-dmg and layered mitigation

Mistake early on here. Defense cap works out to 1000 * 0.1, not 0.05.

DamageAdmitted = DamageDelivered * (50% - Defense%/50%)

= 1000 * .05/.5 = 1000 * .10 = 100

Those are the odds of getting hit by that many attacks in a row (and even then, only if we pretend that the enemies we're most worried about being hit multiple times by are all +0 minions). The chance of getting hit at least once, out of 20 incoming attacks, is ~64%. The chance of getting hit at least three times out of 20 incoming attacks (that is, taking at least 3x the average amount of damage from those attacks, since on average you'd get hit only once - aka, a large spike in incoming damage) is ~8%, which is low, but less unlikely than missing with a capped hit chance, and I'm sure you've seen how that happens pretty regularly. It's unlikely, but in the same sense that Scrapper crits are unlikely: you can't really count on when it will happen, but it definitely will happen, and it will happen frequently enough to matter. And many enemies, especially the ones you'd be worried about getting hit by, have some bonus accuracy from rank or level or baked into their powers, and they'll be even more likely to hit you.

Whoa. So that isn't correct. In fact I'm not precisely certain what you are doing with those numbers.

I'm so not sure I'm going to start from scratch. Suppose a critter attacks you 100 times with an attack that hits for 100 points of damage base. If this is a normal critter with base tohit, then 50% of those attacks will land by default with no defense. We then have:

0% resistance, 0% defense:

100 attacks * 0.5 basetohit = 50 attacks land.
100 points of damage per attack * (1 - 0 resistance) = 100 points of damage per attack.
Total damage = 50 * 100 = 5000.

75% resistance, 0% defense:

100 attacks * 0.5 basetohit = 50 attacks land.
100 points of damage per attack * (1 - 0.75 resistance) = 25 points of damage per attack.
Total damage = 50 * 25 = 1250. That's 25% of 5000, which means this player takes 25% of the total damage someone with no defense and no resistance would take. That's what we call "75% damage mitigation"

90% resistance, 0% defense:

100 attacks * 0.5 basetohit = 50 attacks land.
100 points of damage per attack * (1 - 0.9 resistance) = 10 points of damage per attack.
Total damage = 50 * 10 = 500. That's 10% of 5000, which means this player takes 10% of the total damage someone with no defense and no resistance would take. That's what we call "90% damage mitigation"

0% resistance, 45% defense:

100 attacks * (0.5 basetohit - 0.45) = 5 attacks land.
100 points of damage per attack * (1 - 0 resistance) = 100 points of damage per attack.
Total damage = 5 * 100 = 500. That's 10% of 5000, which means this player also takes 10% of the total damage someone with no defense and no resistance would take. That's why we call 45% defense also "90% damage mitigation" (at base tohit). Aka the soft cap.

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.

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.

No, I mean mathematically continuous, as in a smooth line if plotted versus time at any time scale.

The closer incoming damage (and HP recovery) are to this, the less likely random walks that will kill you become. More usefully, the smaller the quanta of damage you're facing are as a percentage of your HP, the less likely this is. 10 HP damage per hit is a big deal if you have 50 HP, but not such a big deal if you have 2400.

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

Yes, but I didn't say it because I missed that. I said it because it was an example of what I meant when I said "continuous", which your response indicated was not clear to you. "Continuous" meaning the delta from moment to moment is small, and specifically "small" is defined here relative to your HP.

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.

Actually, what Uberguy said was that the more continuous - and thus less bursty - damage and health recovery are, all other things being equal, the less likely it is that an unlucky burst will kill you quicker than the average calculations would predict. Which is true.

In other words, 100 dps sent to you as 1 attack dealing 1 point of damage every 5 milliseconds with a 50% chance to hit is much less dangerous than 100 dps sent to you as 1 attack dealing 1,000 points of damage every 5 seconds with a 50% chance to hit, because the first case is much more likely to generate rates of damage very close to the calculated average most of the time. The second case is almost *never* going to generate exactly the calculated damage in any short stretch of time.

The delta Uberguy is referring to is the damage delta from moment to moment, not the time delta.

Indeed. Thank you.

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, we'll have to fix that!

Contentiousness of health recovery relative to total heal does matter if incoming damage is also highly non-continuous compared to total health. The reason is simply because if you recover health in (large) discrete quanta, and you suffer damage in (large) discrete quanta, you might suffer two large quanta of damage before you get your next quanta of healing. This is just an extension of models we've discussed above, which I think we now (or possibly all along) agreed on. It's just that, initially, I was holding HP recovery constant to keep the discussion about non-continuous damage simpler.

If your HP recovery is continuous and your incoming damage is overwhelms it, it mostly doesn't matter if the incoming damage overwhelms your HP recovery in a continuous or discrete way - it may just affect when exactly you are defeated if the damage is arriving in large, spaced out chunks. However, if your incoming damage and HP recovery are comparable, you could still die when the averages wouldn't suggest it because you didn't get a chunk of HP back in time to save you from the next chunk of damage. It's related to but a bit more complex than the case of discrete damage and time-continuous healing.

