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

Warning: Theorycraft inside.

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

Postby Zothor » Wed Sep 23, 2009 6:38 am

Blizz needs to time their patches better against your schedule so we can get updated theorycraft the moment we want it!!

... I am so waiting to be told "yes, the coolest looking tanking sword in the tier is also a very viable threat and mitigation weapon." I'll look so pretty.
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3.2.2 Talent/Spec Analysis

Postby theckhd » Wed Sep 23, 2009 6:52 am

3.2.2 Talent/Spec Analysis

First, we'll look at the breakdown of TPS per talent point spent.

We simulate the DPS and TPS for each of these talent configs, and calculate the value of each talent point through simple subtraction and division:
  1. 5/5 Divine Strength and 3/3 Redoubt, but no other threat talents
  2. #1 + 3/3 One-Handed Weapon Specialization (OHWS)
  3. #1 + OHWS + 3/3 Touched By The Light (TBTL)
  4. #3 + 3/3 Crusade
  5. #3 + 5/5 Conviction
  6. #3 + 5/5 Seals of the Pure (SotP)
  7. #3 + 5/5 Reckoning
  8. #3 - 5/5 Divine Strength
  9. #3 - 3/3 Redoubt

For example, to evaluate Crusade, we subtract spec 3 from spec 4, and divide the result by 3 (the number of points in Crusade). Since OHWS and TBTL are so far ahead, we use those as the base spec with which to compare the other talents.

Setup:
Rotation: 969
Seals: SoV
Glyphs: V only
Talents: Various, in combinations to isolate the benefit of each talent individually.
Gear: Theck's 9.245 Progression Set
File: calc_talent_analysis.m

Code: Select all
Talent     DPS      TPS   (both per point)
Reck      12.8     23.7                   
Conv      20.2     46.0                   
Crus      32.2     76.4                   
SotP      30.3     78.0                   
Red       31.9     82.1                   
DivStr    49.2    117.4                   
TbtL      55.5    142.9                   
C(6%)     65.5    155.0                   
1HWS      92.7    218.4       


Image
Note that the 5% threat nerf from Righteous Fury isn't really visible here because we've upgraded the gear set.

Nothing particularly breathtaking happened here this patch. Divine Strength got a small boost thanks to the TbtL change. Redoubt dropped noticeably, but that's due to the low BV on the new gear set (412 compared to 643 on the T8.5 progression set). Unfortunately, that talent's worth depends heavily on your block value. SotP is still slightly ahead of Crusade for "no-DUH" mobs, and Crusade is still solidly ahead of just about everything for DUH mobs.

The Redoubt question hasn't changed at all since last time, but I'll repost it here since this is the relevant analysis:
Theck wrote:.... the value of each point in Redoubt will decrease exactly the same way block value does in the region of diminishing returns, and will drop to 0 once you're above the ShoR block value cap. Keep in mind that dropping the talent might bring you back into the DR region again though.

The BV break points at which the points in Redoubt actually become useless for threat should be easily calculated. The cap is 3161 BV, so if you let B be the base block value break point when 1.2*B=3161, then the break point with 3/3 Redoubt is 1.3*B=1.3(3161/1.2). Thus:
If you have over 3434 block value with 3/3 Redoubt, you'll see no difference in threat between 2/3 and 3/3 Redoubt
If you have over 3448 block vlaue with 2/3 Redoubt (3736 with 3/3), you'll see no difference in threat between 1/3 and 2/3 Redoubt
If you have over 3477 block vlaue with 1/3 Redoubt (4109 with 3/3), you'll see no difference in threat between 0/3 and 1/3 Redoubt



Next we'll run through the talent spec comparison again.
Setup:
Rotation: 969
Seals: SoV
Glyphs: V only
Talents: Various combinations of SotP (S), Reckoning (R), Conviction (V), and Crusade (C)
Gear: Theck's 9.245 Progression Set
File: calc_talent_analysis.m

