A Call to Arms - MoP Mechanics Testing

Warning: Theorycraft inside.

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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Mon Jul 23, 2012 10:49 am

aaaaaaaaaaaaaaaah~!
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Mon Jul 23, 2012 11:08 am

Fitting of Klaud's latest data sets:
CS: expected 130% weapon damage + 913
Code: Select all
cs_fit =

     General model:
     cs_fit(x) = 0.6504*(a*x+b)
     Coefficients (with 95% confidence bounds):
       a =         1.3  (1.299, 1.301)
       b =       913.1  (912.1, 914.1)

cs_gof =

           sse: 0.0031
       rsquare: 1.0000
           dfe: 1
    adjrsquare: 1.0000
          rmse: 0.0558

Had to only use the first 3 data points again, due to PvP gloves, but the final 3 data points perfectly match the 5% extra multiplicative scaling. Tooltip confirmed again.

Censure: expected (126+0.11*sp)*5 = 630 + 0.55*sp
Code: Select all
cens_fit =

     General model:
     cens_fit(x) = a*x+b
     Coefficients (with 95% confidence bounds):
       a =      0.5501  (0.5499, 0.5502)
       b =       629.9  (628.9, 630.9)

cens_gof =

           sse: 0.9455
       rsquare: 1.0000
           dfe: 4
    adjrsquare: 1.0000
          rmse: 0.4862

Tooltip confirmed.

Seal of Truth: expected 14% weapon damage (unnormalized)
Code: Select all
sot_fit =

     General model:
     sot_fit(x) = a*x
     Coefficients (with 95% confidence bounds):
       a =        0.14  (0.14, 0.14)

sot_gof =

           sse: 0.0033
       rsquare: 1.0000
           dfe: 5
    adjrsquare: 1.0000
          rmse: 0.0255

No question here, still 14% unnormalized weapon damage


Seal of Righteousness: Expect 5% weapon damage
Code: Select all
sor_fit =

     General model:
     sor_fit(x) = a*x
     Coefficients (with 95% confidence bounds):
       a =     0.04999  (0.04997, 0.05002)

sor_gof =

           sse: 0.0161
       rsquare: 1.0000
           dfe: 6
    adjrsquare: 1.0000
          rmse: 0.0517

I had to exclude one point for this fit, since it was obviously wrong. It was considerably off of the perfect fit to the other 7 data points. I haven't looked into what caused the problem, but to be honest I don't care all that much - it's clear this is working as advertised.


Holy Prism: expected (12412 + 1.098*sp) based on tooltip
Code: Select all
hp_fit =

     General model:
     hp_fit(x) = 1.098*x+b+10000
     Coefficients (with 95% confidence bounds):
       b =        1230  (1198, 1262)

hp_gof =

           sse: 4.6415e+003
       rsquare: 1.0000
           dfe: 5
    adjrsquare: 1.0000
          rmse: 30.4679


hp_fit2 =

     General model:
     hp_fit2(x) = 1.098*x+b+10000
     Coefficients (with 95% confidence bounds):
       b =        3567  (3502, 3633)

hp_gof2 =

           sse: 1.9583e+004
       rsquare: 0.9998
           dfe: 5
    adjrsquare: 0.9998
          rmse: 62.5831

Both very good fits with the advertised scaling. Range of 11230-13567 for base damage gives an average of 12400, which is within 0.1% of the advertised 12412. Tooltip confirmed.

We can also fit the healing component when cast on an enemy:
Code: Select all
hpt_fit =

     General model:
     hpt_fit(x) = a*x+b
     Coefficients (with 95% confidence bounds):
       a =      0.8235  (0.8212, 0.8257)
       b =        8377  (8362, 8392)

hpt_gof =

           sse: 213.9595
       rsquare: 1.0000
           dfe: 4
    adjrsquare: 1.0000
          rmse: 7.3137

hpt_fit2 =

     General model:
     hpt_fit2(x) = a*x+b
     Coefficients (with 95% confidence bounds):
       a =      0.8244  (0.8043, 0.8445)
       b =  1.018e+004  (1.005e+004, 1.031e+004)

hpt_gof2 =

           sse: 1.6786e+004
       rsquare: 0.9997
           dfe: 4
    adjrsquare: 0.9996
          rmse: 64.7811

