-Res and Defiance: Math is Hard


Adeon Hawkwood

 

Posted

I know a few of the Scrapper Forum regulars have been creeping over to the Blaster boards lately, so I was hoping one of those math gurus (or any Blaster ones of which I'm unaware) would be able to lend a hand here.

I've got a Sonic/Elec build planned out, which will be able to chain Scream>Electric Fence>Scream>Shriek without gaps. Given the following data, what kind of a damage boost should I be able to expect?

Perpetual -Res of -26%
Perpetual +Dam of 51.6% (Defiance from the 3 attacks above plus some small set bonuses)

Thanks in advance!

EDIT: There will, of course, be occasional spikes due to Amplify and Build Up, but I was hoping to establish a baseline value.


 

Posted

Boost relative to what?

-res simply acts like a flat multiplier once all damage buffs are factored in; 26% -res means you'll do 26% more damage than you would without it, period.

Using those numbers, assuming you've got 95% from slotting, you'd be looking at base * (1 + 0.95 + 0.516) * 1.26 = base * 2.466 * 1.26 = base * 3.107.

That's about 59% more damage than you'd do with slotting alone, but of course that only applies once you've already got the -res stacked. Also, that's ignoring one additional complication you've missed: resistance debuffs inherently debuff resistance debuff resistance. Or to put it another way: -res makes subsequent -res stronger. Stacking two (with that chain you should actually have brief windows of 3 stacked, no?) -13% debuffs doesn't result in -26%, but in -27.69%; the second one becomes -13 * 1.13 = -14.69. A third -13% debuff would then be -13 * 1.2769 = -16.5997.


 

Posted

Shriek, Scream, Shriek, E-Fence would actually produce better numbers, both in -res and DPS (Shriek has better DPA than Scream).

I personally use Shriek, Scream, E-Fence on my Defender, though.


 

Posted

I'm actually quite sure -Res DOES NOT increase the effects of further -Res. -Res should always use the undebuffed Resistance value when calculating how big portion of the effect will take place. If -Res actually did increase -Res values it would be absurdly powerful. Just think about it, after 100 cycles of that attack chain you would be looking at 1.26^100 * 1.13 Resistance Debuff applied by the next Sonic blast.

Which is to say 1.23 * 10^12 % Res Debuff. In one number that is 1 230 000 000 000 % Res Debuff. Quite absurd, yes?


This is assuming my math is right, but the point is we'd see an exponential increase in the Res Debuff we're doing.


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Posted

Quote:
Originally Posted by Wonderslug View Post
That's about 59% more damage than you'd do with slotting alone, but of course that only applies once you've already got the -res stacked. Also, that's ignoring one additional complication you've missed: resistance debuffs inherently debuff resistance debuff resistance. Or to put it another way: -res makes subsequent -res stronger. Stacking two (with that chain you should actually have brief windows of 3 stacked, no?) -13% debuffs doesn't result in -26%, but in -27.69%; the second one becomes -13 * 1.13 = -14.69. A third -13% debuff would then be -13 * 1.2769 = -16.5997.
DSorrow is correct. Resistance debuffs are always resisted at the un-debuffed resistance value. This is why defense is subject to cascading failure and resistance isn't.
http://wiki.cohtitan.com/wiki/Resistance


 

Posted

Quote:
Originally Posted by DSorrow View Post
Just think about it, after 100 cycles of that attack chain you would be looking at 1.26^100 * 1.13 Resistance Debuff applied by the next Sonic blast.

Which is to say 1.23 * 10^12 % Res Debuff. In one number that is 1 230 000 000 000 % Res Debuff. Quite absurd, yes?
Ignoring the fact that the floor on resistance is -400%, yes, that would be absurd. It would also be impossible, because the debuffs on Shriek and Scream only last 5 and 7 seconds.

And -res has to work that way, unavoidably, because of what goes on under the hood. I keep hoping Arcanaville or Stargazer or somebody will write up the whole attribute/aspect shebang in the guide section some day, but the short version is this:

What we colloquially call "damage" is actually several different attributes, one for each damage type (smashing, fire, toxic, etc.). Resistance to a damage type is governed by the RES aspect of the corresponding attribute. However, the RES aspect attempts to resist *any* change to that attribute; this is why buffs are flagged to ignore resistances, or else you'd frequently resist your own buffs. Because a -res debuff reduces the RES aspect of an attribute, that attribute also becomes less able to resist changes. In other words, debuffing the RES aspect of an attribute not only causes it to be less effective at resisting that damage type, but also makes it less effective at resisting further changes to *any* aspect of that attribute.


 

Posted

Quote:
Originally Posted by Adeon Hawkwood View Post
DSorrow is correct. Resistance debuffs are always resisted at the un-debuffed resistance value. This is why defense is subject to cascading failure and resistance isn't.
http://wiki.cohtitan.com/wiki/Resistance
I'm almost certain the wiki's incorrect, there. *casts Summon Arcanaville*


 

Posted

Resistance debuffs aren't cumulative, nor are subject to cascading failure. DSorrow is indeed correct


 

Posted

I stand corrected, then.


 

Posted

So you trust Silverado but not me *pout*. (just kidding, I'd take his word for something mechanics related to)


 

Posted

Quote:
Originally Posted by Wonderslug View Post
I'm almost certain the wiki's incorrect, there. *casts Summon Arcanaville*
I believe Stargazer tested this (there may have been others, but I remember her article specifically). The wiki is correct. When you debuff a resistance value, the non-debuffed strength is used to resist further debuffs, not the debuffed strength.