Code: Select all
Spec         DPS      TPS      TPS(e)   Util
3S           3217     7876     7876     12 
4S           3246     7953     7953     11 
5S           3275     8030     8030     10 
4S+3R        3286     8031     8031      8 
5S+3R        3316     8109     8109      7 
5S+5R        3340     8157     8157      5 
5S+3R+1V     3337     8158     8158      7 
5S+3R+3V     3379     8256     8256      5 
5S+1V        3296     8078     8078      9 
5S+3V        3337     8175     8175      7 
5V           3228     7877     7877     10 
1V+2C        3212     7846     8003     12 
1V+3C        3243     7923     8160     11 
3R+1V+3C     3283     7999     8239      8 
3V+3C        3284     8018     8258      9 
5V+3C        3325     8113     8356      7 
3R+5V+3C     3366     8192     8437      4 
5V+2C        3293     8034     8195      8 
5V+3C-1T     3268     7962     8201      8 

This first plot is sorted by "no-DUH" TPS. The next two are sorted by tree (Ret-heavy specs at the top and Holy at the bottom) and sorted by utility points, respectively:
Image
Image

Image

Really, nothing significant has happened here since 3.2, so I'll just quote myself again:
Theck wrote:As you can see, the difference between SotP and Crusade specs is small for a no-DUH mob, with SotP having an edge, but Crusade dwarfs SotP for DUH mobs. To throw out some numbers, let's compare a 4/53/14 utility spec with a 0/53/18 that takes exactly the same utility talents in prot and ret. This means, for example, comparing 4S to 1V+3C. On a no-DUH mob, the 4S spec is ahead by 25 TPS. But against a DUH mob, the Crusade spec is a whopping 206 TPS ahead. If you're going to spend any time fighting Humanoids or Undead (which is a good bet, given that we're in an expansion cycle that's fairly heavy on the Undeath), you'll probably find the Crusade spec giving you more bang for your buck.

On the other hand, if you're not going deep enough into Ret to pick up Vindication or PoJ, then you can do pretty well with Seals of the Pure and Reckoning. 5S+5R is fairly competitive with 1V+3C even on DUH mobs, and frees up some points for other Prot or Holy talents.

Unfortunately, anything with more than 4 points in SotP will mean skipping points in Vindication or PoJ, which will be a tough call for many players. People who aren't fond of PoJ right now may not mind, and could go with a 5/54/12 spec that still picks up Vindication. Die-hard "let the dps warrior keep up Demo Shout" types could drop down to 6 in Ret and open up more of the Prot or Holy trees.


TLDR Summary:
  • 0/53/18 provides the highest threat potential on DUH mobs, with or without Reckoning.
  • For no-DUH mobs, specs with 5/5 SotP and 5/5 Reckoning are very strong, and will still be decent for DUH mobs (though about 200 TPS behind).
  • As a general rule of thumb for maximizing threat, fill points in the following order:
    • OHWS, Divine Strength, and TbtL before anything else.
    • For DUH mobs, Crusade > SotP > Conviction > Reckoning
    • For non-DUH mobs, SotP > Crusade > Conviction > Reckoning.
Last edited by theckhd on Wed Sep 23, 2009 10:55 am, edited 1 time in total.
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3.2.2 Stat Threat Analysis

Postby theckhd » Wed Sep 23, 2009 8:06 am

3.2.2 Stat Threat Analysis

Now that we've reviewed abilities and specs, let's take a look at how stats will affect our threat in 3.2.2.

Due to the TbtL change, Stamina is no longer a threat stat for us, and has been omitted from the calculations. In addition, I've arbitrarily set the expertise and hit contributions from gear to 0 for this, so we get a clear picture of the entire range of rating.

I've made some slight changes to how I calculate the contributions. In the past I added 1 or 10 ipoints worth of each stat to calculate the bonus. However, recent corrections to the code broke this technique; in particular, the fact that stats get rounded multiple times lead to step-wise features on the graph. To fix this, I'm now adding particular amounts of each stat that work out to whole integers in the end:
STR: 18*5./DivStr
AGI: 10./BoK
AP: 10./UnRage
BV: 1./(Redoubt + BV_Meta)
Everything else is just one point worth.

In the end, the plots look mostly the way they did in the past. The one exception is Strength, because it gets floored not once, not twice, but four times (twice to calculate net STR, twice again for the BV component). This makes it basically impossible to find a nice common factor that gives you whole numbers at the end of each floor() function. As a result, the STR lines will "wiggle" a bit on the STR and BV plots. I've chosen the multiplier above to minimize this effect, so that we still get a clear idea of the average value. This is just one of those "under the hood" details that I thought a few others might be interested in.


