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

Warning: Theorycraft inside.

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Postby theckhd » Fri Feb 27, 2009 2:29 pm

Had some time today to "pretty up" the presentation of this data, as well as get corrected numbers with the updated Exorcism code.

First of all, let's take a look at the DPS of the different rotations for a standard 5/5x/6 spec:
DPS:
Image
TPS:
Image
I've put lines at 3162 DPS and 8181 TPS, which are the baseline values for the default 969 with Judgement and SoV glyphs. These lines will remain at those values for the rest of the plots, so we can see how things compare to that basic benchmark.

There are a few things to notice here:
  • Exorcism on cooldown and Holy Shield substitution rotations always win out for both DPS and TPS. As we'll see soon, this will remain true for all of the specs we'll be looking at today.
  • Judgement substitution is only better if both Judgement and SoV are glyphed, though it's always better than a 969 without the Judgement glyph.
  • Consecration substitution is weaker even if glyphed, and worse yet if it goes unglyphed.
  • Both 6's substitution schemes are just poor all around. The alternating 6's one is so bad it's off the bottom of the chart


Just as a sanity check, let's compare it to a 0/5x/15 spec that picks up conviction:
DPS:
Image
TPS:
Image
Nothing here should be a surprise:
  • The conviction spec does slightly higher DPS, slightly lower TPS.
  • The Consecration substitution rotation gets a little boost here by replacing a spell that can't crit with one that can, but still lags the default-spec 969 in TPS.
  • Judgement substitution is better in both cases as long as Exorcism is glyphed.

If we now look at a Ret subspec that goes 18 into Ret for Sanctified Seals, we notice a big change:
DPS:
Image
TPS:
Image
First of all, we see a noticeable increase in both DPS and TPS across the board. The relative differences within this spec are pretty much the same though, with the JSE Exorcism-on-cooldown rotation edging ahead by a little over 100TPS

Next, Ret subspec that goes 18 into Ret for Crusade:
DPS:
Image
TPS:
Image
Again, an across-the-board increase in both types of output, and again, relative rankings haven't changed, though the Exor-on-cooldown rotation is now closer to 150TPS ahead.

And finally, for the obsessive-compulsive in each of us, the 0/51/20 spec that picks up 3 in Crusade and 2 in Sanctified Seals:
DPS:
Image
TPS:
Image
Again, an increase across the board. The Holy Shield replacement strategy is finally OVER NINE THOUSAND threat. But overall, this graph looks exactly like the other ones I've posted so far.

Some take-home thoughts from this:
  • Consecration substitution, which looked advantages from a mana expenditure point-of-view, always lags a standard 969, regardless of what spec you pick. As such, it's never the answer, even glyphed.
  • Neither of the 6's-substitution schemes ever hold a candle to standard 969, because HotR and ShoR are two of our biggest threat moves, so replacing either with a weaker one is always going to trail a rotation that keeps both of those skills on cooldown.
  • Judgement substitution can boost both DPS and TPS as long as Exorcism is glyphed - without it there's no noticeable gain.
  • Exorcism on cooldown is always the best DPS and TPS output, and performs best when Judgement and Exorcism are both glyphed. I haven't tested without the SoV glyph yet, but since we've narrowed down the rotations we're interested in, I can look into this a little further in a later post.
  • Holy Shield replacement is by far the best DPS and TPS boost, at the expense of Holy Shield uptime. This is likely to be our new prot-dpsing rotation, as well as the rotation we should use against casters that do not melee (or at least, not hard).
  • Note that all of these graphs assume the 1% Sense Undead bonus, but don't assume Exorcism is automatically a critical. I should have taken off the Sense Undead modifier, but frankly I forgot, and since it's a flat 1% bonus, it won't change anything except the final numbers.
  • I intend to test with some version of Exorcism auto-crit later on to see if that helps either of the 6's replacement strategies. However, they're so far behind in most cases that it may not be enough to save them.
Last edited by theckhd on Mon Mar 09, 2009 5:36 am, edited 1 time in total.
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Postby Laz » Fri Feb 27, 2009 2:44 pm

These graphs are awesome.

It's great to see mathcraft support what I've been saying about the Crusade spec. I had anecdotal evidence, but the DPS/TPS difference between 5/60/6 using 6969 vs 53/18 with 5/5 Conviction and 3/3 Crusade is remarkable.

