-dmg and layered mitigation
Aha! So my KM/EA stalker is even more hax than I thought!
This is just a public service announcement; it concerns mostly melee and support, although others may be interested.
I've seen a few comments about -DMG -- for instance, from Kinetic Melee or Kinetics -- synergizing well with +RES. This is not true. Obviously both reduce damage, but the greatest benefit is to characters with no resistance at all. This would only be of cursory interest (less damage is less damage!) except for how it interacts with other forms of mitigation. Given the choice, it is better to match -DMG with +DEF. Why is this? Well, the low-math explanation (sorry, I don't have a no-math one!) is that Resistance mitigates more damage the more damage the character is taking. If the character has gotten 50% resistance somehow, and they're dealt 1000 damage of the type they resist, they take 500 damage. If that damage is first reduced to 800, they mitigate 400 damage -- they only take 100 less damage, whereas a character who had no Resistance at all takes 200 less damage. Kicking up the numbers a notch, this greatly affects survival lines. Let's deal with the same attacker, who deals 1000 damage ordinarily that has been reduced to 800 by -dmg effects. In the case of a character with 50% resistance, no defense, no regen, and 2000 HP, that difference means they can take one additional hit before dying -- in game terms, a probable 10 attacks till death (five hits will kill them, but we're assuming mobs only hit 50% of the time), while a probable 8 attacks would have killed them if the attacks were dealing 500 damage instead of 400. In the case of a character with no resistance, 25% defense, no regen, and 2000 HP, it also would have taken a probable 8 attacks till death... but that's been increased to 12 by the -dmg effect. They can still only take one more actual hit before death, but "one more hit" (probably) means a lot more to them (since three out of four attacks will miss, rather than every other) than it did to the high Resistance no Defense character. This behavior becomes even more pronounced -- and complicated -- when you factor regen or direct heals into the issue, but I'll leave that be for now. However I would like to take this opportunity to point out to all the corruptors and defenders that unless I'm mis-remembering, there's only one blast set with -dmg. (There are a few other ways of getting it, though...) |
Expected Damage = 200/attack (800*0.5*0.5)
therefore 10 attacks until death
Defence @ 25%
Expected Damage = 200/attack (800*0.25)
therefore 10 attacks until death
This is just a public service announcement; it concerns mostly melee and support, although others may be interested.
I've seen a few comments about -DMG -- for instance, from Kinetic Melee or Kinetics -- synergizing well with +RES. This is not true. Obviously both reduce damage, but the greatest benefit is to characters with no resistance at all. This would only be of cursory interest (less damage is less damage!) except for how it interacts with other forms of mitigation. Given the choice, it is better to match -DMG with +DEF. Why is this? Well, the low-math explanation (sorry, I don't have a no-math one!) is that Resistance mitigates more damage the more damage the character is taking. If the character has gotten 50% resistance somehow, and they're dealt 1000 damage of the type they resist, they take 500 damage. If that damage is first reduced to 800, they mitigate 400 damage -- they only take 100 less damage, whereas a character who had no Resistance at all takes 200 less damage. Kicking up the numbers a notch, this greatly affects survival lines. Let's deal with the same attacker, who deals 1000 damage ordinarily that has been reduced to 800 by -dmg effects. In the case of a character with 50% resistance, no defense, no regen, and 2000 HP, that difference means they can take one additional hit before dying -- in game terms, a probable 10 attacks till death (five hits will kill them, but we're assuming mobs only hit 50% of the time), while a probable 8 attacks would have killed them if the attacks were dealing 500 damage instead of 400. In the case of a character with no resistance, 25% defense, no regen, and 2000 HP, it also would have taken a probable 8 attacks till death... but that's been increased to 12 by the -dmg effect. They can still only take one more actual hit before death, but "one more hit" (probably) means a lot more to them (since three out of four attacks will miss, rather than every other) than it did to the high Resistance no Defense character. This behavior becomes even more pronounced -- and complicated -- when you factor regen or direct heals into the issue, but I'll leave that be for now. However I would like to take this opportunity to point out to all the corruptors and defenders that unless I'm mis-remembering, there's only one blast set with -dmg. (There are a few other ways of getting it, though...) |
If you are indeed correct, I apologize but this seems a bit wacky to me.
Triumphant Defenders Forever
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HelinCarnate:OMG it is so terrible. I have the option to take 3 more powers but no additional slots. Boo F'ing hoo.
I am sorry. I am not an expert. If an attacker hit two teammates aoe style, one has resistance one does not, It doesn't matter if the damage is mitigated for -damage first. The character with resistance should take less damage.