Setup:
Rotation: 969
Seals: SoV
Glyphs: V only
Talents: 1V+3C
Gear: Theck's 9.245 Progression set
File: calc_stat_tps.m

As usual, we'll look at STR first. For a point of reference, I have around 1420 STR on my character sheet, so that's about the level of a ToC25 geared tank.
Image
DPS plot
STR got a slight boost this patch with the TbtL change, solidifying its spot at the top of the heap. It is now a good 15% ahead of BV, whereas they were neck and neck in previous patches. Hit and Expertise show their usual patterns, with hit taking over the 2nd place spot after around 1660 STR. Armor Penetration futures are also down due to the 12% rating conversion nerf, but it was our last-place threat stat before the nerf anyway.

Also note that since this gear set is well below the region of diminishing returns on ShoR, we don't see the DR on STR. We'll get to see this later in the BV plot though.

Hit:
Image
DPS plot
Again, nothing surprising here. Hit drops off when you reach the melee and spell hit caps. Everything else is pretty much the same, with slight scaling of damage-increasing stats until you reach the appropriate caps.

Expertise:
Image
DPS plot
Pretty much identical to the Hit graph, expertise loses effectiveness when you hit the soft and hard caps (82 and 328 rating or 26 and 56 skill after talents, respectively), and damage-increasing stats scale differently above and below those caps.

Block Value:
Image
DPS plot
Here we see the effects of the ShoR diminishing returns formula. Strength again exhibits the "wiggle" due to the floor-ing.

The discontinuity at 2400 is due to the piecewise nature of the function and the fact that I'm stepping by ~3 BV at a time in this simulation. The TPS value of each point of BV decreases linearly as we get more BV, which is exactly what we'd expect since the diminishing returns formula is modeled best by a quadratic. By 3161 BV, we find that BV no longer contributes any threat.

Note also that this weakens STR as a threat stat, because its contribution to our BV is also no longer giving us threat. As a result, in high-BV gear sets, hit rating actually becomes the best threat stat until the cap. The crossover point is around 2870 BV. In heavy avoidance gear sets, where we're below the 2400 BV mark, nothing's really changed from the previous round of simulations. Still, we'll probably want to avoid stacking BV for threat, and focus on a mix of STR and hit rating.

The simple bar plots are no longer so simple, since we have to decide where along the Block Value axis we want to be for the plots. It was easy to assume we're below both hit cap and expertise dodge cap, but assuming we have less than 2400 BV is less robust. Instead, I've calculated plots for three points: 2300, 2750 (roughly the middle of the DR region), and 3200 BV.

Again, nothing really special in these plots. We see BV and STR drop in value as we reach the ShoR cap, just like last time.
Image
Image
Image

Image
Image
Image

And finally, here's the single-stat values pulled off of the first graph (STR scaling) at 1400 STR:
Code: Select all
         TPS per 10
Stat   ipoint    stat
STR     28.81   28.81
BV      25.36    8.24
Hit     23.34   23.34
Exp     19.83   19.83
AP      16.34    8.17
Crit     9.24    9.24
AGI      8.96    8.96
Haste    5.83    5.83
SP       4.29    3.67
ArPen    1.59    1.59



TLDR Summary:
  • STR is our best threat stat until around 2900 BV, at which point Hit surpasses it.
  • BV, while nice, isn't really something we should stack for threat. STR is better point per point, and doesn't push you into the DR range of ShoR as quickly. Obviously take what you can get as far as gear goes, but if you get to choose between 10 STR or 31 BV, always take the 10 STR.
  • General gearing strategy for threat: Stack STR until you have 2900 BV, then stack hit rating to 8%, then continue with STR.
Last edited by theckhd on Wed Sep 23, 2009 1:04 pm, edited 2 times in total.
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3.2.2 Glyph Analysis

Postby theckhd » Wed Sep 23, 2009 8:19 am

3.2.2 Glyph Analysis

To calculate the TPS of a glyph, we run the simulation with and without the glyph, and subtract to find the difference it made in overall TPS. Nothing fancy here.

Setup
Rotation: 969, JsA for A
Seals: SoV
Glyphs: V, J, or A alone, as compared to unglyphed
Talents: 1V+3C build, on a "no-DUH" mob type
Gear: Theck's 9.245 Progression Set
File: calc_glyphs.m

Code: Select all
Glyph    TPS
J         65
V         76 (152 below soft-cap)
A        186

Image

SoV is still the best 'always-on' glyph, even in this gear set which is above the 26-expertise soft-cap. AS is still the best single-target threat glyph if you're weaving AS into your rotation.

