Theck's MATLAB thread - Cataclysm/4.x

[Kihra]

The two Ret pieces we'd use are the legs and helm

Why not use legs and chest? They both have Mastery on them. The helm is nothing but threat stats.

[theckhd]

The thing is though, once we get 2pT13 the Judgement glyph will give us a bit of mitigation. Sure it'll be weak, but every other prime glyph is just DPS/TPS, not survivability. Adding in the Ret 2p would make it more attractive and give us some extra HoPo, which definitely raises the possibility of weaving in Inq. With Inq up Judgement will hit harder and thus grant a larger shield.

Admittedly though, perhaps using the Ret 2p might set us back more. The two Ret pieces we'd use are the legs and helm, which would exempt using the Prot pieces that are dodge/mastery and dodge/parry respectively. The sheer CTC on those most would most likely outweigh the little gain we get from the 2p bonus.

If the quick napkin math I did on EJ is any indication, Prot's 2p probably won't do much. The Judgement glyph was worth less than 50 mastery rating in terms of mitigation, which means it's only worth a similar amount of avoidance too. Avoiding a 50k hit for example means we just negated 166 boss DPS during a 5 minute fight. If we assume Judgement does 20k average (which is probably high) and used every 8 seconds (definitely not happening) then the 2p is a 5k shield every 8 seconds, or 625 DPS.

Gah, heck of a time for my handheld calculator to die. Suffice to say, now that I look at it I'm pretty sure the sheer CTC of the prot pieces outweigh any gains we might get from using 2p Ret.

Some assorted comments on this:
1) The Judgement glyph will be a mitigation increase, but a very weak one. You're increasing the shield's value by 10%, but that's still a fairly small amount of extra absorbed damage. It's certainly something, but we get back into the same argument we've had before about SoI - it's another few hundred absorb that we can't control all that well, and will mostly just be negated by creating more overheal on the part of our healers.

If the absorb bubble were considerably larger, we might care about it the same way DKs care about timing their heals/absorbs. But 5k is such a small amount that I don't think we'll go to that extreme - the interruption of our rotation and the impact on HPG and WoG availability are probably enough to make it undesirable. Similarly, I don't think we'll be optimizing for Judgement bubbles. At best, we might switch to using Inq as a finisher, sacrificing DPS to get slightly more mitigation. But even that's questionable at this point.

That said... The only other survival options are WoG and SoI. I'd make an argument for WoG/SoT glyphs being the "default" load-out, because I think that the expertise from SoT impacts your survivability more noticeably than SoI healing. But J would certainly be an option for that third slot. It's just not a very compelling one, since the mitigation bonus is so weak.

2) I don't think that most people will seriously be considering Ret 2pc as a viable progression option. It'd certainly be a large DPS increase, but if the bosses aren't massively undertuned I think the survivability loss (a few hundred avoidance rating, roughly) wouldn't be worth it. You would be able to get off more SotRs and Inqs between WoGs, but in the end that's all it buys you.

For parse-hunting and DPS maximization, it will certainly be an attractive bonus. But that's what you do on farm content, not progression bosses. The vast majority of players won't care about that. Of course, we'll do the simulations anyway, because we have nutjobs like Khira, Meloree, and myself around who do care about that, or at least find it interesting. That shouldn't be taken as an indication that it's relevant for actually killing bosses, though.

[Kihra]

2) I don't think that most people will seriously be considering Ret 2pc as a viable progression option. It'd certainly be a large DPS increase, but if the bosses aren't massively undertuned I think the survivability loss (a few hundred avoidance rating, roughly) wouldn't be worth it.

There are still enough unknowns that I'm not sure about 2pc Ret for progression, but I am actually considering it. For me, it depends on the following:

(1) Whether the 4pc Prot bonus is needed. Our raid is currently so full of CDs already that I'm unconvinced that the 4pc will really be much of a benefit for my raid. Mostly it depends on if there are any fights in Dragon Soul where the 100yd range would be amazing.

(2) On how much of a DPS boost 2pc Ret actually is. I'll be curious to see. Plus I just like the idea of playing with a different rotation for a tier.

As far as giving up a few hundred avoidance, I'm not sure that's much of a survivability loss. The gear in the next tier is strange in that they have done away with Stamina socket bonuses. This closes the EH gap between Ret gear and Prot gear and actually leads to a model where I could see socket bonuses being ignored again.

For example if you use the Ret legs and Ret chest, you give up about 400 points in pure avoidance. However the tier prot legs have no mastery on them anyway, so in terms of CTC, I don't think you end up losing much relative to the prot gear.

