Theck's MATLAB TPS analysis  WotLK/3.x
Moderators: Fridmarr, Worldie, Aergis, theckhd
Majiben wrote:Forgot to ask this sooner but for your cross over graphs what are the assumed hit and expertise values?
The graph assumes 35 expertise rating from gear, 10 expertise from SoV Glyph, and 6 expertise from the Combat Expertise talent.
 Code: Select all
expertise=(Base_exp + SoV + (Gear_Exp+extra_exp)./exp_rating_to_exp) + CE;
where the variables are defined in PallyTPS.m as
Base_exp=0
Gear_Exp=35
SoV=10
CE=6
cordelia wrote:Hmm, if you're going to use Matlab, do you think you could do a mesh plot of the interaction between AP and Hit? It's something I've been meaning to look at since forever, but I'm always busy doing something.
I've also considered a 3d plot of AP, Hit, and Crit interactions with color denoting TPS effect, but I haven't touched matlab in so long I forget what such a graph is called, even.
I can crank out all of this when I get some time. What specifically did you want for the AP/Hit graph, simply a 3D surface plot of DPS on the zaxis with Hit and AP as the x and yaxes?
I can make a 3D contour map for the AP/Hit/Crit graph as well, with multiple surface contours for different DPS benchmarks, but it might be hard to read when condensed down into a single image. I always find it easier to read 3D plots in MATLAB itself where i can spin 'em around and zoom.
Lowgrus wrote:And what it all really means or hell make something like this for new SoR/SoB/SoC.
Most of the commentary is found in the Hit thread this was split off of, you can read it here. It might be worth cloning that post into the OP of this thread, to make it more coherent. If Fridmarr or one of the other mods thinks it's worth it, that is.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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theckhd wrote:I can crank out all of this when I get some time. What specifically did you want for the AP/Hit graph, simply a 3D surface plot of DPS on the zaxis with Hit and AP as the x and yaxes?
Yep. Exactly. Btw, I've always preferred mesh over surf. Easier to examine, IMO.
theckhd wrote:I can make a 3D contour map for the AP/Hit/Crit graph as well, with multiple surface contours for different DPS benchmarks, but it might be hard to read when condensed down into a single image. I always find it easier to read 3D plots in MATLAB itself where i can spin 'em around and zoom.
Yah, I think it would be hard to read. You could always save it as a matlab graph for those of us who can read matlab graphs. And YES, it's always easier to view them on Matlab where you can spin em and zoom em. Too bad journal figures can't be that interactive. And yes, I know some people actually publish 3d images using steroscopic crossfocusing or whatever those magic eye 3d things are called. I've never been able to focus that way at will, though, so those 3d pix are useless whenever I see em.
Cordelia, Council Member of Unleashed
TankadinPoints Theory & Breakdown
TankadinPoints Theory & Breakdown

cordelia  Posts: 630
 Joined: Tue Oct 09, 2007 3:33 am
Majiben wrote:And what was the assumed hit?
61 hit from gear, plus 1% from Draenei aura.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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That actually wouldn't be a bad idea. Even if it was just a simple textbased addon that could spit out your expected DPS to the chat frame every time you swapped gear.
Maybe if I find some time I could throw something simple together. Or someone could write it as a Tankadin2 module.
Maybe if I find some time I could throw something simple together. Or someone could write it as a Tankadin2 module.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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Nice job overall, but I think there's a small error with the plots.
Since you are plotting against Character Sheet Strength on the xaxis, you are actually plotting vs. 1.265*x (scaled by both Divine Strength and Blessing of Kings). The stats you are comparing (Hit, AP, etc.) are not affected by either of these modifiers, so you need to scale them appropriately in order to preserve the units. This will reduce the slope of the lines and push out your cross over points a little bit.
Edit: I think only the Divine Strength modifier is included when determining the xaxis.
Edit2: I totally misinterpreted those plots  thanks for pointing that out and for all the work you've done here.
Since you are plotting against Character Sheet Strength on the xaxis, you are actually plotting vs. 1.265*x (scaled by both Divine Strength and Blessing of Kings). The stats you are comparing (Hit, AP, etc.) are not affected by either of these modifiers, so you need to scale them appropriately in order to preserve the units. This will reduce the slope of the lines and push out your cross over points a little bit.
Edit: I think only the Divine Strength modifier is included when determining the xaxis.
Edit2: I totally misinterpreted those plots  thanks for pointing that out and for all the work you've done here.
