Theck's MATLAB TPS analysis (A Jonesy derivative work)

[theckhd]

What stat gives us the biggest threat boost?

We'll approach this by determining the change in DPS and TPS that 10 itemization points worth of each stat provides. Mechanically, this means we calculate DPS and TPS once with Majiben's default gear set, and then add 10 itemization points of a stat and recalculate. The difference in the two values is the boost we've gained from adding that stat.

Note that since we're doing this in terms of itemization points, it's a measure of how happy we are to see each of these stats on our gear and gems. It is not a good way to compare enchants, which aren't itemized equally - for that see the end of this post for the breakdown per stat point.

Setup:
Seals: SoV
Rotation: 969
Glyphs: Judgement and Vengeance (JV)
Talents: 5 Conviction + 2 Crusade (5V+2C)
Gear: Majiben's progression gear set
Stats: Plot the DPS/TPS bonus of each stat and determine how they scale with STR, Hit, and Expertise.

I'm choosing to stick with the 5V+2C spec here again, for the same reasons I've given before. The last point in Crusade doesn't change anything, and 5V+2C should behave similarly to 3V+3C, which I feel will be another common spec now that I've shown it's a relatively small TPS loss.

As always, we'll take a look at STR first, since that's an easy benchmark:

STR is still king, but Hit has gained some considerable ground. It is now absolutely clear that it is our second-best threat stat - with this change it would be ahead of Block Value even at heroic and weaker gear levels. Expertise has gained some ground as well, as it used to be halfway between AP and Crit. Now it's right on par with AP, and poised to pass it further down the line, perhaps as soon as Icecrown-level gear.
On the DPS plot, Expertise has actually gained enough ground to take the third-place slot, passing AP and Block Value.

Note that since the hit and expertise graphs should have the same starting points, this effect will be mirrored on those plots - Expertise and Hit see a gain on all plots, and expertise will always start off in third place on the DPS plots and 5th place on the TPS plots.

Next, we'll see how things scale with Hit Rating:

Not much has changed here from the last time we ran this simulation aside from the boost to hit and expertise. Hit still drops off at the melee cap, and Expertise still trails BV and AP. Again, I'll remind everyone that the lower limit of the x-axis is 60 hit rating, since that's the base value in Majiben's gear set.
The DPS plot isn't much different.

Expertise:

DPS
More of the same, here we see expertise losing value after the dodge soft-cap. Really nothing surprising here that wasn't on the previous plots. The one really important note is that while Expertise is good, we only need enough to hit the dodge soft cap before it takes a nose dive, which with the SoV glyph and Combat expertise isn't much (10 expertise, or 82 expertise rating). This, in addition to it's weak threat performance, makes it a weak stat to "stack" since we arrive at the cap quickly.

And again, I've made simple charts for Knaughty's FAQ, showing how the stats stack up to one another at the lower end of the spectrum (i.e. well below hit cap and dodge soft-cap). The first one is for equally-itemized stats:


The second is for pure stat points, i.e. 1 STR vs 1 AP vs 1 BV and so on. This is the one you'll want to consult if you're interested in direct point-to-point comparisons, like enchants. Dont' worry though, I'll be re-running that simulation later today as well.

[knaughty]

Can I ask that the threat-per-move chart get re-done as well?

[theckhd]

Next, we'll tackle the questions about Seal of Blood. The plot I posted earlier showed SoB trailing SoV by a pretty wide margin. Let's see whether it's possible for SoB to catch up at all with the new mechanics.

The last time we addressed this question, we noticed that gear set played a large factor in which seal was ahead, and furthermore that the differences could be tracked down to the way each seal scales with hit and expertise. So before we go any further, let's see what those plots look like in the new code.

Setup:
Seals: SoV and SoB
Rotation: 969
Glyphs: Judgement and Vengeance (JV) for SoV, J for SoB
Talents: 5 Conviction + 2 Crusade (5V+2C)
Gear: Majiben's progression gear set as a base
Stats: Plot the DPS/TPS of each seal as we increase STR, hit rating, or expertise rating

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).