[theckhd]

That will really depend on the off-set options as well; good mastery/avoid off-set legs would potentially end up winning that battle.

To be honest though, I haven't had time to look at the PTR gear lists that closely yet.

[lythac]

(1) Whether the 4pc Prot bonus is needed. Our raid is currently so full of CDs already that I'm unconvinced that the 4pc will really be much of a benefit for my raid. Mostly it depends on if there are any fights in Dragon Soul where the 100yd range would be amazing.

Also the tier bonuses aren't final. Warriors were updated not too long ago and is massively overpowered. Enough situationally (DW pt 2 sub 20%) for Fury warriors (IMO) to pick up.

[Sur-Pseudo]

wouldn't a judgement increase of 10% be a straight 10% of Tier bonus increase? e.g. a 20% shield would be a 22% shield, etc.

[RedAces]

Yes, No.
It will always be 20% of your J but yes it will be 10% higher than without the glyph.

[Kihra]

(2) On how much of a DPS boost 2pc Ret actually is. I'll be curious to see. Plus I just like the idea of playing with a different rotation for a tier.

I spent a couple of hours screwing around with SimulationCraft, fixed a few bugs with Prot, hacked the Vengeance calculation to just be constant, and then tested out the T13 Ret 2pc bonus. Take this with a grain of salt, since I don't know what other bugs might be lurking in the Prot module for SimulationCraft, but preliminary results show that Ret 2pc is a 1200 DPS gain for T12H level of gear at max Vengeance for low Hit/Expertise values. I coded it assuming the Judgement had to hit in order to gain Holy Power.

In terms of queues, I tried AS+ > J > AS, AS > J and J > AS, and the differences between them were all negligible. AS+ > J > AS was the winner over J > AS by 10 DPS, and AS > J was about 50 DPS behind.

[theckhd]

Those numbers all sound reasonable. The MATLAB code should be updated to handle 2pc ret now, so I'll try and find some time tonight to fool around with numbers. I've been fairly busy lately this week, what with BlizzCon coming up and trying to finish up some data for a professional conference.

[theckhd]

My 939 numbers are a little different. Here's what I get if I just use the T12 heroic gear set and arbitrarily toggle on the different set bonuses:

Code: Select all


939/SoT, 2% hit, 10 exp, Mandible of Beth'tilac (Heroic) 391
           v=    1           v=    0.3         
           T11   T12   T13   T11   T12   T13   
prot 2pc   219   838     0   143   522     0   
ret 2pc      0   756   526     0   494   310   

939/SoT, 8% hit, 56 exp, Mandible of Beth'tilac (Heroic) 391
           v=    1            v=    0.3         
           T11   T12    T13   T11   T12   T13   
prot 2pc   291   1111     0   190   692     0   
ret 2pc      0   1004   396     0   656   232   

I39/SoT, 2% hit, 10 exp, Mandible of Beth'tilac (Heroic) 391
           v=    1            v=    0.3         
           T11   T12    T13   T11   T12   T13   
prot 2pc   291    988     0   190   615     0   
ret 2pc      0   1004   446     0   656   266

So I'm getting closer to 500 DPS for the T13 ret 2-piece bonus (assuming on-cast rather than on-hit). That's with a standard 939, I'm in the process of putting together T13 gear sets and updating the comprehensive rotation simulator now.

[Kihra]

My 939 numbers are a little different. Here's what I get if I just use the T12 heroic gear set and arbitrarily toggle on the different set bonuses:

Code: Select all


939/SoT, 2% hit, 10 exp, Mandible of Beth'tilac (Heroic) 391
           v=    1           v=    0.3         
           T11   T12   T13   T11   T12   T13   
prot 2pc   219   838     0   143   522     0   
ret 2pc      0   756   526     0   494   310   

939/SoT, 8% hit, 56 exp, Mandible of Beth'tilac (Heroic) 391
           v=    1            v=    0.3         
           T11   T12    T13   T11   T12   T13   
prot 2pc   291   1111     0   190   692     0   
ret 2pc      0   1004   396     0   656   232   

I39/SoT, 2% hit, 10 exp, Mandible of Beth'tilac (Heroic) 391
           v=    1            v=    0.3         
           T11   T12    T13   T11   T12   T13   
prot 2pc   291    988     0   190   615     0   
ret 2pc      0   1004   446     0   656   266

So I'm getting closer to 500 DPS for the T13 ret 2-piece bonus (assuming on-cast rather than on-hit). That's with a standard 939, I'm in the process of putting together T13 gear sets and updating the comprehensive rotation simulator now.

