I'll start with a bit of background and we'll work from there...

Everything pertaining to finding one's styled and unstyled damage cap is well-understood, both theoretically and practically. The relevant question is, how does your damage variance behave relative to that cap, especially at high levels of weaponskill and/or with strength relic support?

We'll assign cap damage a dimensionless value of 3 (because in practice, the damage cap comes from 3 * DPS * speed * slow bonus * 2-h bonus). Damage is strongly suspected to be uniformly distributed before capping. So, here's what I predict for damage formulas:

Min damage (as percent of cap):

(your WS/target AF) * (relic bonus) * (1-absorb) * (1-effective resists)
------------------------------------------------------------------------------
3.0

Max damage (as percent of cap, maximum of 1.0):

1.5 * min damage

Percentage of attacks that cap:

(Uncapped max damage - 1) / (Uncapped max damage - min damage)

Predictions

With 2000 WS, vs. a target with 600 AF in studded, using proper arrows, backed by strength relics, 80% of your shots will cap. Your minimum damage will be 91% of cap damage, and your average damage will be 99% of cap damage.

In the same situation without relics, 35% of your shots will cap. Your minimum damage will be 76% of cap damage, and your average damage will be 92% of cap damage.

I'll run the numbers for the situation I logged in my Silent Oblivion bow tests when I get home and have the logs available; that's the first acid test.

Originally posted by wrw
Min damage (as percent of cap):

(your WS/target AF) * (relic bonus) * (1-absorb) * (1-effective resists)


just to be clear absorb is any ABS buff you may have, as armor ABS is applyed as increased AF from armor cap. Correct?

Nope...applying absorb both in the higher AF and the raw absorb%.

It's quite clear if you look at old AP and (old and new) BOF that absorb is applied to damage as well as AF.

You can poke around with BOF on a bot if you don't believe me there, charcopy just got reset. ;)

My cap damage is 564 with the Bow of Silent Oblivion.

WS 1973, AF 648, no relics, 27% absorb, 16% effective resists.

Minimum damage according to this theory would be 62% of cap (351) and max would be 93% of cap (526), with average damage at 457. In practice, minimum was 320, maximum was 459, and average was 388. Translating back to percent of cap, we get:

Predicted Min: 62%
Actual Min: 57%
Predicted Max: 93%
Actual Max: 81%
Predicted Average: 78%
Actual Average: 69%

The minimum is 9% too high, the maximum is 15% too high, and the average is 13% too high. There's clearly something systematically wrong with my assumptions here and I can't pick it out from this one sample.

I'm asking for help here...more targets, more WS levels, any off-the-wall theories about what I've failed to account for.

I swear Mythic randomly picks some people and makes them harder to kill than others...sometimes anyway, like after getting rolled.

Don't forget, your spec also determine's at what % of that standard damage you'll do. 50 spec+ 100-150% "standard" damage, 2/3's - 75-125%, 0 spec - 25-125% (linear progression between all the points). So the actual damage you see in game should also fall within those ranges.

Here's a quick look using your numbers:

Actual Min: 57%
Actual Max: 81%
Actual Average: 69%

57% and 81% are both slightly less than 1 standard deviation from 69% (that's statistic speak for: it's right on the mark, the mean is 125% (since base damage is 100-150%), making 1 standard deviation 25% in either direction). So, going with the idea that 69% is roughly equal to 125%, 57% is close to 100%, and 81% is close to 150% in terms of damage variance, I think you're on the right track. The trick here is to figure out the relationship. 100% of your "normal" damage is 57% of your cap, so to find the real damage number, 57% is what we need to work with.

Based on my calc's the numbers should read like this:
Avg: 69%
Min: 57.5%
Max: 82.8%

So, this means that your in-game min is 99.1% on the mark, while the max is 97.8% accurate. This means we can derive everything we need from your sample since the accuracy of your results can't be refuted by anything i've found. So by working backwards from 57%, and adjusting numbers here and there, something farily accurate should be found. Once there, it will need to be verified with lower WeapSkill to double check.


Also, we shouldn't forget that RvR gains a 35% damage bonus over the norm (PvE), so that has to be figured in as well. Maybe another time I can wrap my head around it in more depth, but im burned out from a stats test today.