TLDR version:
  • If you like the AS glyph, and know how to use it, go nuts.
  • Otherwise, use SoV.
  • If you're expertise hard-capped (56 expertise skill), use Judgement if you want a threat glyph.
Last edited by theckhd on Wed Sep 23, 2009 10:55 am, edited 1 time in total.
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Side Calculation - Mongoose uptime

Postby theckhd » Wed Sep 23, 2009 9:18 am

Side Calculation - Mongoose uptime

I realized while updating the Enchant/Food calculation that Mongoose was still set at a static 30 agility and 16.4 haste rating (or a 25% uptime). However, these numbers are likely no longer correct - Ratanna reports having 50-75% uptime on the buff based on some WMO parses.

There are two reasons for this, it seems. First of all, research done by the Rogues at EJ suggests that Berserking and Mongoose are both 1 PPM enchants that are not normalized by haste. That means that haste will noticeably increase the uptime on the procs.

Second, it's possible we're seeing another effect of the Holy Vengeance application here. Changing HV applications to melee attacks nearly doubled the rate at which we generated parry-able attacks, which had implications in the Expertise as Avoidance thread. If Mongoose can proc from these applications as well, it will have a similar effect on the buff's uptime, and thus the buff's worth as an enchant.

Here's a quick calculation of the new expected uptime, for both cases of HV application.

Mongoose uptime assuming HV application does not proc the buff
Mongoose can proc off of melee swings, HotR, and Judgement, just like a seal. Thus we generate:
(1/1.26 + 1/6 + 1/9) = 1.0714 attacks per second that can proc the buff.
However, I believe they have to connect to proc the buff, so we need to modify this to:
(1-avoid)(1/1.26+1/6)+(1-miss)/9
where miss is our chance to miss, and avoid is our total dodge+parry+miss chance. In the current gear/buff set, our chance to miss is 3.9808%, and our chance to be parried is 1.7658%. We're above the dodge soft-cap, so our dodge chance is zero. We thus have a 5.7466% total avoid chance.

Thus, the expression becomes:
(0.9425)*(1/1.26+1/6)+(0.9602)/9 = 1.0098 successful attacks per second that can proc the buff.

The correct way to model uptime would be to calculate the chance that the buff will not be refreshed during the duration. In other words:
uptime = 1- (chance_of_noproc)^(number_of_attacks_in_15_seconds)
Here, chance_of_noproc is just 1 - proc_chance, and number_of_attacks_in_15_seconds is just 15 times our 1.088 attacks per second. The proc chance, given 1 PPM for a 1.6 speed weapon, is just 1.6/60=2.67%.

Thus
chance_of_noproc = 1 - 0.0267 = 0.9733
number_of_attacks_in_15_seconds = 15 * 1.0098 = 15.1476

uptime = 1 - (0.9733)^15.1476 = 33.6%

Note that this falls outside of the range observed by Ratanna.

Mongoose uptime assuming HV application does proc the buff
The only difference for this calculation is number_of_attacks_in_15_seconds. Unfortunately, it's a little trickier.
We still have our (1-avoid)(1/1.26+1/6)+(1-miss)/9. But now both the auto-attack and HotR generate an additional attack, which can independently succeed or fail, but only if the original attack succeeded.
As a simple example, we have (1-avoid) chance to connect with a melee attack.
If we succeed, we have a (1-avoid) chance for the HV application to also succeed.
Thus, the chance of success for the HV application is (1-avoid)^2.
So for just auto-attacks, we'd have (1-avoid)(1+(1-avoid)) successful attacks every 1.26 seconds. HotR works the same way.

The formula for our successful attacks per second is thus
(1-avoid)*( (1+(1-avoid))/1.26 + (1+(1-avoid))/6 ) + (1-miss)/9 = 1.8611 successful attacks per second, for a number_of_attacks_in_15_seconds of 27.9164.

Calculating uptime again:
uptime = 1 - (0.9733)^27.9164 = 52.98%
This falls within the range observed by Ratanna, which suggests this is the proper uptime to use.