If you are indeed correct, I apologize but this seems a bit wacky to me. |
Why is this? Well, the low-math explanation (sorry, I don't have a no-math one!) is that Resistance mitigates more damage the more damage the character is taking. If the character has gotten 50% resistance somehow, and they're dealt 1000 damage of the type they resist, they take 500 damage. If that damage is first reduced to 800, they mitigate 400 damage -- they only take 100 less damage, whereas a character who had no Resistance at all takes 200 less damage.
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Let's say that that mob attacks you 10 times with that 1000damage attack for a total of 10,000 damage. Now mob Base tohit chance is 50% so from at base you take an average 5000 points of damage.
On your Example character (50% resistance) your resistance would reduce the damage to 2500, so overall you only take 25% of the total damage thrown at you.
Applying the 20% Damage debuff from your example means that the total damage aimed at you is reduced from 10,000 to 8000, then mob miss rate reduces that to 4000, and finally your resistance reduces it to 2000.
Now lets look at a comparable Defense based character. Since mob ToHit is 50% base, a value of 25% Defense is an equivalent damage reduction to your example of 50% resistance.
10,000 damage is reduced to 5000 damage by mob miss rate, then reduced further to 2500 by your defense (Both of those are actually the same step, I'm just listing them separately to show specifically the effectiveness of the Defense value). Same as the resistance only example.
Now lets apply the damage debuff. 10,000 damage is reduces to 8000. Miss rate reduces that to 4000, 25% defense reduces that to 2000. Again, exactly the same as the Resistance based character.
-Damage is equally effective in both of the examples. It is always 20% less damage taken, regardless of if you're defense or resistance based.
-dmg doesn't favor resistance nor defense, in terms of damage mitigated. If the enemy deals 20% less damage, they deal 20% less damage. The debuff mitigates only 100 damage for the character with resistance, which is half as much, but it's mitigating that twice as often because the resist character gets hit more. Your 10-hit vs 12-hit conclusion is just an artifact of the specific numbers you've chosen, and how overkill can dominate the numbers when talking about such large hits. The difference disappears entirely if we look at 500-damage attacks instead, and can flip the other way with the right numbers.
Now, since defense is inherently unreliable, -damage does help smooth out the spikes that tend to kill defense-based characters. But it doesn't mitigate more overall.
It IS erroneous to say that -dmg specifically synergizes well with -res, though. Resists make you take less damage, and -dmg makes you take less damage, but they don't have any synergy in doing so.
Resistance @ 50%
Expected Damage = 200/attack (800*0.5*0.5) therefore 10 attacks until death Defence @ 25% Expected Damage = 200/attack (800*0.25) therefore 10 attacks until death |
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.
Originally Posted by Oathbound
You're making the mistake of looking at it as single attack damage reduction, and not overall mitigation.
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Originally Posted by Hopeling
Your 10-hit vs 12-hit conclusion is just an artifact of the specific numbers you've chosen and how overkill can dominate the numbers when talking about such large hits. The difference disappears entirely if we look at 500-damage attacks instead, and can flip the other way with the right numbers.
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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.
It IS erroneous to say that -dmg specifically synergizes well with -res, though. Resists make you take less damage, and -dmg makes you take less damage, but they don't have any synergy in doing so.
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Of course building for both makes one very sturdy.
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.
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I understand what you are saying. I guess maybe it should become the norm to state how much mitigation one has instead of breaking it into resistance, defence, -tohit and -dmg...
Resistance is stable defensive parameter it always blocks same amount of damage and only a debuff can make it worse for resistance but than again resist debuff is resisted by resistance itself so higher resistance means less debuff as well.
On defense however it is more luck than statistics. As an SR scrapper I can say doing same mission with same parameters can have so much different result it is not even funny. On one run you could easily finish mission with just your attack chain and not using anything else (including hasten, end or heal mitiogations etc) on another run even though you used your inspirations you may end up dead on first boss.
-dam works like resistance therefore adding it as a second mitigation to defense than adding it on a resist character may seem work better. Especially for a character at resist cap -dam won't be as effective as its original values. However -dam works on all front so it is still good to cover that psi, toxic or whatever hole in your resist character has.
...So while there are situations that favor the Defense character, none (that I can imagine) favor the Resistance character. Defense derives a greater benefit.
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The defense-based character dies in 3 hits with or without the debuff. The debuff provides him with no benefit at all.
Similar things happen at 1500 damage, or 650 damage, or 370 damage, or 320 damage, or 282 damage, or any of arbitrarily many other possible values. There's a whole bunch of intervals on which resist gets more benefit from the debuff, even just for the specific res/def/debuff values in this example. All you're really doing here is looking at the graph of
y = 2*ceil(2000/(.5*.8*x)) - 2*ceil(2000/(.5*x))
compared to the graph of
y = 4*ceil(2000/(.8*x)) - 4*ceil(2000/x)
...and neither graph is consistently above the other.