When 3.1 comes out Crusade is likely to be the canon spec with variants into Pursuit of Justice rather than 5/5 Conviction.
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Postby Dorvan » Fri Feb 27, 2009 3:05 pm

Laz wrote:It's great to see mathcraft support what I've been saying about the Crusade spec. I had anecdotal evidence, but the DPS/TPS difference between 5/60/6 using 6969 vs 53/18 with 5/5 Conviction and 3/3 Crusade is remarkable.


I don't think anyone has ever doubted that 0/53/18 was more threat than 5/60/6, it's just that until 3.1 it requires you to take at least a couple of points out of mitigation talents. Nice to have better quantification of the difference though :)


As for general takeaway conclusions, some observations:

-- For maximizing mitigation, you're best off using a standard 969 rotation. Since the DP glyph is looking pretty mandatory atm, you'll want to glyph SoV/Judgment

-- If you manage to reach hit cap, you can get a very slight threat boost by changing your judgment glyph to Exorcism and using the Judgment-sub rotation, while not losing any mitigation.

-- Switching to a judgment-sub rotation without being hit-capped gets you a small threat boost (0.75-1%) at a cost of a small amount of JotJ uptime (~3% if you're 4% short of hit-cap, 1.5% if you're 2% short).

-- Switching to a HS-sub rotation nets you about 2-2.5% threat in exchange for a loss of 44% HS uptime.

One question:

What mob type was assumed for Crusade? I think it'd be most useful to assume non-special mobs for general summaries, as Ulduar is probably going to be mostly giants and mechanical.
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Postby theckhd » Fri Feb 27, 2009 7:39 pm

Dorvan wrote:What mob type was assumed for Crusade? I think it'd be most useful to assume non-special mobs for general summaries, as Ulduar is probably going to be mostly giants and mechanical.

Looks like it was a 6% bonus, so a special mob. I can change that easily enough though, since I was already thinking about adding an "Undead" flag to incorporate Exorcism crits.
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Postby theckhd » Sat Feb 28, 2009 12:22 pm

Ok, Plots have been updated for a generic (non-undead, non-humanoid, non-demon, non-elemental) boss. That means:
  • Crusade's effect is 3% rather than 6%
  • Sense Undead glyph isn't giving any bonus (though since it's a flat 1% boost that hardly matters)
  • Exorcism auto-crits


If we recalculate for an undead mob, something interesting happens. First, the 5/60/6 spec:
DPS:
Image
TPS:
Image
The Consecration substitution also surpasses the regular 969 for an undead mob. Note that the HotR substitution actually overtakes the 969 against an undead mob, though it's still weaker than Consecration substitution.

For the 0/51/20 spec:
DPS:
Image
TPS:
Image
Pretty much the same as the last plot, with bigger numbers.
Last edited by theckhd on Mon Mar 09, 2009 5:37 am, edited 1 time in total.
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Postby theckhd » Sat Feb 28, 2009 12:23 pm

Oh, and for the code-conscious, here's the Exorcism code at the moment:
Code: Select all
Exorcism = (1087 + 0.15.*AP + 0.15.*SP).* ...    %inherent
    (100 - boss_spell_resist)./100.* ... %hit,
    (100 + 0.5.*(spell_crit.*(1-Undead) + ... %crit for non-undead
                 Undead.*100 + ...            %crit for undead
                 HotC).*Crit_Meta)./100.* ... %HotC, meta bonus
    (OHWS.*Crusade.*GoSU.*GoExor).* ...           %talents/glyphs
    (CoE.*SanctRet) ...                 %buffs/debuffs
    .*boss_resist_reduce;               %boss resist


Where "Undead" is a binary-valued variable that basically toggles whether we use "spell_crit" or a flat 100% crit rate
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Postby theckhd » Sat Feb 28, 2009 3:01 pm

<edit> The values in this table were originally wrong, I've updated them to be accurate as of 3/3/09. See this post for the new calculation.

Hm.... side diversion. A guild member and I were discussing weapon enchants, and he asked if the new Accuracy enchant (25 hit and crit) was any good. I realized that since we made the determination that Hit was our second best threat stat beyond a certain threshold, we have never revisited the topic of weapon enchants.

Our back-of-the-envelope calculation led us to the conclusion that Accuracy was better for threat overall than Potency. I whipped together a little matlab script to get the exact numbers:
enchant_compare.m

The weightings were calculated the same way as the plots on page 2 of this thread, with ~1250 Character Sheet STR (about what I have), a 5/60/6 spec, and the usual 969 rotation. The relevant stats are:
STR gives 1.08 DPS and 2.80 TPS per point
AGI gives 0.33 DPS and 0.83 TPS per point
Hit gives 0.68 DPS and 1.75 TPS per point (rating)
Crit gives 0.34 DPS and 0.85 TPS per point (rating)
AP gives 0.32 DPS and 0.81 TPS per point (rating)

Note that these change with gear somewhat, but the relative ordering is stable.

