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

Warning: Theorycraft inside.

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3.3 Stat Threat Analysis

Postby theckhd » Wed Dec 16, 2009 8:27 am

3.3 Stat Threat Analysis - Single Target

Note: I've arbitrarily set the expertise and hit contributions from gear to 0 for this, so we get a clear picture of the entire range of rating.

The major change this patch has been ShoR moving to the melee table. Now that it can be dodged or parried, we expect that expertise should become a more important stat for us. This has some advantages - warriors and DKs like expertise, so it makes gear itemized with them in mind a little better for us than it was before.

For those interested in the "under-the-hood" mechanics of how this simulation works, see the 3.2.2 Analysis. Nothing in the code has changed since last time.


Setup:
Rotation: 969
Seals: SoV
Glyphs: V only
Talents: 1V+3C
Gear: T10 Progression set
File: calc_stat_tps.m

As usual, we'll look at STR first. For a point of reference, the unbuffed character-sheet STR of the default gear set here is 2070.
Image
DPS plot

The amazing news here is that STR has finally been un-seated from the top spot. Above 1942 unbuffed character sheet STR, both Expertise (up to the soft-cap at 26) and Hit (up to the a few %, see hit graph) give better TPS per point of rating.

We had already expected this would occur for hit, but the real news is expertise. The ShoR change has drastically changed our reliance on expertise. Soft-capping expertise at 26 becomes highly recommended.

Also note that since this gear set is below the region of diminishing returns on ShoR, we don't see the DR on STR. We'll get to see this later in the BV plot though.

Hit:
Image
DPS plot

No surprises here. Hit drops off when you reach the melee and spell hit caps. Everything else is pretty much the same, with slight scaling of damage-increasing stats until you reach the appropriate caps.

The interesting thing to note is that after about 50 hit rating, STR increases enough to equalize the two stats. Note that this is with 0 expertise rating from gear; at the expertise soft cap this number will go up. What this means is that if you're really optimizing for threat on a limited budget, you'd want to balance hit, expertise, and STR. On the other hand, it's hard to come up with a rule of thumb for this, since it will depend on your current STR, hit, and expertise values. In practice it will be more common to just gem STR if you want sustained TPS, and hit if you want snap threat. The difference in sustained will be small enough (~2-3 TPS per 10 points of rating or stat) that hit is probably the better choice.

Expertise:
Image
DPS plot

The dark horse of this patch, Expertise has risen to top dog status with the change to ShoR. As always, expertise loses effectiveness when you hit the soft and hard caps (82 and 328 rating or 26 and 56 skill after talents, respectively), and damage-increasing stats scale differently above and below those caps (see the different slopes on the STR and BV lines in the three regions).

Past the soft cap, expertise drops back down to be roughly equivalent to AP for threat purposes. That would put it at a "don't gem" level as far as threat is concerned, though there are also avoidance benefits to consider.

Block Value:
Image
DPS plot

Here we see the effects of the ShoR diminishing returns formula. We're actually closer to the edge of this, since the default set is sitting at 2216 BV.

The other thing to note is that BV has dropped a little bit across the board this patch, which is directly due to ShoR dodges and parries. STR suffers from this as well, but not as directly - it spreads your threat across many sources, so the ShoR change is a smaller relative effect. However, with BV you put all your eggs in one basket (ShoR), so the change is more noticeable. As a result, BV is generally not going to be our best option for threat (compared to STR) since most people won't be hard-capped on expertise or hit-capped.

The discontinuity at 2400 is due to the piecewise nature of the function and the fact that I'm stepping by ~3 BV at a time in this simulation. The TPS value of each point of BV decreases linearly as we get more BV, which is exactly what we'd expect since the diminishing returns formula is modeled best by a quadratic. By 3161 BV, we find that BV no longer contributes any threat.


For the bar plots, I've decided to just generate one plot for 2300 BV. In the past, there were four threat stats that could all be the best in one configuration or another. Now, BV is basically out of the running, and the stepwise nature of hit and expertise makes it easy to determine whether either is significantly weaker than STR.