The interesting part here is that we're getting ~(8377-10180)+0.823*SP, when we're expecting 8374+0.74*SP. However, the results we're seeing are consistent with the (8374-10234)+0.823*sp on the other half of the tooltip. In other words, the aoe healing observed matches the formula for the aoe damage we're supposed to be doing when we use Holy Prism to heal a friendly target. In my ability_model file, I already have a formula from an earlier mmo-champ database entry that is consistent with what we're observing in the logs, and I vaguely remember a mmo-champ diff showing that they swapped the formulas on the secondary effects. I'm not sure what happened - whether they swapped it and failed to update the tooltip, or whether they accidentally swapped things in the tooltip when they didn't mean to. Either way, I think this data confirms which formula we're seeing, it's just not clear whether it's a bug or not. Once we have the complementary Holy Prism data I asked for, we'll have a clearer idea of what's going on here.

Eternal Flame: expect (4030-4491)+0.377*sp per holy power
Code: Select all
ef_fit =

     General model:
     ef_fit(x) = 3*(a*x+b)
     Coefficients (with 95% confidence bounds):
       a =      0.3771  (0.3702, 0.3839)
       b =        4050  (4007, 4093)

ef_gof =

           sse: 9.1315e+003
       rsquare: 0.9999
           dfe: 3
    adjrsquare: 0.9999
          rmse: 55.1710


ef_fit2 =

     General model:
     ef_fit2(x) = 3*(a*x+b)
     Coefficients (with 95% confidence bounds):
       a =      0.3798  (0.3716, 0.388)
       b =        4450  (4398, 4502)

ef_gof2 =

           sse: 1.3121e+004
       rsquare: 0.9999
           dfe: 3
    adjrsquare: 0.9998
          rmse: 66.1338

We don't quite reach each extreme thanks to the limited nature of the data set, but it's good enough to feel pretty confident that the tooltip isn't lying to us.

We also fit the ticks, which should be 1393*0.16*sp per holy power:
Code: Select all
eft_fit =

     General model:
     eft_fit(x) = 3*(a*x+b)
     Coefficients (with 95% confidence bounds):
       a =        0.16  (0.1599, 0.16)
       b =        1393  (1393, 1393)

eft_gof =

           sse: 0.4090
       rsquare: 1.0000
           dfe: 3
    adjrsquare: 1.0000
          rmse: 0.3692

Tooltip confirmed.


Seal of Insight: expect 0.15*ap+0.15*sp = 0.45*sp
Code: Select all
soi_fit =

     General model:
     soi_fit(x) = a*x
     Coefficients (with 95% confidence bounds):
       a =        0.45  (0.4499, 0.45)

soi_gof =

           sse: 0.8189
       rsquare: 1.0000
           dfe: 7
    adjrsquare: 1.0000
          rmse: 0.3420

Tooltip confirmed.
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Mon Jul 23, 2012 11:10 am

The reason why Prism doesn't fit when it comes to the healing is because the prism data was from before the latest build, where it saw a nerf. Only the healing part of EF was nerfed on the latest builds (the same one where CS and Censure got hit)

The Prism data was collected 2 days before that build.
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Mon Jul 23, 2012 12:09 pm

Was that a stealth-nerf? Because it doesn't show up on mmo-champ's beta build diff.

<edit> nevermind, I found it in build 15851, the one before the CS nerfs.

If you don't mind posting the build # with data sets from now on, that might be helpful in avoiding this sort of confusion.
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Mon Jul 23, 2012 12:22 pm

Another interesting note: apparently EF, HP, and SoI's healing aren't affected by the 5% increase to healing spells granted by SoI. Not sure if that's a bug or intended (hopefully intended, since I would rather not be tanking with SoI).
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Mon Jul 23, 2012 12:46 pm

theckhd wrote:Was that a stealth-nerf? Because it doesn't show up on mmo-champ's beta build diff.

<edit> nevermind, I found it in build 15851, the one before the CS nerfs.