Effective passive worth of Mongoose give the above uptime:
Agility: 120 * 0.5298 = 63.5729 agility, before kings
2% haste: 50.4462 * 0.5298 = 26.7251 haste rating.

These are the numbers I will use in the enchant calculation.
Last edited by theckhd on Wed Sep 30, 2009 5:49 am, edited 2 times in total.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Awyndel » Wed Sep 23, 2009 9:24 am

Excellent work as always Theck. And even in time before tonights raid. Only thing I can say is perfect.

Luckily not too much changes for us facerollers ;)


Maybe I didn't do a good search, but does anybody have any numbers yet on SoC for multiple mobs? Wondering if its worth losing 1 talent point over on boss fights.
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3.2.2 Enchant/Food Analysis

Postby theckhd » Wed Sep 23, 2009 9:26 am

3.2.2 Enchant/Food Analysis

This is similar to the stat analysis, in that I calculate how much TPS each point of a given stat gives you, and then just do some simple multiplication.

Setup:
Rotation: 969
Seals: SoV
Glyphs: V
Talents: 1V+3C
Gear: Theck's 9.245 progression set, below hit cap but above expertise soft-cap.
File: calc_enchants.m

Code: Select all
Enchant        DPS  TPS
Berserking      55  127
Accuracy        37   86
Mongoose        38   82
Ti Weap Chain   28   68
Potency         26   63
SuPotency       25   59
GrPotency       20   46
26 Agi          11   26

Image
The big change here is Mongoose - provided the calculations are correct and HV applications can proc the buff, it becomes an extremely strong choice of weapon enchant. Nearly as much threat as Accuracy, with the benefit of having the added armor bonus with a reasonable uptime.

The armor bonus works out to be 120 * 1.1(kings) * 2(agi->armor) * 1.1(toughness) = 290. That works out to about 26 stamina worth of effective health.

The other, smaller change here is that the TbtL boost to STR now pushes the BC-era Potency enchant back ahead of Superior Potency by a slim margin.

Code: Select all
Food                    DPS TPS
Dragonfin Fillet        53  126
Snapper Extreme         40   96
Fish Feast             38   91
Blackened Dragonfin     18   40
Rhinolicious Wyrmsteak  17   37

Image
Nothing surprising here either, Dragonfin Fillet is still the best food, with Snapper Extreme a distant 2nd and Fish Feast a solid 3rd. Rhinolicious Wyrmsteak will be twice as effective if you're below dodge soft cap, but that's unlikely given ToC itemization. It will still trail the Fish Feast by about 20 TPS though.

TLDR Summary:
  • Accuracy is still the best threat enchant, and helps with taunts, however...
  • Mongoose has suddenly become a very strong contender as of patch 3.2.
  • Dragonfin Fillet is still the best threat food
Last edited by theckhd on Wed Sep 23, 2009 10:54 am, edited 1 time in total.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Zothor » Wed Sep 23, 2009 10:47 am

still patiently waiting on new weapon analysis, at which point I can delete this post...

Gut predictions without doing any math:

2.0 speed will not offset the zero strength/hit on 232 Quel'serrar enough to put it ahead of Titanguard or Shiver.
2.0 speed plus 245 ilvl on Quel'serrar 25 WILL put it past Titanguard and Shiver for threat, but likely behind Sorthalis
Hard mode only Anub weapons from TOC 10/25 will continue to be the desired item.
Also: DPS weapons (slow agi 1handers) should take a slight hit as they no longer have any conversion to spellpower since they all have no strength.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby tlitp » Wed Sep 23, 2009 10:50 am

ppm-based procs were stealthily changed in preparation for 3.1; as Theck already pointed out, proper computation of the average uptime relies heavily on their behavior as far as paladins are concerned

do HV or the seal themselves (specifically SoComm, as it uses the mechanics of regular autoattacks) qualify for ppm-based procs ? some actual testing would be great, something in the lines of :
1. grab a gear set heavy on hit/expertise (aiming for both softcaps) and haste
2. grab a fast weapon (easy picks : sword / mace) for which you have maximum weapon skill, enchant it with Berserking (it's easier to analyze than Mongoose, as it doesn't generate additional haste)
3. maintain a constant haste (eliminate parasite haste sources, buffs/procs)
4. whack a dummy for at least an hour, using only regular autoattacks (+seals)
5. parse the CL for the average uptime, or upload the said CL
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3.2.2 seal comparison

Postby theckhd » Wed Sep 23, 2009 10:52 am

3.2.2 Seal Comparison

Simple calculation of TPS using all three different seals to see which is highest.