Image

Image

And finally, here's the single-stat values pulled off of the first graph (STR scaling) at 2000 STR (with 0 expertise and hit):
Code: Select all
         TPS per 10
Stat   ipoint    stat
Exp     37.86   37.86
Hit     31.80   31.80
STR     30.80   30.80
BV      21.88    7.11
AP      18.21    9.10
Crit    11.62   11.62
AGI     11.27   11.27
Haste    6.98    6.98
SP       4.93    4.22
ArPen    1.97    1.97



TLDR Summary:
  • The ShoR change, while seemingly minor, made a huge difference in stat weighting.
  • Expertise is now our best threat stat below the soft-cap of 26 (above that it's fairly weak).
  • Hit is better than STR, point for point, after you reach around 2000 unbuffed character-sheet strength. But it will remain close, and they synergize such that adding one makes the other better.
  • STR is our third best threat stat, but it becomes our best after we soft-cap expertise. Adding more expertise or hit will make STR even better.
  • BV, while nice, isn't really something we should stack for threat. STR is better point per point, and doesn't push you into the DR range of ShoR as quickly. Obviously take what you can get as far as gear goes, but if you get to choose between 10 STR or 31 BV, always take the 10 STR.
  • General gearing strategy for threat:
    • Stack Expertise to 26 (soft-cap)
    • Stack hit rating to 8%
    • Stack STR
Last edited by theckhd on Mon Dec 21, 2009 7:31 am, edited 2 times in total.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby theckhd » Wed Dec 16, 2009 8:35 am

I'll probably be busy for the better part of the day today, so chances are the rest will have to wait until tomorrow.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Saiph » Wed Dec 16, 2009 9:21 am

Past the soft cap, expertise drops back down to be roughly equivalent to AP for threat purposes. That would put it at a "don't gem" level as far as threat is concerned, though there are also avoidance benefits to consider.


Just so I'm completely clear on this point, does that mean that below the soft cap it may be acceptable to gem expertise, or that at all levels you shouldn't gem for it? With the amount of defense on gear we are seeing now, would it be an option to gem expertise/stam in a yellow slot instead of defense/stam if you weren't ignoring the socket bonus on a particular piece for whatever reason (and below the soft cap)?
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Grehn|Skipjack » Wed Dec 16, 2009 9:46 am

Well, for one, expertise/stam gems are purple, and have nothing to do with yellow sockets.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby theckhd » Wed Dec 16, 2009 10:09 am

Saiph wrote:Just so I'm completely clear on this point, does that mean that below the soft cap it may be acceptable to gem expertise

Yes.
Saiph wrote:or that at all levels you shouldn't gem for it?

No.

theckhd wrote:
  • General gearing strategy for threat:
    • Stack Expertise to 26 (soft-cap)
    • Stack hit rating to 8%
    • Stack STR
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby beornus » Wed Dec 16, 2009 10:13 am

<------ Has been twatted by this information

/bow you bow to theckd

thanks again for all the great work you do!
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I should have kept quiet and thought a fool then to have typed and removed all doubt.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Thalastor82 » Wed Dec 16, 2009 10:15 am

well, I wasn't expecting this...

so I guess that, taking in account the avoidances + treath bonus of expertise, the expertise/stam gem would be preferable to the agi/stam gem if below the soft cap.

But since expertise is present in many new items and everybody uses the V glyphe, I think that very few people will be in this situation and that some agi/stam will be still sitting somewhere in our equipment
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Saiph » Wed Dec 16, 2009 12:24 pm

Grehn|Skipjack wrote:Well, for one, expertise/stam gems are purple, and have nothing to do with yellow sockets.


Yup, that is just me mixing up the color of expertise with hit.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby danceswithchihuahuas » Wed Dec 16, 2009 4:40 pm

Do these calculations take into account using alternate rotations? I.E. under 15% health, using HoW every other Judgment, or AS instead of Judgment when on cd?

I understand that HoW TPS is less than that of JoV, but I am hesitant, particularly since it hits harder than a judgment, to take it out of a potential maximum TPS rotation. Same with Holy Wrath. Substituting these for every other Judgment, after all, still allows for the JotJ/JoL/JoW debuffs to remain present on the target (assuming hit cap).

As a matter of fact, after seeing this information I feel only more justified in keeping them in my max TPS rotations. TPS doesn't matter when your ability hits twice as hard and has twice the cooldown, when you are substituting it for a half damage half cooldown ability every other rotation.

edit: I am also feeling justified in taking the SoV glyph again, once I dip below soft cap. Woo 40+ expertise! X_X
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Phonic » Wed Dec 16, 2009 4:43 pm

Been reading through pages of the latest updates since Theck posted in my other thread :) If only I read this beforehand!!

The answer might be buried in there, but can someone explain to me in a very simple and easy way why slower DPS weapons are now better?