If you don't mind posting the build # with data sets from now on, that might be helpful in avoiding this sort of confusion.


sounds good.
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Mon Jul 23, 2012 3:53 pm

Blue confirmation of armor DR formula: http://us.battle.net/wow/en/forum/topic ... e=130#2593

DamageReduction = TargetArmor / (TargetArmor + 4037.5*AttackerLevel – 317117.5)

Very consistent with the values I worked out empirically based on melee data. Changes the level 93 dummy reduction factor from 0.6504 to 0.6507, which has no effect on the CS data.
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Mon Jul 23, 2012 6:02 pm

Here you go. Some WoGs were with 2HP, hope it doesnt affect much, and I was also pressing WoG on Divine Purpose proc, at least most of the time
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Mon Jul 23, 2012 6:45 pm

Klaudandus wrote:Here you go. Some WoGs were with 2HP, hope it doesnt affect much

Well, it'll throw off all of the averages and make it annoying to pick out min and max values... but I can probably still get what I need out of it.
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Mon Jul 23, 2012 6:53 pm

blah, I was doing it kinda hurried out as I have a raid (should be pulling soon)...

i can redo the logs tomorrow if you prefer not to work with these...
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 4:49 pm

I can't log on to the beta for some reason, it just hungs up
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 6:04 pm

I'm almost sure that there were no WoG with more than 1 HP in these new sets, and I created a macro that cancels Divine Purpose before casting WoG.

These can also be combined wit the previous log in order to get more data regarding Holy Prism, considering that the cd on that one is 20 secs...

Only did naked, 1, 2 and 7 for the time being... going out to jog, hope I don't get bit by Bruce again.

Once I get back, I'll do set 4 and 6
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Tue Jul 24, 2012 6:34 pm

Two more tests added regarding the L90 talents (#33 and #34)
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 7:34 pm

Theck, question... what do you mean by
Goal: 60 ES/LH casts, 8 LH casts.


Also, just got Colossus and Windsong -- where can I find a 1.4 weapon?
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 7:51 pm

Set 4 and 6 for WoG test
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Tue Jul 24, 2012 7:53 pm

WoG data is a little weird:
tooltip: http://www.wowdb.com/spells/130551-word-of-glory
(3694-4115) + 0.377*sp
fit (min and max):
Code: Select all
wog_fit =

     General model:
     wog_fit(x) = a*x+b
     Coefficients (with 95% confidence bounds):
       a =      0.5291  (0.4915, 0.5668)
       b =        3922  (3710, 4134)

wog_gof =

           sse: 9.8495e+003
       rsquare: 0.9995
           dfe: 2
    adjrsquare: 0.9992
          rmse: 70.1766


wog_fit2 =

     General model:
     wog_fit2(x) = a*x+b
     Coefficients (with 95% confidence bounds):
       a =      0.5362  (0.5001, 0.5722)
       b =        4370  (4167, 4574)

wog_gof2 =

           sse: 9.0587e+003
       rsquare: 0.9995
           dfe: 2
    adjrsquare: 0.9993
          rmse: 67.3003

There's enough error here that the base values could be right, but the scaling seems much higher than the tooltip claims. Maybe there's something obvious I'm missing, since it's late. I'll look at it agian tomorrow. <edit> and I'll add the 4-6 data.
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Tue Jul 24, 2012 7:55 pm

Klaudandus wrote:Theck, question... what do you mean by
Goal: 60 ES/LH casts, 8 LH casts.


Also, just got Colossus and Windsong -- where can I find a 1.4 weapon?

60 casts of ES and HPr, 8 LH. Typo on my part. Either way, ES/Hpr are going to take about an hour each because of the cooldown.

I think the fastest weapon now is a Tomahawk, so use that instead for the Colossus/Windsong tests.
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 7:56 pm

what is HPr? Holy Prism? Also, shouldnt HPr actually be much faster considering that the cd is 20 secs?

Also, in Test #4, you say any gear... but you dont mention anything about hit/exp

just need to be sure before I leave the computer on for an hour
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 8:22 pm

Well, neither colossus nor windsong work on the tomahawk, only works on weapons that are 372 or better. The slowest weapon that qualifies is 2.7 (the plasma sword) but the easiest to obtain are 2.6
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Tue Jul 24, 2012 8:36 pm

I can use this mace http://mop.wowhead.com/item=80795/jade-forest-scepter if you deem it acceptable for the tests
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Wed Jul 25, 2012 3:54 am

Klaudandus wrote:what is HPr? Holy Prism? Also, shouldnt HPr actually be much faster considering that the cd is 20 secs?

