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

[theckhd]

Also had time to re-run the glyph analysis more thoroughly.

First of all, in the last round, we compared pairs of glyph to determine the benefits. In other words, I'd compare JV to JE to see what difference V makes, and so forth. This required careful planning such that the glyph we swapped out wasn't doing anything. Mostly it was me being lazy, because the code inherently assumed you'd have 2 DPS glyphs (because pre-3.1 that was pretty standard).

This time around, we'll do it right - I'll compare the TPS without any glyphs to the TPS with the one glyph to get the result. This eliminates glyph synergies, and makes it easier to work with all around.
Setup:
Rotation: 969, JsE for Exorcism, and JsA for Avenger's Shield
Seals: SoV for most, SoB for the JoBlood one
Glyphs: J, E, V, and A glyphs alone. Unglyphed for the baseline.
Talents: 3V+3C (3/5 Conviction 3/3 Crusade)
Gear: Majiben's T8 progression set

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Glyph  TPS
J (B)   41
J (V)   70
E       70
V      115
A      178

Vengeance is still solidly ahead as long as you're below the expertise soft cap, and Exorcism is tied with Judgement. The change to the two-roll system seems to have increased SoV's value quite a bit; just look at what's happened to the crossover point where Judgement becomes better than SoV:

SoV glyph is 115 TPS, or 11.5 TPS per point of expertise below 26 total (soft cap). It drops to 5.75 TPS per expertise for each point above 26, because it's half as effective. That means the SoV glyph is worth
11.5*X + 5.75*(10-X),
where X is the amount of expertise it takes you to reach the soft cap, from a minimum of 0 (at or above cap) up to a maximum of 10 (far below cap).

Setting this equal to 64, we see that X=1.13. In other words, the Judgement glyph only eclipses the SoV glyph once you have over 24.87 expertise without the glyph. That's a pretty hefty lead, and it's safe to say that for most Paladins SoV will be the clear winner.

TLDR Summary:
Unless you're expertise-capped without the SoV glyph, the SoV glyph will be a larger threat boost than the Judgement glyph.

[theckhd]

I received a private message recently that asked a specific question about Seal of Blood tanking:

To start off I am more of a SoB (In my case since am alliance SoR) user and we all know Ulduar has no Slow tanking weapons what i wanted to ask is Vulmir, the Northern Tempest good for TPS using the SoB as I noticed from your graphs that per expertise and hit rating point (and over) I gain a very good bit of TPS, so as a normal tank would trying to get the Hard Expertise cap without SoV (at 33 Expertise,) as it drops down in TPS from going over the soft cap. As from the mace i noticed that i will lose a fair bit of stamina but with Acc and the slow weapon speed and if you are over the Defense "Minimum" and Avoidance overall is good, then this is the only kind of option (in my own opinion,) for a SoB User to gain this Mace (sadly its Onehanded Mace so Shamans may or may not go for it, in some guilds.)
Main reason why i asked as I do not want to ask for the weapon kindly from our Lootmaster during thorim and then notice its usless and also if this weapon can be based around for SoB users then it could be a ideal tanking weapon for end of Ulduar etc.

In considering this question, I realized that the gear set we've been using lately (the hard-mode progression set that Majiben built in this post) didn't quite match up to what I was using. Many of the pieces are the same (and Majiben included many of them as an alternative option in his post), but there are a few differences that lead to a noticeable difference in the amount of Hit and Expertise. I built a sample set of gear that's very similar to what I'm wearing at the moment:
Head: Helm of the Faceless
Neck: Shard of the Crystal Forest (I actually use Nexus War Champion Beads, see note below)
Shoulder: Shoulderplates of the Deconstructor
Back: Cloak of the Makers
Chest: Conqueror's Aegis Breastplate
Bracers: Mimiron's Inferno Couplings
Gloves: Conqueror's Aegis Handguards
Belt: Indestructible Plate Girdle
Legs: Saronite Plated Legguards
Boots: Spiked Deathdealers
Rings: Platinum Band of the Aesir and The Leviathan's Coil
Trinkets: Heart of Iron and Essence of Gossamer
Weapon: Last Laugh
Shield: The Boreal Guard
Libram: Libram of the Sacred Shield

The difference in threat stats is as follows:

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Gear Set    Theck  Majiben
STR           994     1125
Hit Rating    234       60
Exp Rating     70        0

This large disparity is due to to our tier set pieces. In the set that Majiben built, 4-piece Tier 8 was prioritized, and our tier set has absolutely no hit or expertise. At the moment I only have one tier piece (the chest), and I'm using a lot of off-set pieces that happen to have hit or expertise. I've cheated a little bit here, in that this set I've built includes the gloves for the 2-piece bonus, and I swapped necks to keep the set above the defense minimum. (I actually use Gauntlets of the Iron Furnace at the moment - yes they have lolarmorpen, but they were higher avoidance and EH than T7 according to RatingBuster. I should really grab the badge gloves now that I have some emblems to spare).