Setup:
Rotation: 969
Seals: SoV, SoC, SoR
Glyphs: V (for SoV), J (for SoC), R (for SoR)
Talents: Various
Gear: Theck's 9.245 progression set
File: advanced_comparisons.m

I'm not going to bother with a "pretty print" table for this one, since the details are somewhat irrelevant. Here's the graph:
Image
SoV is consistently ahead in threat by 1.3k or more TPS, depending on spec. SoR is in second place, with SoCom coming in last place. Now that SoCom and SoV both scale with weapon damage, there shouldn't be a situation where SoCom ever overtakes SoV (like we saw occurring with SoB in previous patches).

Since Awyndel asked, let's take a look at the issue of SoC on multiple mobs. Here's the breakdown of ability damage for a 1V+3C spec, with V glyphed or no glyphs (simulating having SoV glyph but not having SoV active):
Code: Select all
Abil     none      V       diff
ShoR     3318    3318      0
HotR     3208    3295     87
Cons     2912    2912      0
Exor     2315    2315      0
JoV         0    1831   1831
JoC       878       0   -878
AS       2267    2267      0
HoW      2233    2233      0
SoV         0     440    440
SoC       440       0   -440
VDoT        0    4021   4021
HS        752     752      0
Melee     717     734     17

Now, let's say you're tanking 3 mobs. Normally, you'd be tab-targetting to spread HV stacks, so let's assume you can keep h stacks of HV on each target, and that you spend an equal amount of time (1/3) meleeing each one.

You'd lose
(1831-878)=953 damage per Judgement.
17 damage per melee attack.

These can be assumed to be evenly spread about the targets, for a net loss of 317 damage per Judgement per target (or 35 dps per target), and 5 damage per melee attack per target, or 4.5 dps per target.

You'd also lose 87 damage per HotR, which is applied to each target, for a net loss of 14.5 dps per target.

The SoV and SoC procs do equivalent damage, so they would end up cancelling on a single target. However, if you're tab-targetting, you'd probably not have a 5-stack on any given target. Instead, you'd be doing h/5 as much damage on that target, meaning that you'd get a 440*(5-h)/5 damage boost per seal proc by switching to SoC. Let's count seal procs:

Every melee attack gives you one SoC proc per target for 440 damage each. Thus, with SoC, you get 440/1.26 = 349 DPS per target. With SoV, you get 1/3 of a proc on each target, and the proc is only h/5 as strong, giving you 440*h/(15*1.26) DPS per target.

Every HotR gives you one proc of either seal on each target, netting you 440*(5-h)/(5*6) more damage by switching to SoC.

Every Judgement gives you one (possibly 2 if it's still bugged) SoC proc per target, netting you 440/9 = 49 DPS (double if it still procs twice). Every Judgement gives you a single SoV proc, or 1/3 of a proc per target, for 440*h/(15*9) DPS.

Finally, you lose the Holy Vengeance damage entirely. This would account for 4021*h/5 damage per target every 15 seconds, or 4021*h/5/15 DPS

So, to summarize, you'd gain:
349*(1-h/15) DPS from procs via melee attacks
440*(5-h)/30 DPS from procs via HotR
49*(1-h/15) DPS from procs via Judgements

But lose:
35 DPS from Judgements
14.5 DPS from HotR
4.5 DPS from melee
4021*h/75 from HV

Here's how that works out as a function of h, after multiplying by 2.574 for holy threat and 1.43 for melee:
Code: Select all
h                 1           2           3           4           5
p_melee         838         779         719         659         599
p_HotR          151         113          76          38           0
p_Jud           118         109         101          92          84
p_static       -134        -134        -134        -134        -134
p_HV           -138        -276        -414        -552        -690
total           835         591         347         103        -141



So it's going to be roughly a 350 TPS gain on trash by switching to SoCommand, as compared to keeping a 3-stack of HV on everything and tab-targetting. It gets even stronger should h drop to 2 or 1, but gets weaker on longer-living trash (which could feasibly reach a 5-stack of HV). It will also weaken somewhat as the number of mobs increases since it's fairly easy to keep a HV stack on many different mobs, but seal of Cleave won't hit more than 3.

