Jack_NoMind

The more continuous damage is as seen relative to your HP; the more continuous HP recovery is as seen relative to the damage. We can really only notice HP recovery as it approaches incoming damage; we'll hardly notice continuous HP recovery at all at 1% (1/100th) of incoming damage, we will likely notice it at 10% (1/10th), we will definitely notice it at 50% (1/2). In this case, I think 'notice' works almost equally well if it's interpreted as 'improves resolution of model' or 'is noticeable to many players in actual gameplay.'

So the 'burstiness' of 1 damage/5ms vs, say 10 damage/50ms is probably not noticeably different to characters with several thousands of HP -- it depends, of course, on exactly how inexplicably anal that person is being in constructing the particular minutiae of a model they are making that no one actually cares about but are now evidently picking a pointless fight with two separate people about. The burstiness of 1 damage/5ms vs 1000 damage/5s is probably not noticeably different to characters with several million HP.

Similarly, health recovery to the tune of 1 health per 100 damage interval probably isn't noticeable; nor is 100 health per 10,000 interval, or so on and so forth. It isn't noticeable even if the damage is dealt over millisecond increments and the health regeneration occurs even more nearly continuously than that. It also really doesn't matter what % of your health these numbers are, because it won't matter either to your model or to your play experience since you'll be dead well before they make a difference for literally any value of health.

10 hp/interval or 50 hp/interval is noticeable, using the 100 damage example, but again only insofar as it occurs over that interval and not with regard to how actually continuous it is.

Conversely, irrespective of the damage interval, a 1000 health-restoring event is noticeable to a <10000 HP character because it will immediately reduce the % of health remaining each damage event causes. The burst health restoration event, in other words, is just as relevant to damage as burst damage is to health.

Contentiousness of health recovery does not matter respective to total health; burstiness of damage only matters after a certain point. That is all I have been trying to say, and I don't even think anyone has actually argued otherwise.

I meant continuousness. Damn autocorrect.

Okay, okay. Sorry UberGuy.

Anyway, good thread! I usually don't engage in assassinating my own, but I think we were pretty much done anyway.

Well... no, the magnitude of time expressed as a percentage of your HP is not particularly relevant.

I realize that isn't what you meant -- you meant that a smaller event interval grows more significant as the percentage of health lost per event rises -- but it is what you actually said. I do not think you are reading carefully enough what either of us is actually saying. I have actually said that continuous HP recovery is less relevant than being able to achieve a high % of HP on-demand. I said this exactly because of

, which I didn't explicitly state myself because you are obviously aware of it, and felt you would recognize this rather than me having to explicitly connect those dots. The importance of this is small; I am merely irritated at the unnecessary exchange.

NERRRRRDDD FIIIIIIIGHHTT.

I kind of anticipated this in how I phrased my response to you. ;p

Yes. So all else being equal, a Defense-only character who's at 20% life is in a more precarious position than a (90%) Resistance-only character at 20% life, even in the case of relatively small amounts of per-hit damage. I assume this is part of why there are no Defense-only armor sets anymore.

If by 'continuous' you also mean 'equal,' yes, of course. But actually spiky on-demand HP recovery is extremely useful to Defense sets, because it can push them quickly out of dangerous health %s.

Bweh? What is this supposed to represent? How on earth does it sound right to you that a character with 90% resistance takes 60% of the attack's original damage?

It looks like you are subtracting the 50% hit chance from the damage resisted and then treating the result as damage taken, which I do not even understand.

As UberGuy points out, this isn't how we figure admittance. Hopeling summarized, but I'll elaborate.

So Canny has her tirade about the logical basis of admittance calculations and whatnot, but the short of it is simply that you have to be consistent with how you're figuring damage. I prefer her method, but let's use yours for a moment. With corrected math (and I'm going to use Brute/Tanker resist caps, because it doesn't need to be proven that Defense or layered with Defense is the best way to go for anyone else), it looks more like this...

Attack damage: 1000. With 90% resistance, you can model it as either 900 damage resisted (so 1000 * .9) or 10% damage taken (1000 * .1). You are treating it as damage resisted, so we'll go with that. However, in addition to the damage being resisted, the mob has a 50% chance to miss each attack. So we resist 50% of all attacks made, and ignore 50% of attacks. Your version should look like this :

((1000 * .9) * .5) + (1000 * .5) = 950

It's hard to read and doesn't make much intuitive sense, which is why we usually measure damage taken, rather than damage resisted:

1000 * .5 * .1 = 50

And even that isn't all that logical because it looks like we're taking 95% less damage than some arbitrary person, when in fact no one at all would be taking an average of more than 500 damage in the first place, so Canny has her rant. But we'll set that aside for now.

Edit : Or she can beat me to it anyway.

