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

[theckhd]

Maybe you already included it, but are you using the t8 2pc in your math? If not, with the removal of Blood in the bonus, I'd imagine SoV would be considerably ahead of Blood by even more in almost every circumstance.

This is already including the T8 2-piece and 4-piece bonuses, since Majiben's T8 set uses 4 pieces of T8. Without the 2-piece bonus, SoV is still ahead for low-hit sets, but not by as much.

[theckhd]

UPDATE: New version here as of 3.1.2 (Ulduar 10 hard mode weapons were upgraded this patch).

How is broken promise with SoB bearing up vs Last Laugh with SoV? I assume all of this was done with Last Laugh, but Broken promise gains significantly with SoB due to its slower weapon speed.

Wow, you guys are slave drivers!

For one thing, I've re-run the Ulduar weapon analysis, which I will hopefully get time to post tomorrow.

I made some time this morning just to get this posted, since you asked. I'll probably be busy the rest of the day, so the rest of the graphs will probably have to wait until Monday.

Since this analysis is pretty straightforward, I'm going to go with another big plot that's got everything on it, rather than making separate plots for SoV and SoB. Luckily, this one is pretty readable even when this densely packed with information. If you have trouble reading it, find some 3-D glasses with blue and red color filters and look at the graph through those (one eye at a time!).

Setup:
Rotation: 969
Seals: SoV (blue), SoB (red)
Glyphs: Judgement+Vengeance (JV) for SoV, Judgement+Exorcism (JE) for SoB - note that this is basically just J since Exorcism isn't used
Talents: 5V+2C
Gear: Majiben's T8 progression set, with weapons substituted as below
Weapons: Broken Promise (BP), Last Laugh (LL), Titanguard (TG), Sorthalis, Hammer of the Watchers (ST)


The convention here is that Last Laugh is the circles, Broken Promise is the squares, Titanguard is the diamonds, and Sorthalis is the triangles. Solid lines for currently-available weapons (LL and BP), and dotted lines for Ulduar weapons (TG and ST).

First, we'll look at SoV, which are the blue curves. We see that as expected, the higher DPS (or ilvl) weapon always wins for SoV rotations, as would be expected for HotR scaling. Basically everything here is an incremental upgrade, nothing amazing or noteworthy to point out.

The red curves tell a different story for SoB though. We already knew that Broken Promise was better than Last Laugh for SoB, and this graph confirms that once again. In fact, the slow weapon speed on BP makes it a better choice than Titanguard as well. Sorthalis is the first fast weapon that's able to pull ahead of BP for SoB. So if you're an emo tank that likes cutting themselves, stick with your BP until you get your hands on Sorthalis.

As for SoB+BP vs. SoV+LL, we see that with this low-hit, low-expertise set SoV+LL wins by a decent margin. This is due to both the weakness of SoB with low expertise and the T8 2-piece bonus. Of course, as we ramp up the expertise, we know that the SoB curves can move up by as much as 150 TPS, which would put SoB+BP ahead of SoV+LL (and probably SoV+TG) even before we consider substitution rotations. However, it would take a very specialized build (heavy in Reckoning, like the 5V+3R build) for SoB+BP to ever break even with Sorthalis+SoV. And of course, if you have ST, you'd be better off using that than BP anyway, according to the plot.

TLDR summary:

• For SoV, just go by weapon DPS or ilvl to determine what weapon gives you better threat.
• For SoB, Broken Promise is the best tanking weapon available until you get your hands on Sorthalis
• Unless you have high expertise, BP+SoB won't keep up with LL+SoV in TPS.
• If you want to maximize your dps while not tanking (assuming dual-speccing Ret isn't an option), and have some expertise/hit (i.e. ret) gear, BP+SoB is likely to be your best DPS option until you get Sorthalis, especially if you can hit the expertise cap and attack from behind. Don't forget to substitute for Holy Shield and/or Judgement.

[æ]

Basically, any analysis that only looks at SoV or SoB should give similar results. It's only when you're comparing one to the other that we should see noticeable differences, because one depends strongly on the two-roll structure and one doesn't.

Yeah, so if we have 3/3 SancOfBattle, wouldent the crit do more for a SoB rotation? And seeing how exo/AS sub loves the SoB rotations longtime (more than SoV) wouldent the +15% to exo do more for SoB? From that graph it looks like SoB gains 240~ TPS from exo sub alone @ 3/3, but I assume 2/3 would be a better option.

