Defense vs. Dodge/avoidance

squirrelloid

I'm trying to figure out what the actual numbers are to determine what's the best investment for Heroic+ gear for my Glacier AT.

AFAIK, the effect of defense (at the +x% defense level of abstraction) is to reduce damage by 1/(1+def), so +100% defense = 1/2 damage. I assume this formula holds true for all characters, but various players insisted in-game that ATs have a 'softer cap' - i don't even know what that could possibly mean. Do AT's calculate the effect of defense differently?

I'm also trying to figure out what the dodge/avoidance curves look like, or just get some numbers on what dodge chance and avoidance percent are when you have no other investment except from primary gear. Unfortunately, the relevant stickied thread's links are mostly broken - if anyone has a formula for dodge and avoidance or a working link to the relevant posts, that would be helpful.

pantagruel01

ATs behave differently on offense -- if you have +X% damage from one source, +Y% damage from another source, an AT will get (X+Y)% from both combined, a freeform will get somewhat less. It is not clear why this is true.

aiqa

There is not any diminishing return on the +X% damage bonus you get from offense. There is a diminishing retun on how much +X% you get per point of offense, but not the +X% itself.

You can find a lot of scaling info here:
http://www.arcgames.com/en/forums#/discussion/247878/gift-horse/p1

raighn

To my knowledge, the damage "resistance" calculation for defense is what you have stated 1/(1+def)... however... 100 defense does NOT equate to 50% damage reduction... it does equal 50% damage resistance though... that may sound a bit odd... but just a little testing with values has lead me to understand that 50% damage resistance is closer to 25% damage reduction (give or take 5%)...

Avoidance however is a direct translation to damage reduction. 50% avoidance = 50% damage reduction. Unless you have a reliably high dodge chance though, then you'll find it more beneficial to invest into Defense.

Additionally, the conversion of resistance to reduction is on a curve, it takes progressively more resistant to gain more reduction. 50% resistance from a passive +50% resistance from defense will get you roughly 37% reduction from what I've seen. This is exactly why blocking can grant you 200% resistance and yet damage is still not reduced to 0. The only way to effectively reduce damage to 0 (or 1 given how the game works) is through flat reductions stacked on top of resistances.

I'm not sure on the exact formula for avoidance, but... the base is 20% and some calculations from my gear comes up with a rate of +1% per 2.75~ points of avoidance from gear. (the actual result I got was something like 2.75193... and so on and so forth with no end in sight...)

blkjackwilliams

I think the last time I checked it was when they nerfed the dodge/avoidance and crit curves. Back then it was

100 - (100 / (1.25 + Avoid percentage + (Avoidance Rating * .006994))) If they didn't change anything since then it should still be that.

Defense is Damage/ (1 + Defense decimal + Resistance Decimal) when you block or are affected by Redirect force you divide the result of that again by your Bonus Resistance Value. I believe Block and Redirected force are both on the same layer called bonus resistance, but it's been forever since I've tested that and cant remember 100%

AT's and FFs both have the same curves for defense.

aiqa wrote: »

There is not any diminishing return on the +X% damage bonus you get from offense. There is a diminishing retun on how much +X% you get per point of offense, but not the +X% itself.

You can find a lot of scaling info here:
http://www.arcgames.com/en/forums#/discussion/247878/gift-horse/p1

I don't think he meant offense as in the stat, rather offense as in offensive buffs both additive and severity level, which do DR on some curve other than just the normal additive curve. I'm currently trying to work it out, but it's a PITA to get all the damage buff information needed. Annoyingly enough I have a whole weekend I could have pulled numbers, but It's not letting me on PTS right now, so hopefully that gets fixed and I can start doing tedious things again for fun and profit. Well not really profitable, but fun in it's own little psychotic way.

Funny thing, even the role bonus seems to DR, though in a different way to the other buffs.

squirrelloid

raighn wrote: »

To my knowledge, the damage "resistance" calculation for defense is what you have stated 1/(1+def)... however... 100 defense does NOT equate to 50% damage reduction... it does equal 50% damage resistance though... that may sound a bit odd... but just a little testing with values has lead me to understand that 50% damage resistance is closer to 25% damage reduction (give or take 5%)...