And for small hits, the difference of a fraction of an attack of overkill is swallowed into negligibility.
Also, realistically, enemies that can 2-shot you usually have more than one attack, and their attacks do not usually all deal the same damage. And very far from every enemy can 2-shot a character with 2000 health. And you're very often fighting multiple enemies (of multiple types, each with multiple attacks of different strengths) anyway, so reading too far into exactly how many of a specific attack you can survive is not very illustrative.
Reducing the enemy's damage by 20% means they deal 20% less damage. The granularity of attacks can matter, but doesn't consistently favor one over the other.
Well sure, yeah. It's yet another layer to get mitigation from. But -dmg doesn't have any special bonus when combined with resist, is all I'm saying; a -50% damage debuff reduces incoming damage by half, no matter how much resistance you have. Having 90% resist and 90% -dmg prevents 99% of incoming damage, but so does softcapped defense and 90% -dmg.
With the same 2000 hp, 50% resist/25% defense, and a -20% damage debuff, but an attacker that deals 900 damage instead of 1000, the resist-based character will take 450 per hit, and will die in 5 hits. With the debuff, he'll take 360 per hit, and will die in 6 hits. The debuff bought him one extra hit before death.
The defense-based character dies in 3 hits with or without the debuff. The debuff provides him with no benefit at all. |
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.
Reducing the enemy's damage by 20% means they deal 20% less damage. The granularity of attacks can matter, but doesn't consistently favor one over the other. |
And you're very often fighting multiple enemies (of multiple types with multiple attacks of multiple strengths) anyway, so reading too far into exactly how many of a specific attack you can survive is not very illustrative. |
a -50% damage debuff reduces incoming damage by half |
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.
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Or were you referring to something else?
And yeah, defense wins across the board on granularity in general, for average performance. But that's not really -dmg favoring defense, but the mechanics favoring defense at a more basic level. Although I think, in practice, the effect of granularity tends to be swallowed by other factors, not least of them the inherently unreliable nature of defense.
Resistance is stable defensive parameter it always blocks same amount of damage and only a debuff can make it worse for resistance but than again resist debuff is resisted by resistance itself so higher resistance means less debuff as well.
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On defense however it is more luck than statistics. As an SR scrapper I can say doing same mission with same parameters can have so much different result it is not even funny. On one run you could easily finish mission with just your attack chain and not using anything else (including hasten, end or heal mitiogations etc) on another run even though you used your inspirations you may end up dead on first boss. |
-dam works like resistance therefore adding it as a second mitigation to defense than adding it on a resist character may seem work better. Especially for a character at resist cap -dam won't be as effective as its original values. However -dam works on all front so it is still good to cover that psi, toxic or whatever hole in your resist character has. |
-damage will also add to the mitigation of defence capped toons even if they are at the softcap.
I like -damage because it brings extra surviveability no matter what. I also like being able to say I can give a resistance capped toon 99% psuedo resistance. However, I guess I need to change that to just plain old mitigation now... Definately less sexy...
Actually -tohit is same as +def except it works for everyone that target attacks. Since it is actually a math like (tohit-defense)*acc that checks attack while for damage received it is dam-(dam*resist/100) so -dam and resist are two different mitigations but -tohit and defense are on same mitigation. Now if it was -acc it would be another story. |
I think the one reason why it is better to build for -dmg on top of def softcap is because the softcap is much easier to hit for just about any build, where the resistance cap is not.
I think the one reason why it is better to build for -dmg on top of def softcap is because the softcap is much easier to hit for just about any build, where the resistance cap is not.
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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.
See this thread (if one hasn't already) about -damage.
http://boards.cityofheroes.com/showthread.php?t=294944
Note what I would certainly call synergy talked about between -resistance and -damage.
Applying -resistance to a target first can make any -damage applied more effective.
Doomguide
The reason players are drawn to the -dam and res coupling is that it is easy enough to calculate and it can help shore up a difference between the sets.
For instance, my NA/DP defender offering 48% resistance to S/L can add 53% -dam to aoe damage. This leaves him with an effective amount of S/L resistance of (100-53(dam*.48) or 77.4% effective resistance.
Compared with the Inv tank next to me with 90% S/L res who (due to my -dam) is now at 95.2% effectively.
Before calculating in -dam we are 42% apart on our S/L res. Factoring in the -dam we are only 17.8% apart.
While -dam is equal throughout his analysis, the major flaw is in the ability to state def or res is a constant in game.
The amount of baddies with -def is tremendous in the game and those with +acc is growing. Both of these factors will affect a def based mitigation more than a res bases one.
Res, on the other hand, does not care about either of those factors. It does care about debuffing res but that is only one type of debuff that can be applied. It's a simpler form of mitigation because of this. I also believe that this kind of debuff is less prevalent than -def or +acc on enemy mobs.