What does this mean for the analysis? Well, I'd expect that for SoV, Majiben's set would be better, since SoV loves STR. On the other hand, SoB will eat up the juicy Hit and Expertise rating in the set that I've constructed.

To see what sort of difference this makes, and to answer the question posed in the private message I quoted, I re-ran the weapon analysis with the gear set I constructed

Setup:
Rotation: 969
Seals: SoV (blue) and SoB (red)
Glyphs: JV for SoV, JE for SoB
Talents: Various. Abbreviations: S = SotP = Seals of the Pure, R=Reckoning, V=Conviction, C=Crusade. So 5S+5R means 5/5 Seals of the Pure and 5/5 Reckoning.
Gear: Theck's Ulduar progression set (heavy on the off-set pieces)
Weapons:Broken Promise (BP), Last Laugh (LL), Titanguard (TG), Shiver (ilvl 232 version) (SH), Sorthalis, Hammer of the Watchers (ST), and Vulmir, the Northern Tempest (VM).
For the red sockets on SH and ST, I used 8 AGI / 12 STAM gems.



As you can see, in my current set of gear, SoB is roughtly competitive with SoV, at least for Ret specs. It lags behind for the weaker weapons, though with Sorthalis SoB is actually ahead by virtue of its inherent 32 expertise as well as higher base weapon damage. It may also be worth pointing out that specs with 5/5 SotP still heavily favor SoV, while specs with 5/5 Reckoning favor SoB.

The plot does answer the question posed in the private message as well: If you're tanking with SoB, a slow DPS weapon like Vulmir, the Northern Tempest will give you a huge threat bump. Vulmir is approximately the same weapon DPS as Last Laugh, but because it's a slow weapon it gives you a 400 TPS boost over Last Laugh with SoB.

By the way, I checked Vulmir with SoV as well, despite omitting it from the graph. As expected Vulmir is in last place, roughtly tied with Last Laugh's SoV performance. Weapon DPS is king for SoV, and Vulmir isn't a strong contender in that category.

Just to make it clear how volatile these values are, let me show you one more plot. The only change I'll make is to swap the shield from The Boreal Guard to Northern Barrier, which grants us 28 more hit rating, 28 more expertise rating, and 3 Strength (before kings) at the cost of some stamina and avoidance.


Setup:
Rotation: 969
Seals: SoV (blue) and SoB (red)
Glyphs: JV for SoV, JE for SoB
Talents: Various
Gear: Theck's Ulduar progression set (heavy on the off-set pieces), but with Northern Barrier instead of The Boreal Guard
Weapons: Same as above

Suddenly SoB outperforms SoV for threat for any of the Ret specs. SotP still favors SoV though. It should probably be noted that the whole set of SoV curves has gone up by around 100 TPS as well on this graph, SoB just happens to scale so much better with hit and expertise that it gains ground.

Now, I still don't suggest tanking with SoB; the reflective damage may be small, but it's still extra damage you're taking that you don't need to be, for bonus threat and DPS that you probably don't need. But it's hard to deny that it can out-threat SoV in current situations, with gear available from normal-mode fights in Ulduar.

However, for those die-hards that decide to go this route, the contents of this post should serve as a word of warning. Be very careful to make sure that your gear is on par with what I've laid out in this analysis. You should be very nearly hit-capped and/or expertise soft-capped before you attempt to tank with SoB, otherwise you're probably putting out less threat than you would with SoV, which means you're taking damage for no discernible benefit.

If I have time, I'll try and make a mesh plot to show what combined hit + expertise it takes for SoB to surpass SoV, but extrapolating from the numbers in this post it looks like it's around 3% total chance for your hits to be missed + dodged (along with around 9.5% to be parried).

TLDR Summary:
In gear sets with high hit and expertise, SoB can be competitive with SoV for threat, even with tanking weapons. Theck still thinks this is a bad idea, but has these suggestions if you insist on emo-tanking:

• If you have 5/5 SotP, don't bother with SoB - it only works with deep Ret specs (3+ Conviction).
• If you have less than 200 Hit rating and 100 expertise rating (from gear alone!), don't even worry about SoB.
• Since there are no slow tanking weapons, you may choose to use a slow DPS weapon like Vulmir, the Northern Tempest if you're willing to give up some survivability for threat. Alternatively, Broken Promise is still quite good for SoB.
• Be smart about it. There's no reason to emo-tank every boss.
  