To revisit the possible gear sets, I'll copy/paste the most relevant threat stats of each set:

Code: Select all

    'Stat'     'T8maji'    'T8suba'    'T7suba'    'T7BV'
   'STR'      [  1125]    [  1228]    [  1112]    [ 1163]
   'Hit'      [    60]    [   235]    [   211]    [  129]
   'Exp'      [     0]    [    42]    [    57]    [   62]

From above, we expect that as we ramp up hit and expertise rating, SoB should gradually catch up to and eclipse SoV. Suba's T8 set has 7.17% hit and 2.56% total dodge/parry reduction for a total of 9.73%, while the T7 sets have 6.43%+3.48%=9.91% (Suba's) and 3.93%+3.78%=7.72% (T7BV) reduction respectively. We can plot the TPS output of each of these gear sets for the 5V+2C spec, to see how they compare now:

Setup:
Seals: SoV and SoB
Rotation: 969
Glyphs: Judgement and Vengeance (JV) for SoV, J for SoB
Talents: 5 Conviction + 2 Crusade (5V+2C)
Gear: Majiben's T8 gear set (T8maji), Suba's T8 gear set (T8suba), Suba's T7 gear set (T7suba), and the old T7 Block value set (T7BV).


This plot immediately tells us that it's not overall hit/parry/dodge reduction that matters - Suba's T7 set, despite having only ~0.2% more reduction than his T8 set, shows the largest bias towards SoB, and the T7BV set with high expertise but low hit and an overall lower total reduction almost breaks even. It's very clear that the sets that are expertise-heavy win out on this analysis.

The logic behind this is apparent upon further scrutiny of the graphs above. Most of our rotation scales with hit, so adding hit helps both seals (despite helping SoB a little more). On the other hand, very little of our rotation benefits from expertise, so adding expertise gives the SoB configuration a much more noticeable boost. So it isn't just SoB scaleing exceptionally well with expertise that matters, it's also the fact that the rest of our rotation scales very poorly with expertise.

What this means is that SoB can be made to caught up to SoV if we stack expertise. However, by doing so, you'll generally end up with far lower TPS than you would have if you had stacked an equal amount of Hit, STR, or even AP or BV. Expertise that we happen to get on gear of course helps, but it will have to be around 120 or so in T8 gear to be enough to dig SoB out of the hole.

This concludes part 1 of the SoB tanking analysis. This part has solely looked at the two seals in the context of a pure 969 rotation. In the next part, I will take a look at how substitution rotations can help, and what benefit they'll provide for each seal.

TLDR summary:

• SoV will be our tanking seal of choice in Ulduar, as it is ahead in TPS (and DPS) in most gear configurations.
• SoB can surpass SoV in DPS/TPS in high-expertise gear sets, but those gear sets will be generally inferior for TPS as compared to gear sets that focus on STR, Hit, or pure avoidance (i.e. low-exp, low-hit).

[theckhd]

Can I ask that the threat-per-move chart get re-done as well?

It's coming in part 2. It seemed to make the most sense to put it in the section where we discuss options for swapping abilities in or out of the basic rotation. It hasn't changed much either way though.

[æ]

/cheer

Considering the sheer amount of tanking exp/hit gear in ulduar, one may see before even getting to the hard modes that SoB starts surpassing SoV and becomes a higher TPS option. At the same time DPS starts to gear up, so I'm wondering if that would further result in SoV -> SoB changeover mid-content.

Items like Northern Barrier and Bladebearer's Signet are going to already give a pretty good headstart in both areas. There may be a avoidance or block reduction, but alot of us are several % over blockcap and might not mind shedding some block rating.

This is the link im looking at Click

[knaughty]

TLDR summary:

• SoV will be our tanking seal of choice in Ulduar, as it is ahead in TPS (and DPS) in most gear configurations.
• SoB can surpass SoV in DPS/TPS in high-expertise gear sets, but those gear sets will be generally inferior for TPS as compared to gear sets that focus on STR, Hit, or pure avoidance (i.e. low-exp, low-hit).