And if so, by the graph a few pages back, for threat, Broken Promise out-TPSs my Shiver? Should I switch to that for threat and trash tanking?
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby danceswithchihuahuas » Wed Dec 16, 2009 4:46 pm

Phonic wrote:Been reading through pages of the latest updates since Theck posted in my other thread :) If only I read this beforehand!!

The answer might be buried in there, but can someone explain to me in a very simple and easy way why slower DPS weapons are now better?

And if so, by the graph a few pages back, for threat, Broken Promise out-TPSs my Shiver? Should I switch to that for threat and trash tanking?


I would say that depends on whether or not you're hitting expertise soft cap without Broken Promise. Otherwise Shiver seems to pull slightly ahead. Also note that Shiver boasts more stamina and defensive statistics, which would tell me that unless you're having threat problems, or you're trying to get a big enough threat lead to use Hand of Barkskin effectively, Shiver is a better choice.

As to your other question, I'll just steal directly from Theck here:

* Slow weapons are good for us, because SoV 5-stack proc rewards weapon speed, at roughly 28 TPS per 0.1 weapon speed.
* The only spec-related choice that can change the outcome is Reckoning. Each point in Reckoning will add 24-28 TPS for a 1.5-1.6 speed weapon, while it will add 40-45 TPS for a 2.5-2.6 speed weapon.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Phonic » Wed Dec 16, 2009 5:03 pm

Hmm interesting... Thanks for the info. I don't think I'll "roll back" to Broken Promise, just curious. I ditched Hand of Sac glyph a while back since I'm in a guild where I can almost never afford to lose that 20% (stupid threat-capped locks).

Just always trying to find ways to work on threat! Need to keep my reputation solid! haha
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby theckhd » Wed Dec 16, 2009 7:38 pm

danceswithchihuahuas wrote:Do these calculations take into account using alternate rotations? I.E. under 15% health, using HoW every other Judgment, or AS instead of Judgment when on cd?

Yes.

danceswithchihuahuas wrote:I understand that HoW TPS is less than that of JoV, but I am hesitant, particularly since it hits harder than a judgment, to take it out of a potential maximum TPS rotation. Same with Holy Wrath. Substituting these for every other Judgment, after all, still allows for the JotJ/JoL/JoW debuffs to remain present on the target (assuming hit cap).

Hammer of Wrath does only slightly more damage than Judgement, but less than Judgement+SoV proc. So the damage of a single Judgement cast is greater than the damage of a single HoW cast. HoW also has a shorter cooldown than Judgement, not longer.

Maybe you meant AS? But even that is a DPS loss if it's unglyphed.

danceswithchihuahuas wrote:As a matter of fact, after seeing this information I feel only more justified in keeping them in my max TPS rotations. TPS doesn't matter when your ability hits twice as hard and has twice the cooldown, when you are substituting it for a half damage half cooldown ability every other rotation.

I'm not sure what you're basing this decision on, but it's not math. You're right that TPS is irrelevant for substitutions, raw damage per cast is what matters. But both HoW and unglyphed AS do less raw damage per cast than Judgement, not 2x more.

danceswithchihuahuas wrote:edit: I am also feeling justified in taking the SoV glyph again, once I dip below soft cap. Woo 40+ expertise! X_X

SoV was already our highest TPS glyph in 3.2. Nothing's changed about that.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby danceswithchihuahuas » Thu Dec 17, 2009 12:44 am

Ah, I see; I hadn't taken into account the additional SoV proc vis a vis melee strike. Makes sense now. Is this based on Judgment proccing a melee swing, Judgment proccing a SoV (which, the more I think about it, the more likely it seems to be the case), or HoW resetting the swing timer? (I'm sure the information is in there... I just can't seem to find it). If it's the latter, then theoretically by watching my swing timer I can sometimes squeeze a HoW in there to maximize TPS assuming perfect timing if it happens to be the next button on my rotation right as my swing timer resets to 0.

Far as the glyph goes, I was referring to the expertise loss on gear in 3.3, not necessarily any new information presented... Sorry XD!

Thanks for the clarification :)
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Zibey » Thu Dec 17, 2009 3:59 am

As Theck pointed out long ago - SoV glyph was best tps glyph even if it was all above soft cap.

Also - Judgement, HotR, and ShoR all proc SoV, just as melee attacks do. Hence whenever you hit with them, you also hit with 1/3 of your white attacks damage.
You cant squeeze HoW into rotation instead of Judgement and have more TPS, because HoW dmg < Judge dmg + SoV tick dmg.
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