[theckhd]

Yeah, so if we have 3/3 SancOfBattle, wouldent the crit do more for a SoB rotation? And seeing how exo/AS sub loves the SoB rotations longtime (more than SoV) wouldent the +15% to exo do more for SoB? From that graph it looks like SoB gains 240~ TPS from exo sub alone @ 3/3, but I assume 2/3 would be a better option.

I think you can get this all from the other plot, but since I have a new one already anyway, I'll post it and we'll dissect it in detail:

Setup:
Rotations: 969, JsE, JsA, JsAE
Seals: SoB only
Glyphs: JE (969 and JsE), JA (JsA and JsAE), EA (JsAE)
Talents: 5V+3C+3R, with both 0/3 and 2/3 Sanctity of Battle
Gear: Majiben's default gear set - note that since this is low on hit, these numbers will go up as you stack hit/expertise


First of all, Sanctity of Battle will clearly do more for SoB than for SoV, since you're more likely to be subbing in Exorcism for JoB than for JoV, and crit helps SoB far more than SoV in the first place. For SoV, Sanctity of Battle is almost exactly equivalent to one point in Conviction. So it's never worth speccing into Sanctity of Battle over Crusade if you're using SoV.

As for SoB, we can estimate the benefit of Sanctity of Battle per point from that plot - 2/3 Sanctity of Battle gives SoB 140 DPS for JsE, so each point is worth about 70, which is almost on par with Crusade (though Crusade gets better with 5/5 Conviction and with each point in Sanctity of Battle too). So we'd expect Crusade to be generally better than Sanctity of Battle even for SoB, though the margin is much slimmer.

Since a point in Sanctity of Battle isn't considerably better than a point in Crusade, we don't expect Sanctity of Battle to help SoB gain any ground on SoV in the analysis. Just to check for sure, let's run the numbers quickly.

Setup:
Rotations: JsE
Seals: SoBV and SoB
Glyphs: Judgement and Vengeance (JV) for SoV, Judgement and Exorcism (JE) for SoB
Talents: 5V as a base, with either 2/3 SancBat and 3/3 Crusade (blue bars), or 3/3 Sancbat and 2/3 Crusade (red bars)
Gear: Majiben's default gear set - note that since this is low on hit, these numbers will go up as you stack hit/expertise

We see here that both SoV and SoB get a bigger benefit from Crusade. The difference for SoV is quite noticeable (as expected), while the difference for SoB is on the order of ~5 TPS. The gap between the two seals is smaller with 3/3 SancBat, but both setups generate lower TPS in that configuration, so you're cutting off your nose to spite your face, so to speak.

TLDR summary:

• Sanctity of Battle's worth varies depending on the Seal you use.
  
  • For SoV, SancBat is equivalent to Conviction.
  • For SoB, it's almost as good as Crusade (but not quite).
• Crusade is strictly better than Sanctity of Battle in all cases.

[theckhd]

SoB Analysis Part 3 - Breakdown of TPS stats

Since I have these plots generated, I may as well post them. In case anyone was wondering how our gearing priorities change when considering SoB-tanking, here they are.

First, the STR plot:

DPS plot
So again, Hit and Expertise win for SoB. Expertise is better for overall DPS, and roughly equivalent to hit for TPS.

Next, Hit:

DPS plot
Not surprisingly, Hit drops like a rock at the melee hit cap.

Finally, Expertise:

DPS plot
Similarly for Expertise - after the dodge soft cap it drops in effectiveness.

Well below both the melee hit cap and the dodge soft cap, the breakdown in bar plot format looks like this:


And in terms of pure stat points:


TLDR summary:
If you're using SoB, the best way to improve DPS/TPS is to stack Expertise until you hit the dodge soft-cap, then stack Hit until you reach the melee hit cap. After that, stack STR.

[theckhd]

What's the best weapon enchant for DPS/TPS?

Re-ran this analysis quickly, since it was an easy one. Added pretty graphs too.