Well, SoB didn't last long as "Trash Seal of Choice". Down to two advantages:
• No DoT, making it easier for slow/lazy CC classes to get control of stuff we splashed HotR+SoV onto.
• Marginally better TPS on secondary targets that aren't having SoV stacked to 5 all that quickly, but still die fast (IE: Secondary trash targets).

Off to update FAQ...

[majiben]

Bladebearer's Signet

Is a dps ring. Mid content cross over? Not likely, the T8 progression sets are really more of T8 hard mode progression sets. That is they have mostly ILVL 226 gear.

[theckhd]

SoB Analysis Part Deux - What do substitution rotations do for SoB (and to a lesser extent, SoV)?

So far, we've seen SoV mopping the floor with SoB in most calculations. Now we'll focus on an area where SoB still has an upper hand - substitution rotations. First, let's look at how our abilities compare to one another in terms of damage per cast.

Setup:
Rotation: None
Seals N/A
Glyphs: Judgement (J), Avenger's Shield (A), Exorcism (E), and Consecration (C) for their respective abilities
Talents: 5/5 Conviction + 2/3 Crusade (5V+2C)
Gear: Suba's T8 Progression set


Since all of this is holy damage, the threat per cast plot would look identical with all of the numbers multiplied by (1.43*1.9).

We see again here that Job is our weakest ability. Thus, we'd expect to see a noticeable threat increase by substituting a higher-damage ability in for JoB. It's clear that glyphed AS is the biggest gain, with Exorcism (glyphed or unglyphed) coming in second, and HoW and unglyphed AS lagging slightly behind.

So there are two obvious reasons that SoB will benefit more from substitution rotations than SoV will. The first is what we've just pointed out: JoB is our weakest ability, so we get a larger boost by replacing it with something else than we do from replacing JoV. The second is due to glyphing - with SoV, we have to swap out one of our dps glyphs (either J or V) if we want to glyph whatever we're substituting. With SoB, there's only one DPS glyph: it's J or bust. So we have a free glyph slot at our disposal, essentially giving us the glyph's dps for free.

We can also confidently state that it's not worth substituting for anything but Judgement; everything else in our normal rotation is higher DPS than anything we could substitute for it. This is clearer if we look at a DPS plot, where we divide each of the values in the plot above by the ability's effective cooldown. For this exercise, we'll say the effective cooldown of Exorcism is 18 seconds, since if we're substituting it will be limited to every other Judgement. Similarly, the effective cooldown of Avenger's Shield is 36 seconds, and Hammer of Wrath is 9 seconds (because there's no point using it in a 6's slot, since it's weaker than either of those options).



So this shows that ShoR and HotR are our biggest DPS components, closely followed by Consecration (ignore the glyphed version, it's more damage per cast, but it's not accurately represented here because it breaks our rotation). Reading this graph is a little more subtle than the previous one, because we can't just compare the bars directly for the long-cooldown abilities. For example, Exorcism on an 18 second cooldown is substituted for every other Judgement, so we'd have to compare Exorcism's DPS to half of Judgement's DPS to see whether it'd be a viable swap. Similarly for Avenger's Shield (which needs to be greater than 1/4 Judgement's DPS). Hammer of Wrath can be compared directly, since it's a 9-second effective cooldown here.

So this plot tells us that Exorcism, Avenger's Shield, and Hammer of Wrath are all viable substitutes for JoV or JoB. The increase will be very small when substituting a Hammer of Wrath, or an unglyphed Exorcism or Avenger's Shield in for JoV, but all three will give a noticeable boost over JoB. From the plot, a glyphed AS should be the largest boost we can possibly get by substituting a single ability for either Judgement.

Note that all of these are still allowing for 100% Holy Shield uptime. We already know that if we're not tanking, swapping in abilities for Holy Shield is our best course of action to boost DPS. We won't revisit that analysis here, since it shouldn't have changed at all.