I think we're talking past each other because i was being imprecise. I thought damage reduction = 1 / (1+damage resistance). Note that this never lets you get to 100% damage reduction. (Actually, that would be damage that gets through, so 1 - damage reduction).

From the relevant sticky, one of the links that does work is: http://i.imgur.com/mfjm9.png, which says there's a linear relationship between defense and damage 'resistance'. (Sorry, i kept referring to damage 'resistance' as %def, that's my being imprecise because I wasn't looking at my character screen). Maybe that's no longer true, i'm not sure, but it seems to roughly match what I'm seeing on my character sheet.

Note this matches with your math. 50% damage resistance -> 1/(1+.5) = 1/1.5 = 2/3 damage suffered (~33% reduced), which is about what you said.

Anyway, assume for the moment that the character has, let's see, (6.5+6.5+9.5+19+19+29) x 1.8 spec = 161 defense = +38.664% resistance from gear, and 70+% resistance from invulnerability = ~108% resistance. Is it worth investing in more defense (another +20 heroic type + mod (say 20 for easy math) x 1.8) or avoidance/dodge to maximize reduction of incoming damage? Obviously this depends on exactly how big invulnerability is, but it's approximately +18% resistance, so even in the minimal case listed, we go from 1/2.08 to 1/2.26 damage suffered a ~3.8% difference in damage taken. If a dodge mod increased dodge chance by 19%, that alone would be equal to the 10% increase in defense. (More generally, the combined dodge/avoidance gains would have to result in a 3.8% average damage avoidance). And the higher Invulnerability gets, or the more defense you manage to pull from elsewhere, the easier it gets to outweigh the marginal change in defense.

Side question: the flat damage reduction from invulnerability - does that happen before or after damage reduction or dodge/avoidance? What's the order of operations here?

blkjackwilliams wrote: »

I think the last time I checked it was when they nerfed the dodge/avoidance and crit curves. Back then it was

100 - (100 / (1.25 + Avoid percentage + (Avoidance Rating * .006994))) If they didn't change anything since then it should still be that.

What's 'avoid percentage' vs. 'avoidance rating'? Is avoidance percentage the flat 20% everyone starts with?

Any idea on the formula for dodge chance?

Edit:

aiqa wrote: »

There is not any diminishing return on the +X% damage bonus you get from offense. There is a diminishing retun on how much +X% you get per point of offense, but not the +X% itself.

You can find a lot of scaling info here:
http://www.arcgames.com/en/forums#/discussion/247878/gift-horse/p1

Nevermind, this doesn't give me the formulas, but it does give me the quite relevant breakpoints.

And wow, heroic avoidance primary with dodge core is vastly better than stacking more defense. Over 2x as good. Still interested in the order of operations question for when the flat damage reduction happens.

blkjackwilliams

squirrelloid wrote: »

What's 'avoid percentage' vs. 'avoidance rating'? Is avoidance percentage the flat 20% everyone starts with?

Any idea on the formula for dodge chance?

The 20% everyone starts with is the 1.25

1 - (1/1.25)= .2 or 20%

Avoidance rating is the large number you get from LR, Gear, Fluidity, and maybe some other sources I'm not remembering. Avoidance percentage is when a power doesn't say "Avoidance Rating" and instead say it grants "X% Avoidance". The power doesn't add a flat amount of avoidance, instead it's just more potent rating that happens to be given in such small amounts that you don't really benefit from the potency. Example of powers that grant avoidance percentage are Swinging W/advantage, Quarry, and Dragon Kick W/advantage (IIRC that's the one with lashing dragon tail).

Can't remember dodge off the top of my head. I'll see if I can find it somewhere for you. Generally speaking though, if you're already stacking dodge, and have and offense/defense loop going, it's usually better to just keep stacking dodge. There's an escalating return to dodge/avoid. However if you don't already have dodge/avoid, it's a good idea to calculate mitigation and see if a given value of resist may be better.

carrionbaggage

squirrelloid wrote: »

aiqa wrote: »

There is not any diminishing return on the +X% damage bonus you get from offense. There is a diminishing retun on how much +X% you get per point of offense, but not the +X% itself.