Setup:
Rotation: 969
Seals: SoV
Glyphs: Judgement + Vengeance (JV)
Talents: 5V+2C

Code: Select all

Ench      DPS   TPS
Berserk    45   108
Acc        33    82
TWeapCh    26    66
Pot        22    55
SupPot     21    50
GrPot      16    39
Mong       15    32
26 Agi     10    24

The Titanium Weapon Chain now pulls ahead of Potency as far as TPS goes. Accuracy is still the winner, though.


Also ran the simulation for some raid foods. The abbreviations are:
DFF = Dragonfin Filet (+40 STR, +40 STA)
FF = Fish Feast (+80 AP, +46 SP, +40 STA)
BDF = Blackened Dragonfin (+40 AGI, +40 STA)
RW = Rhinolicious Wrymsteak (+40 Expertise Rating, +40 STA)
SX = Snapper Extreme (+40 Hit Rating, +40 STA)

Code: Select all

Food  DPS   TPS
DFF    46   115
SX     39   100
FF     35    88
RW     30    65
DFF    18    43

Interestingly (though perhaps not unexpectedly), Snapper Extreme is quite a bit better than Fish Feast, but still not as good as Dragonfin Filet.

I ran the analysis again for SoB (and can post exact numbers if people care). Here are the plots, for those interested:
Enchants
Food
We probably could have guessed at these results anyway. Accuracy is still the best enchant, since Hit is much stronger than STR for SoB. Titanium Weapon Chain is a distant 2nd, and Potency a distant 3rd. Interestingly Accuracy is even better than Berserking here - I wonder whether that's the case for Ret as well?
Rhinolicious Wyrmsteak (+expertise) and Snapper Extreme (+Hit) are the top two foods, with Dragonfin Fillet a distant 3rd.

TLDR summary:

• For TPS with Seal of Vengeance, Accuracy > Titanium Weapon Chain > Potency > anything else, and Dragonfin Fillet is the best food buff.
• For TPS with Seal of Blood, the enchanting order is the same but there's a much larger gap between the weapon chain and Potency. For foods, Rhinolicious Wyrmsteak and Snapper Extreme are your best food buffs.
• All of this assumes you're below the melee hit cap and dodge soft cap. I shouldn't have to tell you what happens if you're above those thresholds (hint: when in doubt, STR is your friend)

[Rasmfrackn]

First, for STR:
Again, the two scale roughly similarly, with SoV scaling ever so slightly better.

For hit:
As before, SoB scales noticeably better with hit than SoV does. In fact, we have to be careful with our wording here, because the scaling in these plots is due to the entire rotation. In the case of SoV, the seal's DoT component doesn't benefit from hit at all, though Judgement does. So most of the scaling we see for SoV is due to the rest of the rotation. On the other hand, SoB gains the benefit from hit rating on two of the three rolls that determine a SoB proc, so it scales considerably better.
However, unlike the last round of simulations, it never overtakes SoV now. While hit can help SoB catch up, it can't independently boost it ahead of SoV.

Finally, for expertise:
Again, we need to be careful here - SoV gains absolutely nothing with expertise, so all of the scaling we see here in the "SoV" plot is due to the rest of the rotation (i.e. melee attacks). SoB, on the other hand, gets benefits from expertise twice. Again, here is the plot with just the contribution of the seals and judgements themselves.
Last time we ran this, it took very little expertise for SoB to surpass SoV. This time, it takes roughly 120 expertise rating from gear, or 14.6 expertise, to reach the break-even point. SoB does scale considerably better though, and past this point has the potential to make some real gains. Note that with Combat Expertise, this would be 20.6 expertise as read off of the character sheet (or 30.6 with SoV active and glyphed).

I'm having a little trouble finding the intuition behind these. If all that changed was modifying the model to use a 2-hit system, shouldn't the SoV vs SoB curve look the same as it used to at and above the hit cap? I guess it's probably due to assuming 0 of the other stat for each curve, right? (e.g. assuming 0 expertise while varying hit, assuming 0 hit while varying expertise)

If I cap hit and soft-cap expertise, SoV still comes out ahead now with the 2-roll system just due to the remaining 7.5% parry rate? Or maybe did the "new" T8 set bonus come in at the same time to skew things enough...

[æ]

You're the man.

Your plots and graphs are like candy.

[Cidx]

Do you you do threat/DPS based things? I see that Accuracy great for TPS/DPS but how about the new Bladeward enchant? 200 Parry Rating and extra damage on your next parry? or unable to test this as of yet?