Yeah, take my numbers with a grain of salt, since I have no idea how much SimulationCraft gets wrong. I know I coded the HP gain correctly, but maybe it does something stupid like allowing overflow.

Do you understand why your numbers show the T13 Ret 2pc to be less of a DPS boost at high Hit/Exp than at low Hit/Exp? That seems counter-intuitive to me.

[theckhd]

Putting together gear sets will take longer than I thought, so I quickly just manually toggled the flag on and off in the rotation simulation. Here are the results:

939, SoT, 2% hit / 10 exp, T12 gear set:

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                                            DPS            SHPS            E    I    mps
  Q#  Priority                              V=100%  V=30%  V=100%  V=30%   %    %       
   1  SotR>CS>AS>J                          20053   12673     0       0   0.0   0.0   115
   2  SotR>HotR>AS>J                        18307   11392     0       0   0.0   0.0   115
   3  SotR>CS>J>AS                          20029   12643     0       0   0.0   0.0   245
   4  SotR>AS>CS>J                          19897   12568     0       0   0.0   0.0   191
   5  AS>SotR>CS>J                          19649   12415     0       0   0.0   0.0   183
   6  SotR>CS>AS+>J>AS                      20071   12679     0       0   0.0   0.0   158
   7  SotR>AS+>CS>AS>J                      20079   12685     0       0   0.0   0.0   167
   8  SotR>AS[buffGC<2][buffGC>0]>CS>AS>J   20057   12676     0       0   0.0   0.0   117

Toggling on the T13 ret flag gives

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                                            DPS            SHPS            E    I    mps
  Q#  Priority                              V=100%  V=30%  V=100%  V=30%   %    %       
   1  SotR>CS>AS>J                          21001   13250     0       0   0.0   0.0   197
   2  SotR>HotR>AS>J                        19373   12056     0       0   0.0   0.0   197
   3  SotR>CS>J>AS                          21175   13347     0       0   0.0   0.0   294
   4  SotR>AS>CS>J                          20899   13178     0       0   0.0   0.0   268
   5  AS>SotR>CS>J                          20815   13131     0       0   0.0   0.0   241
   6  SotR>CS>AS+>J>AS                      21095   13304     0       0   0.0   0.0   229
   7  SotR>AS+>CS>AS>J                      21029   13261     0       0   0.0   0.0   252
   8  SotR>AS[buffGC<2][buffGC>0]>CS>AS>J   21004   13253     0       0   0.0   0.0   198
 

So the holy power on Judgement pushes J>AS above AS>J by about 200 DPS, and above AS+>J>AS by about 80 DPS.

I was a bit surprised by the bonus giving a smaller benefit at high hit/exp, but I can think of several reasons that make sense. First, the J gain is coded on-cast, which means that it isn't seeing a potential reduction by low hit/exp. We need some PTR testing to determine if that model is correct, or whether it should grant on-hit like CS does.

More importantly, at low hit the Judgement HoPo will be a significantly larger portion of your overall HP gain because of CS misses. As you decrease the probability of CS missing, the rotation tightens up and may negate some of the Judgement HoPo's benefit.

For example, in an ideal case, you might have:
CS-J-CS-SotR
CS-AS*-CS-SotR
CS-J-CS-SotR
But that pushes back J by 3 seconds, reducing the rate of HPG from J. You can also imagine other situations, like CS-AS-CS-J-SotR, which push back CS by a GCD, and thus aren't as big a DPS gain. These might be more common in the high-hit/exp regime than the low one.

Those are just guesses at this point though, it'll take some more digging to figure out if that's really what's going on.

[Kihra]

So it looks like our numbers are pretty close after all. In that final table you linked, it looks like 100% Vengeance is a 1000 DPS boost with 2pc Ret for most queues? And 1100 DPS for SotR>CS>J>AS?

If so, that meshes pretty closely with what I got. I used Kihra's actual gear and current talent builds rather than a stock gear set (and of course SimulationCraft will also cast Heroism and assume you use buffs like Avenging Wrath), so that may just account for the remaining difference.

So it seems we are on the same page after all.

[theckhd]

Yeah, that simulation seems to agree with your results. I think I've figured out why the tier bonus sim disagreed; it was using SotR>CS>AS>J>Cons>HW, which sees a smaller DPS increase (fewer empties to start with, hence the SotR speed-up isn't as critical). Switching it to SotR>CS>J>AS brings it up to a 919 DPS boost at low hit/exp.