This is basically true, but I think I'm going to end up showing that the -20Res on the Defense character is more likely to actually terminate in death in most cases. (For the same reason I think -dmg is more beneficial to def than res, increased damage taken is more harmful. There's not a lot of difference between +res and -dmg to the defense character, incidentally, but a def/res character isn't what I want to look at here.)

All three of those layers -- the hit/def layer, the dambuff layer, and the resistance layer -- are multiplicative with each other in a general sense. Although the basis of my argument is a very specific criticism of the model Bunny posted, it does work very well in that general (sort of Newtonian) sense to get a simple percentile mitigation number.

Similarly, while I am making a strong attack on a common misconception (that -dmg% pairs especially well with resistance for some reason), many people in the thread have demonstrated the weaker (but more certainly true) claim that at worst the possible pairings of def/res, -dmg%/res, or -dmg%/def are equivalent for similar values.

Edit : And no, I'm not updating my model until I get some sleep, regardless of how many or few times I post on the forums before doing so.
Edit 2 : My lack of commentary on post 15 in this case is intended to indicate I agree with it.

Okay, technically correct -- I should've phrased my statement better. That extra hit does benefit the resistance character and not the defense character, but it only benefits the character in such a way as to return to parity: the resistance character has a survival line of 10/12 hits, and the defense character has one of 12/12 hits. At no point will the resistance character have more probable hits than the defense character.

Although that's interesting. Hmm. I believe I have legitimately oversimplified the issue and I will have to incorporate health restoration to demonstrate the case properly.

It appears that defense is consistently favored by probability; at its worst it breaks even with resistance. However, you've won the issue until/unless I do mock up a regen-inclusive model, since this behavior is not created by -dmg debuffs.

It would indeed be much better to create an-even-more-granular model, but the increased complexity won't change the behavior; it will simply create more peaks in our graph.

No it doesn't (necessarily speaking). Reducing enemy damage by half reduces damage by half, but that only sometimes is caused by a -50% damage debuff.

One of my points here is that -dmg is another layer of mitigation entirely; it's erroneous to describe it as related to resistance, even though it's intuitively similar (since they both reduce damage by a percentile). So you could theoretically (although I believe this is impossible without a specific team build) floor your enemies to 10% damage and also have 90% resistance (on certain ATs), but this is basically the same as having 90% resistance and 45% defense.

Using that model, let's look at two 1000-hp characters with 90% resistance and 45% defense respectively taking 10000 damage per hit.

Resistance @ 90%
Expected Damage = 500/attack (10000 * 0.1 * 0.5)
therefore 2 attacks until death

Defense @ 45%
Expected Damage = 500/attack (10000 * 0.05)
therefore 2 attacks until death

The first case is arguably false; the second case certainly is. Model's bad. Granularity matters and your model does not support it.

See above. "Hits taken," while harder to work with, is in fact much more important than "damage mitigated."

Hmm... half right. Sort of.

Let's consider 100 damage attacks that are reduced to 80 damage. The resistance character can take ten additional hits before dying (40/50); the defense character can take only five additional hits before death (20/25). That means the resistance character can probably survive ninety-nine attacks and will die on the hundredth, and the defense character can probably survive ninety-nine attacks and will die on the hundredth.

So there are cases where the two characters benefit equally from this effect, right? Hmm. Can we get one where the Resistance character comes out on top? Okay, what about scaling it up the other way? Say the attack deals 4000 damage, which is enough to one-shot either character, but the -dmg effect reduces it to 3200, which will one-shot the defense character but now requires two hits to kill the resistance character. I'm not saying I'd bet money on the defense character, but mathematically it's actually only restoring equilibrium -- the resistance character before had a probable survival time of 2 attacks, and now has a survival time of 4 attacks, whereas the defense character had a probable survival time of 4 attacks and still does.

...So while there are situations that favor the Defense character, none (that I can imagine) favor the Resistance character. Defense derives a greater benefit.

And, and, here's where it gets crazy. Let's play with the magical lies of statistics for a moment.

Our heroes are in dire straits. The attacks are weak -- merely 100 damage base, reduced now to 80 -- but our heroes themselves have been worn down and now only have 200 HP each.

Hmm. That's oddly similar to our original scenario, isn't it? The Resistance character will now die on the fifth subsequent hit, while the Defense character will die on the third. That gives the Resistance character a probable window of nine more attacks he can survive -- he'll die on the tenth. The Defense character, on the other hand, can probably survive eleven more attacks (only two of which will, in our magical world of flat hit chances, actually land), dying on the twelfth.

Defense wins again! ...Unless our characters are regenerating, in which case, flip this pancaking cook, I'm going to bed.

An important qualifier, because if you'd said MOG, it wouldn't be true. Canny, don't you know LPC?

There is no hyperbole in that. And the fear, which I share, is likely more on her end than yours.