[theckhd]

I'm having a little trouble finding the intuition behind these. If all that changed was modifying the model to use a 2-hit system, shouldn't the SoV vs SoB curve look the same as it used to at and above the hit cap? I guess it's probably due to assuming 0 of the other stat for each curve, right? (e.g. assuming 0 expertise while varying hit, assuming 0 hit while varying expertise)

If I cap hit and soft-cap expertise, SoV still comes out ahead now with the 2-roll system just due to the remaining 7.5% parry rate? Or maybe did the "new" T8 set bonus come in at the same time to skew things enough...

The scaling should be pretty close to what it was before. To be completely accurate, SoB should scale even better with hit and expertise in the 2-roll system than it did in the one-roll system, and that's reflected properly on the graphs. What's changed is the starting points, as you identified - basically the SoB curve has been shifted down a good bit, because the 2-roll system reduced its overall DPS, and the T8 2-piece has increased SoV's overall DPS.

So SoB scales better, but starts out far worse in the low-hit, low-expertise regime. Each graph is plotted assuming the base value of the other (so 60 hit rating, 0 expertise, and whatever the lower bound is on the STR graph).

If you look at the expertise graph, you'll notice that you don't need to even hit the dodge soft-cap for SoB to pull ahead. So your statement about capping hit and dodge isn't true - capping dodge alone is enough to make SoB the higher-threat seal. Adding hit will reduce the threshold of expertise required for the crossover point, but will never reduce that point to 0 expertise.

To put it more qualitatively, the "gap" between SoV and SoB is reduced by both hit and expertise. Expertise just reduces it faster than hit. Hit alone can't reduce it to zero, but a combination of hit and expertise can reduce it to zero or less (meaning SoV < SoB).

Qualitatively, you could model it something like this:
Delta = A - B*hit_rating - C*expertise,
where
Delta is the DPS difference between SoV and SoB,
A is the baseline difference (~230ish according to the plot, but that's for 60 hit rating, see below)
B is the difference in slopes on the hit rating plot (according to the plot, this is 3.1034-2.3470 = 0.7564)
C is the difference in slopes on the expertise plot (according to the plot, this is 3.1207-1.4716 = 1.6491)
If we extrapolate back to 0 hit rating with the value for B, we get A = 275ish.

Note that this is only valid below the hit cap and (more importantly) the dodge soft-cap for SoV, which means 82ish expertise rating. After that, the slope of the SoV line changes to 0.7368. A more accurate formula would be:
Delta = A - B*hit_rating - C*expertise_rating_below_82 - D*expertise_rating_above_82,
where D would have a value of 3.1207-0.7368 = 2.3839

So
Delta = 275 - 0.76*hit_rating - 1.65*expertise_rating_below_82 - 2.38*expertise_rating_above_82

If Delta > 0, SoV > SoB. Otherwise, SoB > SoV.

Just checking some easy numbers, let's put in 60 hit rating and 120 expertise:
Delta=275 - 0.76*60 - 1.65*82 - 2.38*(120-82) = 3.66, which is pretty close to 0, and within the error bounds of all the rounding I've been doing here.
Let's instead try 150 hit rating, and 100 expertise:
Delta=275 - 0.76*150 - 1.65*82 - 2.38*(100-82) = -17.14, which is <0, indicating that SoB would do more DPS here. It's clear from this result that the crossover point on the expertise graph has moved down to below 100 expertise rating as a result of the added hit rating.

If we want to solve for the crossover, we can set Delta=0. Since we had to split expertise rating, we need to represent it as two equations. First, pretend that the expertise rating is less than or equal to 82, so that expertise_rating_above_82=0. Solving the equation then gives:
expertise_rating_below_82 = 166.67 - 0.46*hit_rating, (up to a maximum of 82 expertise rating)
Similarly, setting expertise_rating_below_82 = 82, and solving for expertise_rating_above_82 gives:
expertise_rating_above_82 = 58.70 - 0.32*hit_rating

So for a given hit rating, the expertise crossover is:
expertise_rating = min([82 expertise_rating_below_82]) + max([0 expertise_rating_above_82])

[theckhd]

Do you you do threat/DPS based things? I see that Accuracy great for TPS/DPS but how about the new Bladeward enchant? 200 Parry Rating and extra damage on your next parry? or unable to test this as of yet?