Keep in mind this should be compared to the threat loss incurred by dropping whatever talent you skip to pick up SoC, which would presumably be Conviction. That would be roughly 50 TPS spread amongst as many targets as you tab-target between, or 17 TPS on 3 targets.


TLDR summary:
  • Don't spec SoCom for single targets
  • For trash tanking, SoCom is a viable choice, though a costly investment just for trash.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
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3.2.2 Weapon Analysis

Postby theckhd » Wed Sep 23, 2009 11:37 am

And now the plots you've all been waiting for...

3.2.2 Weapon Analysis

If you haven't read the earlier version of this calculation, here's the short short version:
Theck wrote:
  • Slow weapons are good for us, because SoV 5-stack proc rewards weapon speed, at roughly 28 TPS per 0.1 weapon speed.
  • The only spec-related choice that can change the outcome is Reckoning. Each point in Reckoning will add 24-28 TPS for a 1.5-1.6 speed weapon, while it will add 40-45 TPS for a 2.5-2.6 speed weapon.
This means that for a weapon with equal DPS but a 2.6 weapon speed, it will be about 280 TPS ahead of a tank weapon with 1.6 weapon speed, and the swap will give you an additional 16-17 TPS for each point you have in Reckoning.


Since most tanks will likely go the 53/18 route, we'll just look at a 1V+3C spec, as well as a 3R+1V+3C spec for those who choose to pick up Reckoning with their discretionary points. If you spec 5 into Reckoning somehow, you'll have to add 60 to 80 TPS to these numbers as appropriate to get an accurate comparison.

I've included all of the 2.6-speed melee DPS weapons from Coliseum, as well as Vulmir from Ulduar for a benchmark. There's no point in adding the 1.6-speed melee DPS weapons, as we'd be better off using a tanking weapon if we're going with a fast weapon. In addition, the difference in TPS between fast tank weapons and fast DPS weapons is very small.

Since there are different names for many of the items, I've generated tables and plots for both Alliance and Horde versions of the weapons. Note that this list is not incorporating racial expertise bonuses - in a close race, the expertise bonus will probably tip the scales in favor of the race's preferred weapons. Be sure to factor that in for yourself if you're using this to gauge an upgrade.

Setup
Rotation: 969
Seals: SoV
Glyphs: V
Talents: 1V+3C and 3R+1V+3C (see the Glossary or the talent analysis if you don't know what these mean)
Gear: Theck's 9.245 Progression Set
Weapons: Too many to list, basically every epic tank weapon in WotLK as well as all 2.6-speed melee DPS weapons from Coliseum and Onyxia and Vulmir from Ulduar.

The data table and first plot will be sorted both by instance and type. The top group on the graph is all slow DPS weapons, the middle group is Coliseum tanking weapons, and the bottom group is Ulduar and Naxx tanking weapons. The table is inverted (DPS weapons at the bottom, tank weapons at the top).
Code: Select all
Alliance List (scroll down for Horde)
                                             TPS       
Weapon                           ilvl   1V+3C  3R+1V+3C
Broken Promise                    213    7744    7856 
Peacekeeper Blade                 219    7514    7584 
Stoneguard                        219    7618    7694 
Legacy of Thunder                 219    7661    7741 
Last Laugh                        226    7683    7760 
Titanguard                        232    7739    7818 
Shiver                            232    7741    7819 
Sorthalis                         239    7777    7856 
Gleaming Quel'Serrar              232    7637    7732 
Crusader's Glory (232)            232    7696    7770 
Burnished  Quel'Serrar            245    7749    7848 
Crusader's Glory (245)            245    7825    7902 
Honor of the Fallen               245    7848    7928 
Silverwing Defender               258    7996    8079 
Singed Vis'kag the Bloodletter    232    7759    7880 
The Grinder (232)                 232    7923    8045 
The Lion's Maw (232)              232    7941    8063 
Caress of Insanity                232    7984    8110 
Vulmir, the Northern Tempest      232    7996    8118 
Tempered Vis'kag the Bloodletter  245    7877    8001 
The Grinder (245)                 245    8066    8191 
The Lion's Maw (245)              245    8085    8212 
Stormpike Cleaver (245)           245    8128    8254 
Relentless Gladiator's Longblade  258    8160    8292 
Remorseless                       258    8228    8358 
Stormpike Cleaver (258)           258    8280    8411