  • If you have a 30% threat lead over the highest DPS player, you don't need to emo-tank. Your emo tendencies are just increasing healing load on your healers for no benefit - your DPS still sucks. Switch to SoV.
  • If your DPS is riding your ass the whole fight, even with a perfect 969 (and you better be using a perfect 969 before you bother with this, because otherwise you'd get a bigger benefit by honing your 969 skills and not sucking at 969 than you would by emo-tanking), then you can start thinking about turning up the My Chemical Romance, putting on the black eyeshadow, and SoB-ing it up.

Just as a side note, as a guild leader I would never give Vulmir to a tank over a DPS class that wanted it - it gives the raid a much larger benefit in their hands than it would in a tank's. However, if it'd be disenchanted anyway, what the hell - go nuts I guess.

[theckhd]

By the way, I just fixed an error in the code that was causing it to ignore Holy Shield DPS (erroneously setting the proc rate to 0). I'm not sure how or when it crept in there. My guess is that it was recently though.

I've updated the graphs in the last few posts - they don't look any different because this was a flat amount of DPS/TPS missing to each data point. So the relationships are the same, but the numbers are now just a tad bigger.

Also, I've re-run some more realistic numbers for the glyph analysis, so I'm going to edit that post a little more thoroughly.

[Awyndel]

Usefull as usual. Keep em coming.

[theckhd]

The last time we looked at Substitution Rotations, we came to the conclusion that for SoV, substitution wasn't really worth doing. Since then, I've quoted that section a number of times, particularly the value "5 TPS" as an estimate of how much you gain by substituting Exorcism into the rotation.

However, since then, I've switched from 2 threat glyphs (Judgement and Vengeance) to one threat glyph (Vengeance) to make room for HoSalv. This makes a bit of an impact on the question of substitution - by dropping the Judgement glyph, you've just made Judgement weaker, and a substitution for it becomes more appealing (at least for pure DPS/TPS).

So here's a more complete analysis. First, let's look at the single threat glyph case:
Setup:
Rotation: 969, JsE (Exorcism for every other Judgement) and JsA (Avenger's Shield for every 4th Judgement)
Seals: SoV
Glyphs: J, E, V, and A glyphs.
Talents: Various
Gear: Thecks "WTF Double Vanquisher AGAIN" progression set


I've chosen to use the gear set I posted recently for this analysis, because the high hit rating helps boost the Exorcism substitutions a little bit, which gives us both a "best-case" scenario and makes the plots easier to read.

The first thing to notice is that for all three specs with SotP, substitution is lackluster at best. You only gain ~10 TPS from substituting either Exorcism or AS, and glyphing Exorcism over Vengeance is a net TPS loss, because the Vengeance glyph is so good. The only way to gain anything from substitution with a SotP spec is to glyph AS. I assume most tanks won't do this due to the utility of AS hitting 3 targets, but if you think it's worth the 70 TPS boost on single-targets, go nuts.

On the other hand, the Ret/Crusade specs gain a little bit from substitution. Exorcism substitution nets you about 55 TPS over a regular 969 in this case. Again, the strength of the Vengeance glyph is apparent here - glyphing Exorcism is actually a reduction of overall threat output for a JsE rotation. As for AS, regular substitution nets you a ~35 TPS increase, while glyphed AS is ~115 TPS ahead of a standard 969.

To summarize, here's a bar plot of all that for the 3V+3C spec:



Now, let's revisit the 2-glyph case:
Setup:
Rotation: 969, JsE (Exorcism for every other Judgement) and JsA (Avenger's Shield for every 4th Judgement)
Seals: SoV
Glyphs: JV, VE, and VA glyph combinations.
Talents: Various
Gear: Thecks "WTF Double Vanquisher AGAIN" progression set



Here we see the familiar result from before. If you stick with JV glyphs, substituting Exorcism or Avenger's Shield nets only about 15 TPS here for the Ret specs. This is a little higher than before due to the extra hit rating on this gear set. On the other end of the graph, SotP is still propping up Judgement enough to keep 969 ahead of either substitution rotation.

On the other hand, now that we have 2 threat glyphs, we can keep V and swap out J for E or A. For the ret specs, this results in a noticeable difference for the Exorcism substitution, which pulls ahead of 969 by about 60 TPS now that it doesn't have to lose the Vengeance glyph's bonus. Glyphed AS is ahead by over 160 TPS for the same reason.

SotP doesn't see as big a benefit from the Exorcism glyph, gaining a measly 8 TPS out of the deal, though AS is still ahead by around 120 TPS.

