the immortality line. Do an immortality line calculation, plug in that value for enemy damage output, and you ALMOST get the decision you'd make using a survivability analysis. It is almost equivalent at that point.

The difference is that the survivability analysis goes just a little further. It chooses two different damage levels based on the immortality lines of your two options, not a single one. Each build is capable of facing a different amount of incoming damage. Each build may be mitigating from a different base of damage by the time it is facing any challenge to survivability.

But in any case, that's the long way around. The immortality line calculation IS the survivability calculation. Once you know the damage figures to apply to each build option, you're already done. Those damage figures in and of themselves tell you your answer.

Of course I'm graphing survivability. Nice to finally see you admit that. So, you concede that defense has a non-linear effect on survivability?

Oh, I've stopped trying to convince you of anything. That wasn't the point at all. I've realized that you can read the post and say with a straight face, "No, surviving a lieutenant is just as good as surviving two bosses, two lieutenants and one minion." I've realize that you can look at that graph with its obvious curve and say with a straight face, "No, a straight line is the best model of what defense is doing for us here." I cannot pretend to understand what's going on in your brain that lets you do so, but it no longer surprises me.

No, it's for other people. People who are interested in survivability in terms of what you can actually survive in the game. The post lets those people know, if they were doubtful, that the standard model of survivability DOES correspond very closely to what you observe in the game.

This standard model then allows us to answer many questions, such as the OPs question about whether defense or regen is better. Better here is expressed in terms of what the new build options will allow you to survive. The build that can survive the more dangerous group is the better build. These survivability calculations were done four posts above the one you focused on.

But that post won't show you anything either, as it is trivial to demonstrate that it's the wrong answer in cases where the incoming damage is far lower than would actually challenge the build, cases where it's pointless to worry about such questions. It's trivial to point out that my calculation has many more variables than yours, and that I merely guessed at some of those variables since I haven't seen all hell's actual build options. I'm sure you think that somehow proves it's wrong. That's fine. I just expect everyone else to see through your confusion by this point, and thought they might want a little more information.

OK, take two now that I have the I19 Mids' and can actually see what's going on.

I'm not sure what you mean about putting the Performance Shifter proc in the heal - it doesn't take endurance modification sets. Or did you mean put it in Physical Perfection? The Miracle would provide more. I've kind of accounted for the Theft of Essence, essentially by ignoring the cost of the heal. The heal as you have it is 21 endurance, which pretty much means if I'm surrounded, the heal should be free. And even if it takes a little endurance, it takes a little time too.

Yeah, I don't think I considered the effect of the recharge alpha on Conserve Power. I'm sticking the Miracle in the empty slot in Physical Perfection and trying this again...

While Conserve Power is down, the toggles take 2.72 EPS and the attack chain takes 3.66 EPS for a total of 6.38 EPS. Our recovery is 3.77 EPS plus 0.2 EPS from the Performance Shifter proc plus 20% * 7.5% * 115.4 / 10 = .17. So net endurance drain is 2.24 EPS. It won't even last a minute. Mind you, that's with everything running. As I'd normally run for AV soloing, the toggles are only 2.04 EPS, so net drain is down to 1.56 EPS. That's about 74 seconds. I'm afraid it's not enough to last between Conserve Powers, even with the very rare recharge alpha.