Quick question about Inq

[tlitp]

A more accurate model would try and include Vengeance build-up, maybe by assuming 10% Vengeance accumulation every 2 seconds (...)

If you meant something like Veng=min(0.05*t,1), t being expressed in seconds, don't bother.

During the stationary state, Vengeance can be reasonably approximated by a linear map of time. In the accumulation/decay states, Veng=f(time) isn't even continuous, let alone linear.

I'm not really sure how to read the formula on the Wowhead tooltip.

Use the repo.

[theckhd]

A more accurate model would try and include Vengeance build-up, maybe by assuming 10% Vengeance accumulation every 2 seconds (...)

If you meant something like Veng=min(0.05*t,1), t being expressed in seconds, don't bother.

During the stationary state, Vengeance can be reasonably approximated by a linear map of time. In the accumulation/decay states, Veng=f(time) isn't even continuous, let alone linear.

No, certainly not such a simple linear model. I literally meant a step function, where from t=0 to t=2, you had 0%, t=2-4 you had 10%, and so forth. I think a step function approximation would be pretty reasonable, given that's how we accumulate it. It will obviously have different step sizes based on combat table results (avoid vs. block vs. unblocked vs. magic), and the steps actually decay away in between swings, but for a very simple model we'd abstract that away and just treat it like a step function. I'm only guessing that 10% is appropriate for a step size; it may be a bad guess.

The point was simply to get a gradient of damage values, so that the first 9 seconds are a little less skewed towards Inquisition. If we evaluate ability damage at 10% Vengeance intervals, and then use a rough, step-function approximation of the build-up cycle, I suspect that Inquisition will come out behind by a pretty significant margin. Hopefully large enough that the errors inherent in these approximations aren't significant by comparison.

And of course, there's always the chance that my intuition is wrong, at which point we could think about revising the model, if we wanted to. I think you and I have enough other things to work on right now to make that a low priority, though.

[Mirydon]

I'm not really sure how to read the formula on the Wowhead tooltip.

Use the repo.

Ok, this is getting really unfamiliar now, I haven't done any decent math in over 20 years, and have no experience whatsoever in any programming language. But I think I can deduct from the link you gave that the 'holy power' in the Wowhead tooltip of Seal of Truth has nothing to do with our stacks of Holy Power, so I can ignore that. I'll just ignore the Wowhead tooltip altogether on second thought.

[theothersteve7]

Mouse over the words "holy power" in that tooltip; it's talking about spellpower and any Holy school modifiers (such as Inquisition) applying to the Paladin. Yeah, it's misleading, but they didn't bother renaming their variables.

[Mirydon]

To calculate Seal of Truth damage correctly, I'm thinking of adding a separate row in my spreadsheet. Ability damage would then be taken from the Dmg column of Theck's ability damage list.
I would calculate SoT separately as such: Dmg*mdf.mehit*Censurestack/5 (melee, SotR and CS) or Dmg*mdf.rahit*Censurestack/5 (Judgement)
- Dmg = Theck's value for SoT in the Dmg column
- mdf.mehit/mdf.rahit being the melee/ranged hit modifier (Theck, I'd like to know the values you use in your model if possible).
- Censurestack = number of Censure stacks on target, since Theck's value is for 5 stacks, divide it by 5 and multiply it by the number of Censure stacks.

I can then multiply that value by 1.3 if Inq is up. Would that be correct?

Another problem I can see in my model is I'm taking misses and hits into account for ability damage since it's incorporated in Theck's Dmg values, but not for Censure stacking. If I would use (Censurestack*mdf.mehit) instead of Censurestack on both SoT and Censure damage, would that be more accurate?

[theckhd]

mdf.mehit and mdf.rahit depend on your hit and expertise. For example, you have a base 8% chance to miss a level 88 boss. If your gear set has 2.8% hit, then you reduce that to 5.2%. In that circumstance, mdf.rahit would be 1-0.052 = 0.9480.

Similarly, mdf.mehit incorporates the 6.5% dodge and 14% parry chances against a level 88 boss, which are mitigated by expertise at -0.25% per point of expertise.

In my sims at low hit/exp (2.8058%, 16.6966 expertise),
mdf.mehit=0.8265
mdf.rahit=0.9481
mdf.sphit=0.9429


Your handling of SoT seems to be correct. Censure cannot miss, so there's no need to modify it for that. At worst, the application of a new stack of Censure can miss, which will make the ramp-up time slower on average. But for a simple first approximation, we can probably ignore that.