In a quirky way, he wins the argument because there will be times that def will fail. It makes the -dam his last layer of defense. At least it's more important to def.
A general mitigation number makes more sense to use, but is very impracticle. You have to throw in too many variables for most players to deal with.
See this thread (if one hasn't already) about -damage.
http://boards.cityofheroes.com/showthread.php?t=294944 Note what I would certainly call synergy talked about between -resistance and -damage. Applying -resistance to a target first can make any -damage applied more effective. Doomguide |
While everyone can argue granularity, let's argue about caps for a second Granularity only takes into account "chance" and let's all remember that after 999,999,999 attacks, 90% Resistance is roughly equal to 45% defense.
With a 20% -dam, 90% Resistance is still roughly equal to 45% defense.
With a 20% -to hit, 90% Resistance is > 45% defense.
With a 20% defense buff, 90% Resistance is > 45% defense.
With a 20% resist buff, 90% Resistance is < 45% defense.
With a 20% -Resist buff, 90% Resistance is >45% defense.
With a 20% -Defense Buff, 90% Resistance is >45% defense.
With an enemy having a 20% to hit buff, 90% Resistance is > 45% Defense.
With a Regeneration based character, -dam, -tohit, defense, and resists all increase it's survivability. HOOZAH!
Based on this information, it's safe to assume that -Damage as a debuff is just as effective for both Resistance and Defense based characters. It's all of the other things that make me lean towards a resistance based Brute/Tank and Defense for a Scrapper/Stalker or regeneration for any archetype. It's also the reason that Willpower is so effective for any of the melee archetypes.
I hate to be "that guy", but if you really want to discuss which is better when concerning layered mitigation... someone should start a "time to live" thread.
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Time to live is really the best way to work this, but I'm having some trouble generating my model. And I'm probably going to have to contradict part of my OP, which is always embarrassing (I have to improve the model of Defense behavior to an outcome tree, rather than treating it as a virtual certainty as I did originally to contrast it with Resistance).
Edit : Oh, and I think you might be wrong about the tohit buff on enemy favoring one or the other. I'd have to write it out to be certain, but you're digging into the 50% miss chance even vs Res.
With 0 defense and 90% resistance, given that resistance includes resistance debuff resistance, the debuff is effectively a 2% resistance debuff. That makes your effective resistance 88%. At 0 defense and 88% resistance, you are hit 50% of the time for 12% of the damage, which works out to 6% of the damage.
With 45% defense and 0 resistance, you are hit 5% of the time for 120% of the damage, which is also 6% of the damage.
My math could easily be screwed up, though. Or my understanding of how the game works. But that's what my napkin math showed me.
TEH WERDZ ON SKREEN HURTZ MI BRANE!
Edit : See discussion below. This is a significant oversimplification and flat-out incorrect in some conclusions.
This is just a public service announcement; it concerns mostly melee and support, although others may be interested.
I've seen a few comments about -DMG -- for instance, from Kinetic Melee or Kinetics -- synergizing well with +RES. This is not true. Obviously both reduce damage, but the greatest benefit is to characters with no resistance at all. This would only be of cursory interest (less damage is less damage!) except for how it interacts with other forms of mitigation. Given the choice, it is better to match -DMG with +DEF.
Why is this? Well, the low-math explanation (sorry, I don't have a no-math one!) is that Resistance mitigates more damage the more damage the character is taking. If the character has gotten 50% resistance somehow, and they're dealt 1000 damage of the type they resist, they take 500 damage. If that damage is first reduced to 800, they mitigate 400 damage -- they only take 100 less damage, whereas a character who had no Resistance at all takes 200 less damage.
Kicking up the numbers a notch, this greatly affects survival lines. Let's deal with the same attacker, who deals 1000 damage ordinarily that has been reduced to 800 by -dmg effects. In the case of a character with 50% resistance, no defense, no regen, and 2000 HP, that difference means they can take one additional hit before dying -- in game terms, a probable 10 attacks till death (five hits will kill them, but we're assuming mobs only hit 50% of the time), while a probable 8 attacks would have killed them if the attacks were dealing 500 damage instead of 400. In the case of a character with no resistance, 25% defense, no regen, and 2000 HP, it also would have taken a probable 8 attacks till death... but that's been increased to 12 by the -dmg effect. They can still only take one more actual hit before death, but "one more hit" (probably) means a lot more to them (since three out of four attacks will miss, rather than every other) than it did to the high Resistance no Defense character.
This behavior becomes even more pronounced -- and complicated -- when you factor regen or direct heals into the issue, but I'll leave that be for now.
However I would like to take this opportunity to point out to all the corruptors and defenders that unless I'm mis-remembering, there's only one blast set with -dmg. (There are a few other ways of getting it, though...)