Using these values, here's what we get for the different weapon enchants:
Code: Select all
Enchant           DPS    TPS
Berserking        45.0  113.7  (assuming 140 static AP)
Accuracy          25.6   65.0
Potency (BC)      21.6   55.9
Superior Potency  20.9   52.8
Greater Potency   16.1   40.6
Ti Weap Chain     19.1   48.9
Mongoose (BC)     12.0   27.7  (assuming 30 static AGI)
Ex. Agility        8.7   21.5

Ignoring Berserking, which I added for laughs, Accuracy is clearly the best DPS and TPS enchant we have available at the moment, at least for players with mostly best-in-slot items. The 25 hit alone is inferior, but the 25 additional crit pushes Accuracy ahead of Potency.

Another thing to note is that the Weapon Chain doesn't fare too badly here either, only behind Potency by less than 1 DPS and 2.5 TPS. Potency gives the additional mitigation from the extra Block Value, but the weapon chain gives (potentially) a dps bonus against mobs and bosses that can disarm. So the difference there is very minor.

I think I'm going to go re-enchant my Last Laugh now.
Last edited by theckhd on Tue Mar 03, 2009 1:26 pm, edited 1 time in total.
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Postby majiben » Sat Feb 28, 2009 3:25 pm

Weapon chain's antidisarm effect does not stack with the new shield enchant nor PoJ.
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Postby Mavrix » Sat Feb 28, 2009 3:29 pm

theckhd wrote:Accuracy is clearly the best DPS and TPS enchant we have available at the moment, at least for players with mostly best-in-slot items. The 25 hit alone is inferior, but the 25 additional crit pushes Accuracy ahead of Potency.


I've been using Accuracy and suggested it in other threads a few times. Glad to see some additional evidence backing it as a choice.
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Postby Dorvan » Sat Feb 28, 2009 3:42 pm

Honestly, what disarms? I really can't think of anything, and it's so situational as to be trivial imo and not worth factoring in to one's decision. Also, for mongoose you should add in 0.5% haste (16.4 rating).
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Postby theckhd » Sat Feb 28, 2009 4:24 pm

Dorvan wrote:Honestly, what disarms? I really can't think of anything, and it's so situational as to be trivial imo and not worth factoring in to one's decision. Also, for mongoose you should add in 0.5% haste (16.4 rating).

Is that 16.4 average haste rating, or 16.4 every time it procs?

If it's average, it raises the DPS/TPS values to 12.9 and 30.2 respectively.
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Postby Dorvan » Sat Feb 28, 2009 4:27 pm

theckhd wrote:
Dorvan wrote:Honestly, what disarms? I really can't think of anything, and it's so situational as to be trivial imo and not worth factoring in to one's decision. Also, for mongoose you should add in 0.5% haste (16.4 rating).

Is that 16.4 average haste rating, or 16.4 every time it procs?

If it's average, it raises the DPS/TPS values to 12.9 and 30.2 respectively.


That's average (2% haste per proc, 25% uptime). And I figured it wouldn't have much effect, but might as well have everything modeled :)
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Postby Liaene » Mon Mar 02, 2009 5:48 am

I'm just wondering, does the math in the exorcism replacing alternating 9's rotation consider the loss of dps/tps on SotR if you are using a Libram of Obstruction? Since exo replacing a judgement would mean you are getting 352 less BV on that next SotR.
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Postby theckhd » Mon Mar 02, 2009 6:01 am

No, the Libram isn't modeled at all. That's something I can try and add when I get time though. Probably the easiest way is to calculate ShoR damage with and without the Libram proc, and re-write the rotations to use them as appropriately.
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Postby theckhd » Mon Mar 02, 2009 7:03 am

Quick update: someone asked in the gear forum about trash tanking, and whether Accuracy is better than Potency if the mob is just getting hit by Consecration and Holy Shield.

<edit> Plots were wrong, so I took them down. See page 7 for updated calculations


Conclusion:
Basically, Hit is the best, and since both abilities use the spell hit cap, this will be true up until you stack 17% hit.

The order is Hit > Strength > AP > SP > Stam. Anything not listed has 0 effect on Holy Shield and Consecration.
Last edited by theckhd on Tue Mar 03, 2009 1:49 pm, edited 2 times in total.
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