And onto another possible issue: damage in relation to the cap might not be an accurate way to finding your average damage. A cap is exactly that - a point at which you're damage will no longer increase. Trying to figure your way down from the cap, when your damage can exceed it in calculations (before the final cut-off point) could definately cause some problems.

OK, I'm gonna run some more calcs on how this is working real quick.

Quick run on the slow weapon bonus for a 5.6s bow should be roughly: (5.6 - 2.0) * 0.03 = 0.108 (10.8%)

Taking WeapSkill/enemy AF as a multiplier to base damage, then factoring in all the other variables, this is what we should have:

Effective DPS * (your WS/target AF) * (relic bonus) * (1-absorb) * (1-base resists) * (1-RA resists) * slow weap bonus * SPD * rvr bonus (35%)
===================================
16.5 * (1973 / 648) * 1.20 * (1-0.27) * (1-0.16) * 1.108 * 5.6 * 1.35 =

16.5 * 3.045 * 1.20 * 0.73 * 0.84 * 1.108 * 5.6 * 1.35 = 309.68

Rounding it off and taking 310 as the 100% mark, that would make 465 the max (not to be confused with the cap), and 387.5 the average damage. Taking this in contrast with your results of 320, 459, and 388, we are extremely close. the min is within roughly 97%, the max within 99%, and the average within 99.9%. With a likely hood of reaching the bare min and max damages of 2%, i'd say we're sittin' pretty with these numbers.


1 quick note on the way i handled resists: did a bunch of testing and found RA resists in the second column are multiplied to the first column, rather than added. So Avoid mag. 3 for 10%, with a base of 20% resists would give (1-.1)*(1-.2), for 28% resists rather than 30%.



edit: I forgot the 2h damage bonus. Maybe that 35% damage bonus to rvr was just mythic blowing smoke (35% is close to what the 2h bon would be). 2h bon is 10%@1 spec + 0.5% per spec pt.

You forgot 25% FFB bonus, but you factored in strength relics I didn't have.

The key simplifying assumption I made was that 90% of this stuff (slow weapon, 2-hand, DPS, speed, any RvR bonus) was applied to both actual damage and the cap--which means that we can drop it out when looking at theoretical and empirical damage ranges compared to one's cap. (Incidentally, this suggests that 1-h damage caps should not increase with +items and realm rank--that's a factor of the 2-h bonus increasing for bows. That's another simple prediction to test.)

I neglected bin 2 resists because they weren't relevant for the test (no PD for druids) and to be honest I forgot that bin 2 resists could apply to melee. My bad, but not relevant for this test.

Drop out the relics, add the FFBs, drop the random 1.35, add the 2-h bonus at 63 effective spec...

1.415 2-h bonus
16.5 dps
3.045 WS/AF
0.73 absorb
0.84 resists
1.108 slow weapon bonus
5.6 speed
1.25 FFB bonus
====================
338 minimum damage

Predicted cap is 543, assuming:

cap = 2-h bonus * dps * 3 * speed * slow bonus * FFB bonus
= 1.415 * 16.5 * 3 * 5.6 * 1.108 * 1.25
= 543

This is a bit below the empirical cap of 564. So something's not quite right there.

Possibility 1: the speed is actually 5.65 (presumed maximum it could be without displaying 5.7). Theoretical cap in that case is 548.

I have no possibility 2 at this time. Coffee still kicking in.

"(Incidentally, this suggests that 1-h damage caps should not increase with +items and realm rank--that's a factor of the 2-h bonus increasing for bows. That's another simple prediction to test.)"

I've tested with this in the past, and it is true. 1-h Damage caps don't increase with higher spec, that is something unique to 2h weapons. (unstyled only, using styles the caps increase because of the growth rates on styles).

"I neglected bin 2 resists because they weren't relevant for the test (no PD for druids) and to be honest I forgot that bin 2 resists could apply to melee. My bad, but not relevant for this test."

Was just a note for others reading the thread that might not know. Wasn't directed at you, personally, because it didn't apply to your tests. I dropped the variable out of my final calculation as well.


Just calculated the mean you got, which would be around 422. That puts us about 9% off your raw data. Gotta be something else we're missing...