Actually, I recall there was a further complication. Unresistable resistance debuffs actually reduced the resistance to further debuffs.

In other words, the game engine seemed to be doing this:

Start: Initial Resistance

Next: Working Resistance = Initial Resistance - Unresistable Resistance debuffs

Last: Final Resistance = Working Resistance - Total Debuffs * (1 - Working Resistance)


I may be misremembering, but that's my recollection.

/Summon Stargazer


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Posted

When are they going to give you your own forum, Arcanaville?


 

Posted

Quote:
Originally Posted by Arcanaville View Post
I believe Stargazer tested this (there may have been others, but I remember her article specifically). The wiki is correct. When you debuff a resistance value, the non-debuffed strength is used to resist further debuffs, not the debuffed strength.

Actually, I recall there was a further complication. Unresistable resistance debuffs actually reduced the resistance to further debuffs.
Aha. That does sound familiar and is probably what I was thinking of, since the impression was cemented in my head by a rad/sonic defender I used to (try) to fight in the arena when defenders still had unresistible PVP debuffs.


 

Posted

Quote:
Originally Posted by boardthug View Post
When are they going to give you your own forum, Arcanaville?
The Arcanaville forum is honestly not all that interesting. Only one person ever posts there, and I think there's only one person reading it as well.


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Posted

OK, good info thus far; thanks to Silverado for fixing the attack chain, and to Wonder and Arcana for the -Res debate. You guys solved some misunderstandings I was harboring about -Res.

On the other side of things, I'm still wondering about the multiplicative effects of the attack chain; i.e., the interplay between Sonic's -Res and the Defiance inherent. I may be misunderstanding both of these, as well, in a number of ways. My current understanding is that Sonic's -Res are only applied by unique attacks--i.e., Scream's debuffs do not stack with themselves--whereas Blaster attacks do stack the Defiance effect; i.e., Scream's 11% Defiance boost becomes 22% after the second application. Further, and I dove into Kossy's excellent Kin/Sonic guide to check my memory, the -Res and +Dam should be multiplicative, not additive, correct?


 

Posted

Resistance debuffs from Sonic Attacks do indeed stack with themselves (ie you can stack Scream up to 2x and Shriek up to 3x because of their duration-recharge ratio) as do the Defiance buffs. Damage buffs are all added together (enhancements, BU, Aim, Defiance) and then applied to the base value of the attack. Resistance debuffs are a multiplier to the total damage (base + buffs)

Resistance stacking and recharge-duration-activation ratios are the reason why Shout does not belong in a good sonic DPS attack chain


 

Posted

Quote:
Originally Posted by StormDevil View Post
the -Res and +Dam should be multiplicative, not additive, correct?
Yes, but technically they don't influence each other multiplicatively: that's just how the math works out. The more straight forward way to look at it is that +Damage increases the damage per attack and -Res increases the damage the target takes per attack independently.

So +Damage will make an attack go up 20% (for example). -Res will make the damage a target takes go up 30%. These two effects happen independently, so an attack that has 100 damage without these effects will get increased to 120 (100 * 1.2), and then when that damage arrives at the target the target will take 156 (120 * 1.3).

It isn't that they affect each other multiplicatively, its that both are independent damage multipliers. Multiplying by two things is the same as multiplying the two things together and then multiplying by the total, which is why it looks like they multiply.

But whenever in doubt, just work it out with one attack step by step, dealing with each factor in turn, and it will generally be obvious which things add and which things multiply.


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Posted

Quote:
Originally Posted by Arcanaville View Post
I believe Stargazer tested this (there may have been others, but I remember her article specifically). The wiki is correct. When you debuff a resistance value, the non-debuffed strength is used to resist further debuffs, not the debuffed strength.

Actually, I recall there was a further complication. Unresistable resistance debuffs actually reduced the resistance to further debuffs.

In other words, the game engine seemed to be doing this:

Start: Initial Resistance

Next: Working Resistance = Initial Resistance - Unresistable Resistance debuffs

Last: Final Resistance = Working Resistance - Total Debuffs * (1 - Working Resistance)


I may be misremembering, but that's my recollection.

/Summon Stargazer

Sorry for the delayed response.

It's almost like that, but not quite.

What we get is:

Final Resistance = Unresistable Resistance + Resistable Resistance * (1 - Unresistable Resistance).

If we like we can separate buffs from debuffs, giving us:

Final Resistance = Unresistable Resistance Buffs - Unresistable Resistance Debuffs + (Resistable Resistance Buffs + Resistable Resistance Debuffs) * (1 - Unresistable Resistance Buffs + Unresistable Resistance Debuffs)

Since Resistance Buffs as a rule are Unresistable, this can generally be simplified to:

Final Resistance = Resistance Buffs - Unresistable Resistance Debuffs - Resistable Resistance Debuffs * (1 - Resistance Buffs + Unresistable Resistance Debuffs)


Looking at it as two steps would give:

Working Resistance = Resistance Buffs - Unresistable Resistance Debuffs
Final Resistance = Working Resistance - Resistable Resistance Debuffs * (1 - Working Resistance),

which is basically the same as what you wrote, with "Total Debuffs" replaced by "Resistable Resistance Debuffs".

(and I think that's what you meant)