Has anyone gone over to the test server to see what changes they added to Resistance for IO Set bonuses? I noticed they changed a lot of them to include S/L damage resistance.

Going one step further with what Yogi stated earlier about layered mitigation, what would the best combination be for adding in things like absorb? I might go through and see what each melee armor has going for it and assign an arbitrary number. I'm worried that Willpower is still going to be the best, though. Bio might be close.

Buffs
Resistance
Defense
Absorb
Regeneration

Debuffs
-Damage
-To Hit
-Recharge

Any ideas on making a TTL calculator?

Werner create a spreadsheet that calculated a numerical score for survival that I believe was predicated on TTL. It almost certainly has not been updated to account for Absorb mechanics, but everything else should be there.

Note that such a calculator is based on average performance. I think he had some facility for fudge factors for things where averages were a poor representation, or just general cases where the spreadsheet wasn't good at scoring how good something was at keeping you alive due to mechanical complexity.

More with the disagreeable agreements. I said the interval and magnitude of health recovery respect only interval and magnitude of damage, to which you said no, they matter relative to interval and magnitude of damage.

So yes. If your health recovery events are spaced further apart then the damage intervals, making them faster will matter even if the overall magnitude of health recovery is kept the same. If they are not, it won't, no matter how long or short those intervals actually are.

The relationship of health total and (edit: *continuous*/low-interval) health recovery magnitude seems significant only because if you're taking damage you care about, it's going to be large amounts of your health, so mitigating large amounts of that damage with health recovery is also going to be a noticeable portion of your health probably. And again, it isn't a terribly important distinction to make, because it's almost always going to be that way, but damnit Jim, I'm a logician, not an engineer.

Further edit: As I said earlier, higher-frequency lower-magnitude damage actually responds better to discrete (higher interval) health recovery, magnitude of low- or high- interval recovery events being equal, because the burst recovery kicks you out of a health total where that low magnitude is still a significant % into one where it's not. It is mitigation bursting, which works to reduce the severity of continuous damage just like burst damage works to reduce the effectiveness of continuous recovery.

waaaahhhhhhrrrgggghhhh.

Conversely, I love 90% across-the-board damage mitigation without having to be a tanker or brute. Specifically a Stone, Dark or Invuln tanker or a Stone brute. Also, we showed several ways in which Defense is superior to Resistance in this thread.

You seem to be assuming the intervals are constant. The intervals for healing may constant, barring various debuffs, but the intervals for damage are random, because of the chance to miss/hit that's evaluated for every attack. So if you are hit more than an average amount in a window where your heal has not recharged (or your +regen has not "ticked"), you may die when the average analysis of HP recovery says you would not.

No. Logician. Statements are true or false; non-constant intervals can make statement sometimes true and sometimes false, but that isn't my concern.

Are we powerlevelling our post counts?

Then it was unwise of you to tackle this topic, because a correct treatment of it calls for considering that non-constant interval behavior. Making statements that ignore it don't do the topic service.

I'm posting because I am seeing what appears to be incomplete or incorrect understanding of topics, most of which are actually relevant to the topic of layered mitigation (assuming one is willing to consider HP recovery "mitigation", and I am someone who is so willing).

If you think what I am posting is factually incorrect, then please offer correction (or ask clarifying questions). Descending into deeply semantic sparring over logic vs. engineering suggests you don't really care any more about the topic at hand. Which is fine, but I still do, so if, in your non-caring replies I see what looks like misunderstanding or error, I will still reply to it. After all, you and I (probably) aren't the only ones reading the thread.

Actually, no. Assuming both characters are actually under the influence of that debuff, both will take 20% more damage when under the influence of a -20% resistable resistance debuff (and essentially all normal critter debuffs are resistable).

The resist set will resist 90% of the debuff, reducing it to -2%. Their effective resistance will then be 88%. The defense set will not resist the debuff, and their resistance will be -20% resistance.

The damage formula for resistance is Net Damage = Base Damage * (1 - Resistance).

For the resist character, that will be Base Damage * (1 - 0.88) = 0.12 * Base damage. That's 20% more damage than before, when they were taking 0.10 * Base Damage: (0.12 * Base) / (0.10 * Base) = 0.12/0.10 = 1.2 = 20% more.

For the defense character, that will be Base * (1 - -0.2) = Base * (1.2) = 1.2 * Base Damage which is also 20% more than before.

Yes.



My idea is that in the long run, writing code that calculates the values is probably better than attempting to do the entire thing in Excel.

(That's not a joke by the way, that's my I13 defensive secondary proliferation spreadsheet partially updated to I23, or rather a picture of it. Don't make the same mistake: a mind is a terrible thing to waste.)