I can't model this because I don't have any details on the exact mechanics behind it (and I haven't had time to look, unfortunately). If someone can point me to a resource, or better yet come up with a formula that describes it, I can crank it through the simulation.

My impression is that it's an avoidance enchant though, not a threat/dps one.

[Rasmfrackn]

So SoB scales better, but starts out far worse in the low-hit, low-expertise regime. Each graph is plotted assuming the base value of the other (so 60 hit rating, 0 expertise, and whatever the lower bound is on the STR graph).

If you look at the expertise graph, you'll notice that you don't need to even hit the dodge soft-cap for SoB to pull ahead. So your statement about capping hit and dodge isn't true - capping dodge alone is enough to make SoB the higher-threat seal. Adding hit will reduce the threshold of expertise required for the crossover point, but will never reduce that point to 0 expertise.

To put it more qualitatively, the "gap" between SoV and SoB is reduced by both hit and expertise. Expertise just reduces it faster than hit. Hit alone can't reduce it to zero, but a combination of hit and expertise can reduce it to zero or less (meaning SoV < SoB).

Ok, so that still makes sense to me then. (And the hit/dodge cap statement was more of a question... ) I suppose you'd need to create a surface to show the interaction between hit and expertise visually to compare SoV to SoB. (Not necessarily a request. ) It just seemed a bit odd that hit rating never lets SoB catch up to SoV when it did under a 1-roll system, but it makes sense in the context of 0 expertise.

I like to assume a minimum of ~15 to 20 expertise skill, and I hate dropping below 150 hit rating. I guess I need to go back and re-check Majiben's gear set to see how low it is on hit and expertise that SoB doesn't pull ahead in basically any talent setup.

-- Ok, yeah. The first column of gear is only like 2% hit and 3-5 expertise skill. No wonder.

[Cidx]

Do you you do threat/DPS based things? I see that Accuracy great for TPS/DPS but how about the new Bladeward enchant? 200 Parry Rating and extra damage on your next parry? or unable to test this as of yet?

I can't model this because I don't have any details on the exact mechanics behind it (and I haven't had time to look, unfortunately). If someone can point me to a resource, or better yet come up with a formula that describes it, I can crank it through the simulation.

My impression is that it's an avoidance enchant though, not a threat/dps one.

My feeling would be the same but definitely whatever mechanics may be it could be just as good as say our Holy Shield doing damage when we block. This enchant could also very well scale with Reckoning in that it has chance to proc when an extra attack happens due to reckoning.

[theckhd]

Ok, so that still makes sense to me then. (And the hit/dodge cap statement was more of a question... ) I suppose you'd need to create a surface to show the interaction between hit and expertise visually to compare SoV to SoB. (Not necessarily a request. ) It just seemed a bit odd that hit rating never lets SoB catch up to SoV when it did under a 1-roll system, but it makes sense in the context of 0 expertise.

You wouldn't actually need a surface plot unless you really wanted to know the exact magnitude of the difference. If you're just interested in a binary "SoV is better" or "SoB is better," you could easily plot the function I posted in 2-D, with Hit Rating on one axis and Expertise Rating on the other. I can run through a more accurate analysis (with graphs) if I get time later this week.

I like to assume a minimum of ~15 to 20 expertise skill, and I hate dropping below 150 hit rating. I guess I need to go back and re-check Majiben's gear set to see how low it is on hit and expertise that SoB doesn't pull ahead in basically any talent setup.

-- Ok, yeah. The first column of gear is only like 2% hit and 3-5 expertise skill. No wonder.

Note that this is expertise rating from gear only - It's already assuming a base 6 expertise skill from talents, and 10 from the SoV glyph (for SoV only of course). Racial expertise bonuses for weapons would count towards the "expertise rating from gear" though, since that's not already included in the analysis.

[theckhd]

While perusing the patch notes, I noticed this:

Armor Penetration Rating: All classes now receive 25% more benefit from Armor Penetration Rating.

I assume this is just a flat factor of 1.25 increase on the amount of armor it reduces? If anyone has a link to testing on this, I'd be interested to see it. It's not an urgent matter, since it still won't be a great threat stat for us, but it may shuffle around the rankings at the lower end of the spectrum, and I'm a perfectionist.