This leaves us with a few different possibilities. Rather than giving you a string of graphs, each showing one new comparison of several rotations, I'm going to attempt to condense this all into one graph. We want to compare a few different combinations of Seal+Rotation+Glyphs:

• SoV and SoB with default 969
• SoB with Exorcism substituted for every other Judgement (JsE) with JE glyphs
• SoB with Avenger's Shield substituted for every 4th Judgement (JsA) with JA glyphs
• SoB with Exorcism and AS substituted for Judgement (JsAE) - i.e. a Exor->AS->Exor->Judg cycle in the Judgement slot of usual 969. For this we'll use EA glyphs.
• SoV with JsA and VA glyphs for good measure

You'll note I left a SoV-JsE rotation off of the list. It turns out that for deep ret subspecs, this only manages to beat a standard 969 by 5 TPS on average without glyphing Exorcism, and only 20 TPS on average with VE glyphs (JE glyphs are actually worse TPS due to the strength of the Vengeance glyph). It's close enough that on a big graph like I'm about to show you, adding these just makes the graph harder to read without conveying much extra information, so I've left them off.

So, without further ado, let's dive into the big ugly:

Setup:
Rotation: 969, Exorcism substitution (JsE), AS substitution (JsA), and E+AS substitution (JsAE)
Seals SoV and SoB
Glyphs: Combinations of Judgement (J), Avenger's Shield (A), Exorcism (E), and Vengeance (V)
Talents: Variuos (see plot)
Gear: Majiben's T8 Progression set


The solid curves here are default 969 rotations, and the dotted curves are substitution rotatiosn of various sorts. Blue curves are SoV, red/black/magenta curves are all SoB. The legend should provide enough information to tell which curve is which.

The first thing we note here is that SoB really loves substitution - 200ish TPS from substituting Exorcism, 250ish from Avenger's Shield, and almost 440ish by substituting both of them in. However, in a low-hit, low-expertise set like Majiben's, this barely pulls it up even with what can be accomplished from a basic SoV rotation. On the other hand, SoV doesn't get as much of a benefit from substitution - Avenger's Shield barely gives us 150 TPS, and we've seen before that Exorcism is a paltry 5-20 TPS.

Coupled with the fact that AS has lots of utility un-glyphed, it's not likely that many tanks will stray from the default JV. So our first conclusion is that it's really not worth deviating from the default 969 if you're tanking with SoV, unless you're using your second spec for a high-single-target threat build of some sort. In which case you want VA glyphs and want to use Avenger's Shield in place of every 4th Judgement.

Returning to SoB, there's a lot we can do to help matters. First of all, a simple JsE rotation boosts SoB enough to catch up to basic 969 with SoV. While this jeapordizes JotJ uptime, it also has the benefit of reducing the JoB backlash damage. If you have someone else to put up the debuff, you could go nuts and use JsAE with EA glyphs, dropping you to one Judgement cast every 36 seconds and reducing the backlash even further.

Also keep in mind that this is for a low-expertise, low-hit set. If we boost expertise some, all of the SoB curves gain ground relative to the SoV curves, giving SoB substitution rotations the crown when it comes to maximum TPS with 100% Holy Shield uptime. A simple SoB-JsE with enough expertise will even beat out SoV-JsA, and heavier SoB substitutions will do even better. And again, Holy Shield substitution should do even better (with either seal) if you can afford to drop it.

TLDR Summary:

• Seal of Blood gains a lot of ground with Judgement replacement rotations due to the weak performance of JoB, at the risk of reduced JotJ uptime.
• Avenger's Shield (JsA) gives a slightly bigger boost than Exorcism (JsE), with JsAE being stronger than both.
• It is generally not worth substituting anything for Judgement in a SoV 969, unless you're willing to glyph Avenger's Shield.

Despite all of this, I'd say that SoV is still clearly the best choice as a tanking seal. It performs excellently with standard 969, and doesn't carry the baggage of backlash damage. The only case where it seems like SoB is worth considering is a fight where we absolutely need that extra few hundred TPS, can live with the chance that JotJ will fall off, and can gear for heavy expertise (i.e. high expertise and hit) rather than full avoidance. This narrows the subspace considerably, such that I doubt it's worth considering SoB much further until we identify a few fights that fit this mold.

