Theck's MATLAB TPS analysis - WotLK/3.x

<edit> Updated plots are available, see the table of contents.

DPS


Pretty much the same as the other plot, but the integration of spell miss to Holy Shield DPS significantly shifts the crossing point. By the time your character-sheet STR is higher than 865, Hit will grant you more DPS than BV per itemization point.

TPS


Same as DPS - the crossover happens far sooner now, around 1075.

Again, this is the character-sheet STR, so you can read it directly off of the Armory to determine where you are on this graph.

theckhd wrote:Also, I feel bad about the thread title - It's not my spreadsheet, it's Jonesy's. I've just taken the math from his spreadsheet and put it into MATLAB, which is (basically) a programming language, so that I can do analysis more easily.

"Theck's MATLAB TPS analysis" would be more accurate, but I still feel bad that Jonesy doesn't somehow get credit for doing 90% of the work.

Just to put your mind at rest, I really don't care. I do think it's funny that I wrote it in Excel so as to be more accessible (my preference would have been a python script) but that it's received almost as much attention since you ported it to Matlab than it did as an Excel sheet.

It's all about the pretty pictures

Another thing I noticed. As much as I hate to say it, we should probably model Judgments of the Just in here just to get some firm numbers of the tps cost of the ability (not that it'll be a DPS gain if you have any mage except a FFB mage with you).

Yeah, I can add a swing timer value.

That would be modeled by changing

Code: Select all

swing_timer=2.4;

which is the boss's swing_timer in seconds, I believe. JotJ would just increase that value by 20%, which would nerf the Holy Shield threat component.

Just to test, if I change that constant to 1.2*2.4, the crossover happens at 905 for DPS and 1131 for TPS.

If instead you were wondering what the DPS and TPS breakdown looks like for a boss with 2.4 swing_timer with and without JotJ, it is:

With JotJ: DPS=133.7, TPS=370.5
Without: DPS=160.4, TPS=444.7

None of the other abilities are affected. Their values are as follows, from the "with" case:

Code: Select all

DPS_breakdown =
    'HS'       [133.7074]
    'ShoR'     [911.3134]
    'JoV'      [294.0537]
    'DoT'      [418.9201]
    'HotR'     [568.4219]
    'Cons'     [365.3158]
    'Melee'    [443.5974]
TPS_breakdown =
    'HS'       [   370.5487]
    'ShoR'     [2.5256e+003]
    'JoV'      [   814.9229]
    'DoT'      [1.1610e+003]
    'HotR'     [1.5753e+003]
    'Cons'     [1.0124e+003]
    'Melee'    [   647.0312]

So for that boss, it's about a 74 TPS loss. HS depends on swing_timer as 1/swing_timer, so the difference in threat should always be (1-1/1.2)=1/6, or roughly 17% of the base value.

Using the above numbers, the other abilities generate 7,736 TPS, while Holy Shield is generating 371 (or 445), which is 4.5% (or 5.4%) of your total threat. So comparing 7736+445 to 7736+371, we see that your threat drops from 8181 to 8107, a drop of 0.9%.

More generally, threat production should follow something like:
A + B/swing_timer, where A is the threat caused by other abilities, and B is a coefficient that models HS's threat. In our case, B/swing_timer=445, so B should be roughly 1068, and A is 7736. The total reduction in threat should scale as

[(A+B/x)-(A+B/(1.2*x))]/(A+B/x), which simplifies to

(1/6)*1/(1+A*x/B)

Quickly checking this in matlab: For a 1.0 speed boss, this is a 2% reduction in total threat output, and drops to around 0.7% for a 3.0 speed boss. I can post the plot later if anyone's interested.

Looks good. I'm actually assuming that 2.4 was taken from the assumption of a boss swing timer of 2 seconds (quite common) with JotJ then added on, but that's not really all that important to the overall picture.

Dorvan wrote:Looks good. I'm actually assuming that 2.4 was taken from the assumption of a boss swing timer of 2 seconds (quite common) with JotJ then added on, but that's not really all that important to the overall picture.

That's entirely possible, but Jonesy would have to answer that question.

For x=2.0, it evaluates to a 1.08% threat reduction.

Forgot to ask this sooner but for your cross over graphs what are the assumed hit and expertise values?

Hmm, if you're going to use Matlab, do you think you could do a mesh plot of the interaction between AP and Hit? It's something I've been meaning to look at since forever, but I'm always busy doing something.

I've also considered a 3d plot of AP, Hit, and Crit interactions with color denoting TPS effect, but I haven't touched matlab in so long I forget what such a graph is called, even.

Btw, good work w/respect to all of this.

First off love the name cordie. (Angel/Buffy were amazing).

Second you guys should like break this down for retards like me who are really really good at math but hate statistics/graphing stuff.

And what it all really means or hell make something like this for new SoR/SoB/SoC.

Majiben wrote:Forgot to ask this sooner but for your cross over graphs what are the assumed hit and expertise values?

The graph assumes 35 expertise rating from gear, 10 expertise from SoV Glyph, and 6 expertise from the Combat Expertise talent.

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expertise=(Base_exp + SoV + (Gear_Exp+extra_exp)./exp_rating_to_exp) + CE;

where the variables are defined in PallyTPS.m as
Base_exp=0
Gear_Exp=35
SoV=10
CE=6

cordelia wrote:Hmm, if you're going to use Matlab, do you think you could do a mesh plot of the interaction between AP and Hit? It's something I've been meaning to look at since forever, but I'm always busy doing something.

I've also considered a 3d plot of AP, Hit, and Crit interactions with color denoting TPS effect, but I haven't touched matlab in so long I forget what such a graph is called, even.

I can crank out all of this when I get some time. What specifically did you want for the AP/Hit graph, simply a 3D surface plot of DPS on the z-axis with Hit and AP as the x- and y-axes?

I can make a 3D contour map for the AP/Hit/Crit graph as well, with multiple surface contours for different DPS benchmarks, but it might be hard to read when condensed down into a single image. I always find it easier to read 3D plots in MATLAB itself where i can spin 'em around and zoom.

Lowgrus wrote:And what it all really means or hell make something like this for new SoR/SoB/SoC.

Most of the commentary is found in the Hit thread this was split off of, you can read it here. It might be worth cloning that post into the OP of this thread, to make it more coherent. If Fridmarr or one of the other mods thinks it's worth it, that is.

And what was the assumed hit?

theckhd wrote:I can crank out all of this when I get some time. What specifically did you want for the AP/Hit graph, simply a 3D surface plot of DPS on the z-axis with Hit and AP as the x- and y-axes?

Yep. Exactly. Btw, I've always preferred mesh over surf. Easier to examine, IMO.

theckhd wrote:I can make a 3D contour map for the AP/Hit/Crit graph as well, with multiple surface contours for different DPS benchmarks, but it might be hard to read when condensed down into a single image. I always find it easier to read 3D plots in MATLAB itself where i can spin 'em around and zoom.

Yah, I think it would be hard to read. You could always save it as a matlab graph for those of us who can read matlab graphs. And YES, it's always easier to view them on Matlab where you can spin em and zoom em. Too bad journal figures can't be that interactive. And yes, I know some people actually publish 3d images using steroscopic cross-focusing or whatever those magic eye 3d things are called. I've never been able to focus that way at will, though, so those 3d pix are useless whenever I see em.

Majiben wrote:And what was the assumed hit?

61 hit from gear, plus 1% from Draenei aura.

Now can you convert this into an addon so when I swap gear around in-game I can tell what my expected increase in threat/etc. will be? :-).

Great work, keep it up!