[Mirydon]

At worst, the application of a new stack of Censure can miss, which will make the ramp-up time slower on average. But for a simple first approximation, we can probably ignore that.

If I would multiply the number of stacks by mdf.mehit, wouldn't that accommodate for any missed applications of new Censure stacks?

[theckhd]

Not unless you allow for more than 5 stacks. mdf.mehit doesn't limit the total number of stacks, just the rate at which they get applied. It would be more accurate to just apply them more slowly, which is tricky because you'd need finer granularity in your time steps. That's why I suggested you just ignore that for this pass.

[Mirydon]

A friend of mine works at the university here and has access to MATLAB, so he got me the values. I'll post an updated spreadsheet as soon as I've entered the values.

[Mirydon]

So here is the update after the proposed changes: https://spreadsheets0.google.com/ccc?key=tsoMf7X6pVqAU2pMOHkOTfg#gid=0.
Changes are:
-Values used are now from Matlabadin r208, running calc_abilitydmg.m, then taking the values from dmgarray1, column 2. No changes have been made to the code except to calculate the damage values for different levels of Vengeance (see below).
-To calculate the values for each level of Vengeance, we changed the value in line 5 in calc_abilitydmg.m, from 1 for 100% to 0 for 0% Vengeance.
-I calculated 4 different pulls: the first 2 were the base of the argument that lead to all this, the last 2 I made seemed to be the most optimal ones for respectively Inq and SotR. Any suggestions for other pull sequences are welcome.
-Melee attacks now happen every 1.75 seconds to account for parry haste and Reckoning procs(player.wswing=1.7456).
-Seal procs are now calculated separately and take Censure stacks and miss chance into account.

If I entered all the data correctly, and we can agree on the model as it stands, it seems that the Inq-Exo-AS pull generates the most threat. Here's a graph for the first 12 seconds.



Strangely enough, the graph I had when all damage was calculated with 100% Vengeance, looked exactly the same.

[theckhd]

Something's grossly wrong with your numbers. My numbers match yours at 0% Vengeance. But whoever ran the code for you screwed up the Vengeance scaling. Your 100% values are smaller than the code's output for 30%.

Here are the appropriate values, with the new Vengeance formula:

Code: Select all

Ability    0%     10%    20%    30%    40%    50%    60%    70%    80%    90%   100%
ShoR      8735   9631  10526  11422  12318  13213  14109  15005  15900  16796  17691
CS        5731   6286   6841   7396   7951   8506   9061   9616  10170  10725  11280
JoT       6475   7219   7962   8705   9449  10192  10935  11679  12422  13165  13908
AS        8262   8981   9700  10419  11139  11857  12577  13296  14015  14734  15453
HW        5230   5230   5230   5230   5230   5230   5230   5230   5230   5230   5230
HoW      11148  12010  12871  13732  14594  15455  16317  17178  18040  18901  19762
Exor      6599   7203   7806   8410   9014   9617  10221  10825  11428  12032  12635
SoT        573    631    688    745    803    860    917    975   1032   1090   1147
SoR        535    591    647    704    760    816    873    929    986   1042   1098
SoJ        242    268    293    319    344    370    395    421    447    472    498
Cens      6784   7779   8772   9766  10760  11754  12748  13742  14736  15730  16723
Cons      6362   7025   7688   8352   9015   9678  10341  11005  11668  12331  12994
HotR      1030   1133   1236   1339   1442   1545   1648   1751   1854   1958   2061
HaNova    3719   4159   4598   5038   5478   5917   6357   6797   7237   7676   8116
Melee     1787   1965   2144   2323   2502   2681   2860   3039   3217   3396   3575

In addition, here are two more sequences to consider:

Exo+AS-CS-J-CS-Cons-CS-SotR-DP-SotR-(usual 939)
J+AS-CS-Cons-CS-HW-CS-SotR-DP-SotR-(usual 939)
J+AS-CS-Cons-CS-(wait 0.5)-J-CS-SotR-DP-SotR-(usual 939)

The last two simulate a boss that starts far enough away to get two ranged casts off before it reaches you.

[Mirydon]

Changed the values (don't know what happened there), and added more pull sequences. I will start a new topic in the theorycrafting section to post it, because this doesn't really belong here.

[theckhd]

Probably a good idea, since we're not done yet. We still have to incorporate Sacred Duty interactions.