I'm done for the night, but I still have more things I can post when I get time. For one thing, I've re-run the Ulduar weapon analysis, which I will hopefully get time to post tomorrow. Another one I'd like to revisit is the enchant analysis, since the increase in effectiveness of hit may have a noticeable impact.

[knaughty]

Despite all of this, I'd say that SoV is still clearly the best choice as a tanking seal. It performs excellently with standard 969, and doesn't carry the baggage of backlash damage. The only case where it seems like SoB is worth considering is a fight where we absolutely need that extra few hundred TPS, can live with the chance that JotJ will fall off, and can gear for heavy expertise (i.e. high expertise and hit) rather than full avoidance. This narrows the subspace considerably, such that I doubt it's worth considering SoB much further until we identify a few fights that fit this mold.

SoB for trash might still be reasonable, mostly due to SoV stacking time on secondary targets.

Doesn't read as viable for bosses.

Assuming 18 sec CD (sub every 2nd judgement) what's the DPS impact of:
• Glyph of Judgment for V/B
• Glyph of Exo.

It looks like subbing Exo every 2nd judge is always a TPS gain, so there's little reason to judge every 9 once you have your replacement libram. Hit/Expertise levels are high, so missing JotJ is unlikely, as well as the fact that other people can put up the debuff.

Is it up passively for Bestiality druids, even in Kitty form?

[Levantine]

If they're in a tank-Feral spec, then yeah, it's up automatically. DPS-Ferals don't take the talent.

[æ]

Hmmm..

I wonder how 2/3 Crusade and 3/3 Sanctity of Battle vs. 3/3 Crusade and 2/3 Sanctity of Battle stacks up for SoB with a JsE/JsAE rotation? Seems like it would benifit well from the extra crit and the 10-15% higher exo numbers.

[Varmin]

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.

[Candiru]

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.

[theckhd]

Assuming 18 sec CD (sub every 2nd judgement) what's the DPS impact of:
• Glyph of Judgment for V/B
• Glyph of Exo.

It looks like subbing Exo every 2nd judge is always a TPS gain, so there's little reason to judge every 9 once you have your replacement libram. Hit/Expertise levels are high, so missing JotJ is unlikely, as well as the fact that other people can put up the debuff.

This was buried in the text of the post, but Glyph of Exorcism is a 15 TPS upgrade over glyph of Judgement for the JsE rotation with SoV. And the difference between 969 and JsE is only 5 TPS if you're using JV glyphs. So while it's a TPS game, it's almost not worth bothering with, especially since Judgement will scale better with hit than Exorcism will due to crit mechanics (Judgement is x2, Exorcism is x1.5). I expect with a higher hit set, it will be a net threat loss to sub in Exorcism while using SoV. I'll look into this more in-depth when I get time this week.

Since the difference is so small at first, and should get even smaller with gear, I'd say it's never worth subbing in Exorcism when you're tanking with SoV. This guarantees JotJ uptime even in low-hit gear, and lets your dps players focus on their job rather than keeping Tclap up.

On the other hand, when using SoB it's always worth substituting Exorcism, because Judgement of Blood is anemic.

As for the glyphs, this analysis should still be mostly correct. The numbers will shift a little bit, but the result should be pretty much the same. Exorcism will always give a bigger benefit, because if you're casting an equal number of Judgements and Exorcisms, a 20% boost to the larger-damage ability will always beat out a 10% boost to the weaker-damage ability.

[theckhd]

Hmmm..

I wonder how 2/3 Crusade and 3/3 Sanctity of Battle vs. 3/3 Crusade and 2/3 Sanctity of Battle stacks up for SoB with a JsE/JsAE rotation? Seems like it would benifit well from the extra crit and the 10-15% higher exo numbers.

I already looked at that situation in this post. While the numbers might be slightly off (because that's a one-roll calculation), the overall result shouldn't have changed any, since it should affect everything in that analysis equally.

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.