Again, here's a summary bar chart for the 2-glyph case, with the 3V+3C spec:


TLDR Summary:
If you're specced into SotP, don't bother substituting. Stick with 969 and use the Vengeance glyph (or JV if you use 2 threat glyphs). The only exception to this is if you want to glyph AS.

If you're some sort of Ret subspec:

• If you use 1 threat glyph, go with the Vengeance glyph. Substituting Exorcism will give you 55 TPS, AS will give you 35 TPS. Again, the only exception is if you want to glyph AS, in which case you get ~115 TPS from JsA.
• If you use 2 threat glyphs, you have some options.
  
  
  • Again, if you want to glyph AS, go with VA glyphs and do JsA.
    
  • If you don't want to glyph AS, VE glyphs are the second-best option if you will be substituting Exorcism religiously for every other Judgement. If you forget to sub Exorcism in, you'll actually be losing threat by going with this method though.
    
  • The JV glyphing is still a respectable option, but you only get a 15 TPS boost from either substitution scheme. However, this leaves Exorcism and AS free to use as ranged pulling and snap aggro tools, and makes JotJ uptime much more reliable.

Theck's Advice: I personally value Exorcism and AS very highly as ranged aggro tools, so I tend to stick to a standard 969. As such, that's still my recommendation for both new and intermediate tanks, so I'd reccomend Vengeance as your first glyph, and Judgement if you're using a second threat glyph.

Experienced tanks may want to switch up to a substitution rotation on fights where they want that extra aggro boost, but since they're likely to be using the HoSalv glyph, there's no point in glyphing anything but Vengeance. If you want to carry around a stack of Exorcism and HoSalv glyphs, you could always swap them on the fly for fights that require extra threat.

[daiceman]

Hey, something I've been toying around with is a straight up Holy Shield->Hammer of Reightous->Judgement->Shield Slam->Consecration->Holy Shield

So instead of 9696969696 indefinitely its more along the lines of 86868 then a .5 second pause and then repeat (in this case you would get 2/2 imp judgment). While this may seem kind of odd waiting .5 seconds every rotation, in reality, I never notice that I lose the .5 seconds, partially due to lag, but also because I have 2 libram swapping macros. so it will sometimes give a slight increase to the GCD. Basically, what it does is make it so both LoO and LotSS are up for EVERY slam every time.

Any chance you could simulate how this would work against a normal 96969 rotation? Just wondering if the .5 seconds lost (which in reality, I don't notice) is worth the extra block value on the slams.

[Soralin]

Unless you're using ShoR as soon as its off cooldown your rotation is likely to be a TPS drop rather than increase.

[lythac]

In the gear list* it doesn't mention which libram is being used. In calculations is [Libram of Obstruction] the being used, if so how does it look with [Libram of the Sacred Shield]?

I am wondering whether [Libram of the Sacred Shield] has enough of an impact to make substitution worthwhile.


Edit - *Gear list used for SoB vs SoV so wouldn't need to list libram.

[theckhd]

In the gear list* it doesn't mention which libram is being used.

Whoops, it was LoSS. Updated the list to reflect that. The last time we looked at this with LoO, Judgement replacement wasn't worth the loss of the Libram uptime. With LoSS, that's no longer relevant.

Hey, something I've been toying around with is a straight up Holy Shield->Hammer of Reightous->Judgement->Shield Slam->Consecration->Holy Shield

So instead of 9696969696 indefinitely its more along the lines of 86868 then a .5 second pause and then repeat (in this case you would get 2/2 imp judgment). While this may seem kind of odd waiting .5 seconds every rotation, in reality, I never notice that I lose the .5 seconds, partially due to lag, but also because I have 2 libram swapping macros. so it will sometimes give a slight increase to the GCD. Basically, what it does is make it so both LoO and LotSS are up for EVERY slam every time.

Any chance you could simulate how this would work against a normal 96969 rotation? Just wondering if the .5 seconds lost (which in reality, I don't notice) is worth the extra block value on the slams.

It's not likely to be animprovement; as Soralin pointed out anything that pushes back your 6-second cooldowns will be a DPS loss. Half a second doesn't seem like much, but you're actually pushing your 6-second abilities back by 2 full seconds in that rotation, which is a 25% dps loss on both of your hardest-hitting abilities.