Horde List
                                             TPS       
Weapon                           ilvl   1V+3C  3R+1V+3C
Broken Promise                    213    7744    7856 
Peacekeeper Blade                 219    7514    7584 
Stoneguard                        219    7618    7694 
Legacy of Thunder                 219    7661    7741 
Last Laugh                        226    7683    7760 
Titanguard                        232    7739    7818 
Shiver                            232    7741    7819 
Sorthalis                         239    7777    7856 
Gleaming Quel'Serrar              232    7637    7732 
Ardent Guard (232)                232    7696    7770 
Burnished  Quel'Serrar            245    7749    7848 
Ardent Guard (245)                245    7825    7902 
Blood and Glory                   245    7848    7928 
Orgrim's Deflector                258    7996    8079 
Singed Vis'kag the Bloodletter    232    7759    7880 
Blackhorn Bludgeon (232)          232    7923    8045 
Frostblade Hatchet (232)          232    7941    8063 
Caress of Insanity                232    7984    8110 
Vulmir, the Northern Tempest      232    7996    8118 
Tempered Vis'kag the Bloodletter  245    7877    8001 
Blackhorn Bludgeon (245)          245    8066    8191 
Frostblade Hatchet (245)          245    8085    8212 
Hellscream Slicer (245)           245    8128    8254 
Relentless Gladiator's Longblade  258    8160    8292 
Cudgel of the Damned              258    8228    8358 
Hellscream Slicer (258)           258    8280    8411


Image
Horde Names
The new Quel'Serrar weapons are poor performers, lagging their Coliseum ilvl-equivalents. The Onyxia-25 version barely outperforms Broken Promise. Unfortunately, the 2.0 weapon speed isn't enough to overcome the lack of STR and threat stats. That being said, they're not terrible threat weapons, they're just mediocre. Since they're likely to be more easily available than Sorthalis or Shiver, they might do in a pinch for a tank that's gotten unlucky with drops.

In the 2.6-speed category, we see a similar problem with the Vis'kag variations, as they lag their equal-ilvl challengers by around 200 TPS. I'm not modeling the 2k damage proc here though, which will make up for that difference. If it procs more than once every 14 seconds or so, that would put them back in the running.

The Relentless Gladiator's Longblade, on the other hand, is an excellent threat weapon for players with the PvP skills to obtain it.

The next plots are just sorted differently, with all weapon types mixed together and sorted by TPS.
Image
Horde Names

Finally, here's another "sorted by TPS" plot with only the tanking weapons on it.
Image
Horde Names

TLDR version:
  • Slow weapons are good for threat.
  • Unfortunately, the new Quel'Serrar versions are somewhat inferior to items of equivalent ilvl.
  • If you really want to dish out the TPS, grab a 2.6-speed melee DPS weapon for those threat-heavy fights.
Last edited by theckhd on Thu Sep 24, 2009 11:21 am, edited 1 time in total.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of Grehn|Skipjack.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby daiceman » Wed Sep 23, 2009 1:02 pm

Hey theck, could I get you to do some calculations on how effective blade ward is now? Since 3.2 I've noticed that I regularly get 4-5 stacks when I'm not tanking a mob, and even then, when I'm tanking a 2 stack isn't all that rare.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Iselian » Wed Sep 23, 2009 1:12 pm

Good Lord Theck, why hasn't Blizzard hired you yet?

I'd be curious to Blade Warding as well (though with all the EH necessities, not sure how it would beat out Blood Draining).

EDIT:: Also noticed that Crusade is Demons, Undead, Humanoids and Elementals. Should it be DUHE? >.>
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Zothor » Wed Sep 23, 2009 1:32 pm

Really? With his new finding on Mongoose being WAY better than we previously realized, people are still hoping bladeward will be better?

I guess that red glow IS sexy.

Good luck with this one though. If the uptime on mongoose is way up because of SoV applications proccing it now, I'm pretty sure the the avoidance+threat+armor stacking up are going to make Bladeward feel like a silly enchant.
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Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)

Postby Grehn|Skipjack » Wed Sep 23, 2009 1:34 pm

Iselian wrote:EDIT:: Also noticed that Crusade is Demons, Undead, Humanoids and Elementals. Should it be DUHE? >.>

Doesn't roll as well as DUH.
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