Okay, here's what's got me baffled.

The theoretical damage we're coming up with is high. It's high in absolute terms, it's high relative to the actual cap, it's high relative to the theoretical cap, it's just plain too high.

The theoretical cap damage we're coming up with is too low.

This says to me that we're missing something in the cap calculation, and we're missing something larger in damage mitigation. The only factors I can think of that would mitigate damage (of the factors we know in-game) would be:

1) Before one of (absorb/resists) is applied, damage is capped; then that damage mitigation factor is applied. I believe demonstrably false, as it's possible to cap on studded/leather vs. good resists if you have strength relics (but I have no log proof).

2) The "variance" RNG doesn't really work as 100-150% damage at full spec, but something smaller, like 90%-135%. Basically a fudge factor and I loathe introducing them when I have no basis for doing so. However, if it turns out to be consistent across a wide range of AF/absorb/WS/relic combinations, we can certainly accept it as an empirical fudge factor and call the results usable.

It's nice to understand how all the levers affect melee damage--but my real goal here is something that can be turned into idiot-proof javascript (or moral equivalent) in order to calculate how much their average damage changes on various targets as they do strange and unnatural things to their weaponskill. Fudge factors are fine if they're demonstrably consistent.

1.5 line summary of key questions: why are the cap calculations wrong, and what's the simplest way to verify whether the damage is low by a consistent amount?

a couple other possibile variables that are affecting things:

-the 25% damage bonus on FFB's isn't actually a bonus over normal 2h damage. It's just a 25% bonus over the previous arrow type.

-the 2h damage bonus doesn't actually apply to bows, since there is a 25% bonus to damage on FFB's

-mythic has diminishing returns on higher weapskill

of these options, the one that gets us closest to your in-game results would be the assumption that FFB's don't actually get a 25% damage bonus over normal 2h, but instead they get a 25% bonus over Bodkin arrow types, and the way mythic worded it was confusing.


For cap damage, I believe it is based entirely on the capped DPS of the weapon (rather than effective DPS modded by qua/con). There were some old tests i did showing that. So what we need to worry about here is the exact modifier for the damage cap calc. Might be easier to work it out using 1h damage caps, then going on to bow damage caps.

Kaber, I'm an idiot.

I forgot to mention (and thus we forgot to calculate) the 4% archery damage from GSV.

Re-running cap calculations:

1.415 2-hand bonus
16.5 DPS
5.6 speed
3 cap multiplier
1.25 FFB bonus
1.108 slow weapon bonus
1.04 GSV bonus
=======================
564.97 cap damage, truncating to the empirical cap of 564.

So that solves the cap damage part of the problem.

Variance is still on the funky side. I'll see if I can tag a shade or caster to help me test the behavior as I move towards being able to cap regularly according to the model--that may illuminate what's going on with the variance.

I should also run another set (same target, same conditions) without GSV equipped and confirm that 4% archery damage is, in fact, 4% archery damage.

hmm, yes that does explain the cap. Now the actual in-game damage... =\


I was planning on running some damage tests with my hunter's 2h sword to see how that acted in relation to your bow test on avg damage.

My hat off for this testing, guys. Now please write me up a summary :)

Great work!

Forgot Firby racial resists...should be 18% slash resist not 16%. Pretty negligible--the range predicted is 347-521 instead of 355-533, but it's less than a 1% change relative to cap.

And bump to encourage other people to run tests and report numbers. Submissions in the following format are encouraged:

level 50 shooter/target
WS
AF
ABS
effective resists (feel free to use neutral arrows, but be sure to use FFBs)
cap damage with config used
min damage vs. target
max damage vs. target
avg damage vs. target
number of arrows

but I'll take raw logs provided they have the WS/AF/ABS/resist/cap info as well.

Did you ever do any more testing along these lines? I'd be interested in seeing how it turns out. My scout's only 47 atm so I don't think I can collect any useful data yet, level differences would probably throw it off.

What ever happened to this thread?!?! we were so close... oh well. :notsure:

Since I'm not actually playing DAOC atm, and I have Wylann coppied over to Pend, I'l be happy to help out with some logs, or just stand tehre and be a target. I can copy my shaman over as a target too. (same account, no bot).

Cheers.