There's also a detail I need to sort out regarding the FSM calculation. We get different results depending on whether we use 1 step per GCD or 3 steps per GCD in calculating the state probabilities. I'm looking into it; presumably what's happening is that it's casting J after a half-second gap rather than waiting a full GCD for CS to come off of cooldown. In other words, in this situation (assume all CS's are successful):

CS-J-CS-AS*-SotR-CS-???

7.5 seconds have elapsed since casting J. If we sim with 1 step per GCD, the ??? becomes an empty, and we end with:
empty-CS-J-CS-SotR

If we sim with 3 steps per GCD, we instead wait 1 step (0.5 seconds) and then cast J, which has come off of cooldown. This gives us:
.-J-CS-X-CS-SotR
where "." is the half-second wait period. What this does is push the CS cycle back by half a second. When J doesn't grant Holy Power, the difference between the two sequences is small (~30 DPS). However, once J grants holy power, it becomes a much more important factor, leading to a ~1k DPS discrepancy between the two methods. In addition, it reverses the order of the queues, favoring AS+>J>AS.

To show you what I mean, here are the data dumps for the 4 different scenarios:

1 step, with T13 ret:

Code: Select all

                                            DPS            SHPS            E    I    mps
  Q#  Priority                              V=100%  V=30%  V=100%  V=30%   %    %       
   1  SotR>CS>AS>J                          20036   12665     0       0   0.0   0.0   128
   2  SotR>HotR>AS>J                        18281   11377     0       0   0.0   0.0   128
   3  SotR>CS>J>AS                          20009   12632     0       0   0.0   0.0   258
   4  SotR>AS>CS>J                          19825   12526     0       0   0.0   0.0   199
   5  AS>SotR>CS>J                          19618   12398     0       0   0.0   0.0   197
   6  SotR>CS>AS+>J>AS                      20053   12669     0       0   0.0   0.0   172
   7  SotR>AS+>CS>AS>J                      20017   12648     0       0   0.0   0.0   172
   8  SotR>AS[buffGC<2][buffGC>0]>CS>AS>J   20036   12665     0       0   0.0   0.0   128
   9  SotR>CS>AS>J>HW                       20281   12910     0       0   0.0   0.0   -84
  10  SotR>CS>AS>J>Cons>HW                  20523   13039     0       0   0.0   0.0  -322
  11  SotR>CS>AS+>J>AS>Cons>HW              20538   13040     0       0   0.0   0.0  -276
  12  SotR>AS+>CS>AS>J>Cons>HW              20518   13035     0       0   0.0   0.0  -291
  13  sdAS>sdJ>SotR>CS>AS>J>Cons>HW         20016   12713     0       0   0.0   0.0  -140


3 steps, with T13 ret:

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                                            DPS            SHPS            E    I    mps
  Q#  Priority                              V=100%  V=30%  V=100%  V=30%   %    %       
   1  SotR>CS>AS>J                          21001   13250     0       0   0.0   0.0   197
   2  SotR>HotR>AS>J                        19373   12056     0       0   0.0   0.0   197
   3  SotR>CS>J>AS                          21175   13347     0       0   0.0   0.0   294
   4  SotR>AS>CS>J                          20899   13178     0       0   0.0   0.0   268
   5  AS>SotR>CS>J                          20815   13131     0       0   0.0   0.0   241
   6  SotR>CS>AS+>J>AS                      21095   13304     0       0   0.0   0.0   229
   7  SotR>AS+>CS>AS>J                      21029   13261     0       0   0.0   0.0   252
   8  SotR>AS[buffGC<2][buffGC>0]>CS>AS>J   21004   13253     0       0   0.0   0.0   198
   9  SotR>CS>AS>J>HW                       21097   13398     0       0   0.0   0.0   -14
  10  SotR>CS>AS>J>Cons>HW                  21213   13452     0       0   0.0   0.0  -262
  11  SotR>CS>AS+>J>AS>Cons>HW              21318   13506     0       0   0.0   0.0  -208
  12  SotR>AS+>CS>AS>J>Cons>HW              21206   13448     0       0   0.0   0.0  -242
  13  sdAS>sdJ>SotR>CS>AS>J>Cons>HW         21080   13364     0       0   0.0   0.0  -134


1 step, no T13 ret:

Code: Select all

                                            DPS            SHPS            E    I    mps
  Q#  Priority                              V=100%  V=30%  V=100%  V=30%   %    %       
   1  SotR>CS>AS>J                          20036   12665     0       0   0.0   0.0   128
   2  SotR>HotR>AS>J                        18281   11377     0       0   0.0   0.0   128
   3  SotR>CS>J>AS                          20009   12632     0       0   0.0   0.0   258
   4  SotR>AS>CS>J                          19825   12526     0       0   0.0   0.0   199
   5  AS>SotR>CS>J                          19618   12398     0       0   0.0   0.0   197
   6  SotR>CS>AS+>J>AS                      20053   12669     0       0   0.0   0.0   172
   7  SotR>AS+>CS>AS>J                      20017   12648     0       0   0.0   0.0   172
   8  SotR>AS[buffGC<2][buffGC>0]>CS>AS>J   20036   12665     0       0   0.0   0.0   128
   9  SotR>CS>AS>J>HW                       20281   12910     0       0   0.0   0.0   -84
  10  SotR>CS>AS>J>Cons>HW                  20523   13039     0       0   0.0   0.0  -322
  11  SotR>CS>AS+>J>AS>Cons>HW              20538   13040     0       0   0.0   0.0  -276
  12  SotR>AS+>CS>AS>J>Cons>HW              20518   13035     0       0   0.0   0.0  -291
  13  sdAS>sdJ>SotR>CS>AS>J>Cons>HW         20016   12713     0       0   0.0   0.0  -140


3 steps, no T13 ret:

Code: Select all

                                            DPS            SHPS            E    I    mps
  Q#  Priority                              V=100%  V=30%  V=100%  V=30%   %    %       
   1  SotR>CS>AS>J                          20053   12673     0       0   0.0   0.0   115
   2  SotR>HotR>AS>J                        18307   11392     0       0   0.0   0.0   115
   3  SotR>CS>J>AS                          20029   12643     0       0   0.0   0.0   245
   4  SotR>AS>CS>J                          19897   12568     0       0   0.0   0.0   191
   5  AS>SotR>CS>J                          19649   12415     0       0   0.0   0.0   183
   6  SotR>CS>AS+>J>AS                      20071   12679     0       0   0.0   0.0   158
   7  SotR>AS+>CS>AS>J                      20079   12685     0       0   0.0   0.0   167
   8  SotR>AS[buffGC<2][buffGC>0]>CS>AS>J   20057   12676     0       0   0.0   0.0   117
   9  SotR>CS>AS>J>HW                       20282   12911     0       0   0.0   0.0  -104
  10  SotR>CS>AS>J>Cons>HW                  20524   13040     0       0   0.0   0.0  -342
  11  SotR>CS>AS+>J>AS>Cons>HW              20540   13042     0       0   0.0   0.0  -295
  12  SotR>AS+>CS>AS>J>Cons>HW              20524   13039     0       0   0.0   0.0  -311
  13  sdAS>sdJ>SotR>CS>AS>J>Cons>HW         20106   12770     0       0   0.0   0.0  -193


I'm still thinking about what to do with this. I think that the 1-step simulation is closer to how most of us play. But this doesn't include the CS latency penalty, which could soak up that 0.5s in the majority of cases and make the 3-step simulation more accurate. And there might be other effects going on that I haven't thought of yet.

[Kihra]

There's also a detail I need to sort out regarding the FSM calculation. We get different results depending on whether we use 1 step per GCD or 3 steps per GCD in calculating the state probabilities. I'm looking into it; presumably what's happening is that it's casting J after a half-second gap rather than waiting a full GCD for CS to come off of cooldown. In other words, in this situation (assume all CS's are successful):

I see the same 1k difference in SimulationCraft (which I can basically simulate by refusing to Judge unless CS has > ~1.5 seconds remaining). If I'm interpreting your results (and my results) correctly, it means there's a very real DPS gain to be had by casting Judgement even if CS has < 1.5 seconds remaining on its cooldown. This is actually what was happening by default in SimulationCraft with my changes, and I lost the gigantic DPS gain once I switched to behave like your 1 step model.

This does not surprise me, since the most common scenario is that using Judgement will actually enable Shield of the Righteous to cast faster as well, and because it doesn't require Expertise, Judgement is actually a more reliable HoPo generator than CS. For example, any time you have 2 HoPo, casting Judgement is clearly superior to waiting for CS, because it will accelerate the cast of Shield of the Righteous, and Crusader Strike will still be ready after you've finished the Shield.

Basically it looks like any time you are at the 7.5 second mark from Judgement and you've just gotten out from under the GCD, then casting Judgement again is actually preferred (assuming CS is on cooldown)... my guess is that it's because you will most commonly have 2 HoPo and the # of Shield of the Righteous hits will go up as a result.

In fact, you can even gain ~150-200 more DPS by deferring Holy Wrath and Consecration as fillers if Judgement is coming off CD in 0.5 seconds.

That's really interesting.