Is +16% S/L def worth 6.7hp/s (402hp/m)?

This is why you have in your signature that your maths sucks.

The problem is that his curve in no way allows him to answer the original question.

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.

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.

The curves are the same. Plot it.

You mean it doesn't give the actual number. That is true, but that's just arithmetic. The mathematical relationship is what is really interesting.

I think it is cool that Werner has taken data that shares the shape of the predicted curve.

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.

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*

Only this forum fights over numbers like this.

I find it highly amusing that a lot of people simply assume that scrappers are merely suicidal nutcases who go charging into swarms of bad guys without any sort of thought behind their actions.

I LIKE hanging out in this forum with these shrewd, calculating, mathematically inclined, quasi-suicidal APPARENT nutcases -- and I learn useful things that keep my characters from faceplanting when they're doing what's OBVIOUSLY crazy stuff!

There's a lot more to scrapping than the "here, hold my beer. Now watch THIS!" part....

...but let's keep it quiet and not tell everybody.

Agreed. I've probably learned more about game mechanics from reading the Scrapper forum than all the rest of the forums combined.

Yes, the only real difference is that Bunny is pulling the opponent's DPS number out of thin air, whereas Werner (and most everyone else) is using the immortality line to approximate the opponent's DPS. That's why it's so amusing to see Bunny continue to insist that the rest of us can't do simple arithmetic.

At best, Bunny can argue that all the rest of us are bad at interpreting what the math is telling us, but he hasn't met that burden, nor even really tried. He just keeps setting up examples to disprove that a given amount of regen always outpaces a given amount of DEF (or vice-versa), on paper -- which has thus far proven self-defeating, because every single one of the counter-examples he's cited in this thread is practically irrelevant (featuring an opponent DPS either way below the infinite AFK survivability point, or one way above what any character could reasonably survive without so much buff support that his build decisions are rendered moot).

Screaming over and over again that 10 / 10 = 1 doesn't disprove that 10 / 1 = 10.

Likewise, simply invoking Internal Rate of Return doesn't prove that proportional gains are entirely irrelevant. If you compare, say, baseball players' batting averages, you don't look at a 300 hitter and conclude that he's only marginally more valuable than a 250 hitter on the basis that he hits 0.5 more times per 10 plate appearances (the absolute return). You look at him and realize that he hits 20% more often than the 250 hitter (the proportional return).

That's why 300 hitters make millions of dollars more per year.

Originally Posted by Iggy_Kamakaze Nice build

Actually Behavioural Economists describe it as the Superstar Effect.

http://gulzar05.blogspot.com/2007/08...ar-effect.html

'tis only a blog site and not a good text book read, but it might be of interest to you.

I would advise you look at my thread on "The Defence Myth". The mathematics in this thread is appalling, and what I have written there quite succintly answers a very key problem that yourself and Werner are struggling with.

You keep saying that the math in this thread is appalling, but you also acknowledge in your first post in the other thread that DEF has a non-linear effect on survivability (I think your exact word was, "exponential").

The math is correct; you just prefer a different approach to the same problem. An impractial approach, as it happens. You never did address that.

And your blog is worthless, but thanks.

Originally Posted by Iggy_Kamakaze Nice build

You say this a lot - yet "their" mathematics and "yours" are entirely related.

My calculus is a bit rusty but with some googling to remind me - the reason they are related becomes clear enough

Some DPM number / Defense number = Damage regen vs Defense value breakpoint

Or 402/x

Or essentially 1/x

The Derivative of ...
1/x = -1/x^2

And there is the curve.