Just to check, let's run the numbers. With SoV, the Vengeance glyph, the gear set I listed, and the 3V+3C spec, here's the damage that each of our abilities causes:

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    'ShoR'         [4816]
    'LoO_Bonus'    [ 968]
    'HotR'         [2951]
    'Cons'         [3315]
    'Exor'         [2483]
    'JoV'          [2135]
    'JoB'          [1469]
    'JoR'          [2042]
    'AS'           [2564]
    'HoW'          [2527]
    'SoB'          [ 567]
    'SoR'          [ 334]
    'VDoT'         [4672]
    'HS'           [ 889]

First of all, let's eliminate the ones that are common to both rotations. We don't expect that Holy Shield (HS) uptime will be any different, nor that we'll see any difference in the number of charges used, so we can omit that. Similarly for the DoT portion of our vengeance damage (VDoT) or our melee swings, which I didn't list on the table.

That leaves our four core abilities: ShoR, HotR, Judgement, and Consecration. LoO_Bonus is the extra damage that the Libram of Obstruction grants ShoR, which will be included for your 868 rotation.

For standard 969: In 18 seconds, you get
2 Judgement (x 2135 = 4270)
2 Consecration (x 3315 = 6630)
3 HotR (x 2951 = 8853)
3 ShoR (x 4816 = 14448)
Total damage: 34201, or 1900 DPS.

For your 868: in 8 seconds (5 GCDs + 0.5s gap), you get
1 Judgement (2135)
1 Consecration (3315)
1 HotR (2951)
1 ShoR (4816)
Total damage: 13217, or 1652 DPS

If you use libram swapping macros to get the benefit out of LoO, you get a bonus 968 damage every 8 seconds for an extra 121 DPS, bringing the total up to 1773, still around 130 DPS short of the proper 969.

Where did the dps go? Well, here's a quick comparison of the DPS contribution of each ability for the two rotations:

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                    DPS
    Ability     969    868
    'HS'       [167]  -----
    'ShoR'     [803]  [602]
    'JoV'      [237]  [267]
    'DoT'      [311]  -----
    'HotR'     [492]  [369]
    'Cons'     [368]  [414]
    'Melee'    [639]  -----


Dotted lines indicate no change here. Note that we actually gain about 45 DPS from consecration in an 868 because it has better uptime, and about 30 DPS from casting Judgement more often. On the other hand, we lose a massive 200 DPS from ShoR and 120 DPS from HotR by pushing them back by 2 seconds, in line with the 25% value I predicted.

As expected, this rotation can't possibly keep up with 969, because it doesn't optimize the usage of our heavy hitters, ShoR and HotR. Pretty much any rotation that doesn't cast a 6-second ability every 3 seconds will be weaker than 969 for that reason.

[culhag]

Is it possible to know how much TPS are our 2p-T7 and 2p-T8 bonuses worth ?

I have a hard time deciding if and when I should break 2p-T7...

[theckhd]

In terms of percentages, they're both between 1% and 2% of your total threat. Just looking at a few WWS parses, my HotR damage and my total seal and Judgement damage both hover around 20% of my total output. They vary from fight to fight though, and depend on how well I'm keeping up my rotation. So both set bonuses should be around a 2% overall DPS/Threat increase.

In terms of raw numbers, just look at the last post before yours, which has the T8 set bonus factored in, but not the T7 one. HotR contributes 492 DPS, so the T7 2-piece would boost that by 10% or about 49 DPS.

Judgement is around 237 DPS after the T8 2-piece is factored in, so without the 2-piece it should be doing 237/1.1=215 DPS, for a bonus of 22 DPS.
We also have to include the DoT damage, which is a bit trickier. The damage breakdown above gives 4672 damage over 15 seconds for a 5-stack of the Holy Vengeance debuff. That's 311 DPS, again after set bonus is factored in, which is 283 pre-set bonus for a difference of 28 DPS.

So the T8 2-piece is 22+28=51 DPS

[Jasari]

Are you sure the T8 2pc affects judgement damage?

I haven't tested it, but the difference in wording between it and Seals of the Pure (which specifically mentions judgement damage too) leads me to believe that judgement damage isn't increased.

http://www.wowhead.com/?spell=64881
http://www.wowhead.com/?spell=20332

[theckhd]

Are you sure the T8 2pc affects judgement damage?

No, for some reason I was thinking it was identical to SotP. Since it's only seals, the T8 bonus would only be a 28 DPS increase, a little over half as effective as the T7 one.

[Dread]

Just another reason to have no interest in the T8 set pieces. I'll pass those to guildmates who want them for now and focus on the off set pieces which are better, in my opinon (save for the chest, but hopefully something new could pop up off of Algalon).

[Conaan!]

Theck, question for you, spawned from a hodir thread in this forum, how well does SoB/SoR/SoV hold up against each other when in the context of hodir dps race, with the crit buff, the moonlight haste and singe debuff