You can find a lot of scaling info here:
http://www.arcgames.com/en/forums#/discussion/247878/gift-horse/p1

Nevermind, this doesn't give me the formulas, but it does give me the quite relevant breakpoints.

Check out the later posts in that thread. jimhsua posted some formulas along with graphs.

flowcyto

Could also check Jim's sticky thread- he made a worksheet using all the derived algorithms.
http://www.arcgames.com/en/forums#/discussion/250970/character-sheet-calculating-in-game-combat-values

Selphea also had a worksheet for comparing gear setups, though its a bit older:
http://www.fulldive.nu/2014/03/02/champions-online-gear-comparison/

pantagruel01

blkjackwilliams wrote: »

I don't think he meant offense as in the stat, rather offense as in offensive buffs both additive and severity level, which do DR on some curve other than just the normal additive curve. I'm currently trying to work it out, but it's a PITA to get all the damage buff information needed.

The last time I did numbers on this, which was years ago, Isometry worked out that the formula was 'real damage bonus = nominal bonus * 900 / (nominal bonus + 900)'. This does not apply to archetypes, for them real damage bonus and nominal bonus are the same.
​​

blkjackwilliams

pantagruel01 wrote: »

blkjackwilliams wrote: »

I don't think he meant offense as in the stat, rather offense as in offensive buffs both additive and severity level, which do DR on some curve other than just the normal additive curve. I'm currently trying to work it out, but it's a PITA to get all the damage buff information needed.

The last time I did numbers on this, which was years ago, Isometry worked out that the formula was 'real damage bonus = nominal bonus * 900 / (nominal bonus + 900)'. This does not apply to archetypes, for them real damage bonus and nominal bonus are the same.
​​

Interesting.

What's the nominal bonus defined as? Is that the stated bonus tally from all sources? If not, how do you determine the nominal Bonus?

pantagruel01

blkjackwilliams wrote: »

What's the nominal bonus defined as? Is that the stated bonus tally from all sources? If not, how do you determine the nominal Bonus?

Its the stated bonus tally from all sources that apply a normal-layer bonus (most notably, Offense provides a crit-layer bonus, not a normal-layer bonus).​​

blkjackwilliams

Hmm, I figured that's what you meant, but was hoping not.

Unfortunately that doesn't seem to fit. At least it doesn't match any values that I've got recorded, and I can't predict any values from a given combination of buffs point using it. Unless I'm missing something, which is possible. However, it's likely they softened the drop-off a bit, at some point previously, to make damage buffs more potent.

pantagruel01

Okay, lemme do some testing. It looks like stars don't count into the formula. On a character with 5 strength and no superstats or gear (total +1.4%), annihilate is 1162 damage, implying a base of 1146. Using controlled buffs:

• 1.4%: 1162 (1.4%)
• 51.4%: 1698 (48.2%). Calculated value per above formula is (51.4*900)/(951.4) = 48.6%
• 101.4%: 2193 (91.4%). Calculated value per above formula is 91.1%
• 151.4%: 2631 (129.6%). Calculated value per above formula is 129.6%

The formula isn't perfect, or I'm leaving out a bonus I wasn't aware of, but it's very close, so the real formula is probably similar.​​

blkjackwilliams

Storm Of Arrows(Hybrid/LR passive):

Displayed damage W/ Just SS's and stars is 511

Damage buffs 24(con);19(Int);21(Ego);23(Ranged);8(stars);80(Form);42(Ego surge) Total bonus 217 Offense is 11%

Expected bonus -> (209*900)/1109=169.612263 + 8 -> 277.6123

Implied base damage -> 511 / 1.11 -> 460.36 / 1.873313 = 245.746632

Projected damage -> 245.746632 * 2.776123 = 682.222877 * 1.11 = 757.267394

Displayed damage -> 748

So just a bit more severe at the high end. Like I said they probably just modified it at some point, though honestly with the lack of value to an offensive passive I would not have expected it to become more strict, rather I would have thought they'd loosen it up a bit.

It's close enough for right now, but I do wonder how Role damage increases fit in there.