Oops, yeah. HPr will only take 20 minutes, but the two 1-minute cooldown spells (ES and LH) will take an hour to get 60 casts.

Klaudandus wrote:Also, in Test #4, you say any gear... but you dont mention anything about hit/exp

just need to be sure before I leave the computer on for an hour

It specifies a low-level dummy, so you should automatically hit/exp cap.
Klaudandus wrote:I can use this mace http://mop.wowhead.com/item=80795/jade-forest-scepter if you deem it acceptable for the tests

Yeah, that should be fine. We just want something that's far away from 2.4, so 1.6 should work well enough.
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Wed Jul 25, 2012 4:50 am

ok, i'll do #4 and #33 with windsong and colossus (only enchants i've been able to get) over the next few days -- got a raid tonight, so i can prolly do #4-colossus at least, maybe #4-windsong if i'm lucky
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Wed Jul 25, 2012 4:52 am

Something strange is definitely going on with the WoG data. For example:
Image
The blue line is the following fit to the "max" set:
Code: Select all
General model:
     f(x) = (a*x+b)
Coefficients (with 95% confidence bounds):
       a =      0.5371  (0.522, 0.5523)
       b =        4367  (4270, 4463)

Goodness of fit:
  SSE: 1.009e+004
  R-square: 0.9996
  Adjusted R-square: 0.9995
  RMSE: 50.23

That curve doesn't do a bad job, but note that the intercept is outside the tooltip range (but then again, so is the scaling).

If I try the same thing with the min data, I get the red curve:
Code: Select all
General model:
     f(x) = (a*x+b)
Coefficients (with 95% confidence bounds):
       a =      0.5291  (0.5134, 0.5448)
       b =        3918  (3818, 4018)

Goodness of fit:
  SSE: 1.08e+004
  R-square: 0.9995
  Adjusted R-square: 0.9994
  RMSE: 51.96


So far so good, maybe. However, if you look carefully at the lower 3 data points, something looks fishy. The errors appear systematic - in other words, both the min and the max of the naked set are too high, and both min and max of the ~3k SP data set are too low. A similar (but less significant) effect is happening for the last 3 gear sets. To illustrate that, this is what happens if you fit the lower and upper 3 data points of the min data set independently:
Image
Low:
Code: Select all
General model:
     f(x) = (a*x+b)
Coefficients (with 95% confidence bounds):
       a =      0.4825  (0.2859, 0.6791)
       b =        3995  (3592, 4398)

Goodness of fit:
  SSE: 923.6
  R-square: 0.999
  Adjusted R-square: 0.9979
  RMSE: 30.39

High:
Code: Select all
General model:
     f(x) = (a*x+b)
Coefficients (with 95% confidence bounds):
       a =      0.5405  (0.5139, 0.567)
       b =        3824  (3592, 4056)

Goodness of fit:
  SSE: 47.43
  R-square: 1
  Adjusted R-square: 1
  RMSE: 6.887


Notice that the fits get much better. Admittedly, some of this is because we have fewer data points to fit (and thus more leeway with the parameters), but it's eerie that the three data points ended up so linear. It's almost as if something changed between gear sets naked-2 and gear sets 4+.

I'm going to look at the prism data that's included in these data sets and see if that gives me any clue as to what's happening.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
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Re: A Call to Arms - MoP Mechanics Testing

Postby Klaudandus » Wed Jul 25, 2012 4:55 am

i can repeat the WoG logs again if needed be. it just drives me crazy to try to always make sure that i only have one HP before casting WoG -- but at least it seems my /cancelaura Divine Purpose is working -- and do all 8 (naked + 7) sets
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Re: A Call to Arms - MoP Mechanics Testing

Postby theckhd » Wed Jul 25, 2012 4:55 am

Klaudandus wrote:ok, i'll do #4 and #33 with windsong and colossus (only enchants i've been able to get) over the next few days -- got a raid tonight, so i can prolly do #4-colossus at least, maybe #4-windsong if i'm lucky

That's fine. As far as the L90 talents, I should amend the description slightly to note that you can stop after 10-15 casts as long as you have a few misses. I'm 99.99% sure they're spells rather than melee abilties (since that would be dumb), but what I'm after is whether they can miss, and in ES's case, does each tick roll independently.
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