Last edited by bfraz71 on Wed Jan 06, 2010 3:42 am, edited 3 times in total.
 bfraz71
 Maintankadonor
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Would be interesting but could be problematic. It could either give you the numbers based upon your current stats on the the character sheet making it cover a raid situation only when in a raid. But if assumed raid buffs you would need to draw information directly from the gear and the players talent spec (though you could have the player enter that part manually in the addon).
Amirya wrote:some bizarre lovechild of Hawking, Einstein, and Theck

majiben  Moderator
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bfraz71 wrote:Nice job overall, but I think there's a small error with the plots.
Since you are plotting against Character Sheet Strength on the xaxis, you are actually plotting vs. 1.265*x (scaled by both Divine Strength and Blessing of Kings). The stats you are comparing (Hit, AP, etc.) are not affected by either of these modifiers, so you need to scale them appropriately in order to preserve the units. This will reduce the slope of the lines and push out your cross over points a little bit.
Er... I don't think so. The plots should be correct as is. There's no reason to scale any of the other stats. If your character sheet reads X strength, it reads X strength, not 1.265*X.
In other words, the DPS values are not directly calculated from the xaxis labels. Both the DPS values and the xaxis labels are calculated from an input array representing the total strength contributed by a player's gear. I.e.:
input:
 Code: Select all
Gear_STR=linspace(500,2500);
Outputs:
 Code: Select all
x=(Base_STR+Gear_STR).*DS; < this is the xaxis labels
DPS= big ugly sequence of functions that depends on Gear_STR
The plots are actually generated by calculating the DPS twice  once with the base values, and once with the base values + 10 itemization points of the stat in question. I then subtract the two to get the net benefit that stat afforded you in each case.
Majiben wrote:Would be interesting but could be problematic. It could either give you the numbers based upon your current stats on the the character sheet making it cover a raid situation only when in a raid. But if assumed raid buffs you would need to draw information directly from the gear and the players talent spec (though you could have the player enter that part manually in the addon).
We can pull off most of the relevant stats with:
GetCombatRating()
UnitStat()
UnitAttackSpeed
UnitAttackPower
UnitDamage
It would take some testing to make sure the returns from all of these functions are exactly what we want, and the equations modified as appropriate.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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So, with the PTR going up this week, it got me to thinking about where this project is headed. I don't see too much point in finetuning the formulas for 3.0.8 at the moment  the results won't change too significantly, and the graphs have pretty much done their jobs.
I would like to update it for 3.1 because I can imagine it being a useful tool. The original intent was to be able to extend Jonesy's spreadsheet to be able to do things that a spreadsheet can't easily do, like recalculating the output thousands of times very quickly for different input parameters. Oh, and making pretty graphs, because pretty graphs are fun. But there's no reason that it would be limited to just gear  I can imagine analyzing all sorts of aspects of tanking, including rotations, specs, and so forth. It could be a reasonably powerful simulation tool.
If that's where this is headed, then it requires two basic things:
As it stands, I can imagine translating this into an addon eventually, though I'm not sure I'll have the time to do that part personally. All it would require for a proofofconcept is to be able to grab the information provided in the "base stats" module though, once you have that everything else is just algebra crunching.
I would like to update it for 3.1 because I can imagine it being a useful tool. The original intent was to be able to extend Jonesy's spreadsheet to be able to do things that a spreadsheet can't easily do, like recalculating the output thousands of times very quickly for different input parameters. Oh, and making pretty graphs, because pretty graphs are fun. But there's no reason that it would be limited to just gear  I can imagine analyzing all sorts of aspects of tanking, including rotations, specs, and so forth. It could be a reasonably powerful simulation tool.
If that's where this is headed, then it requires two basic things:
 One is a slight adjustment to the framework, to make it more modular. For example, ability_recalc.m inherently assumes 969 in its calculations  but it wouldn't need to. If instead it calculated each ability's damage, which it then passed to a "rotation" module that took those values and used them to figure out DPS/TPS, testing different rotations would be as simple as swapping out the rotation module for a different one.
As an example flowchart, it would go something like this: base stats
 talents, glyphs, raid buffs, set bonuses, etc.  could be divided into submodules
 ability damage calculations
 rotation
This would make the program more versatile  for example, if we want to test out scaling for Ret, it's as simple as writing an ability module that includes the equations for the Ret abilities, and a rotation function that models FCFS, or whatever rotation / priority system they end up with after the changes are more finalized.
Since this is mostly bookkeeping and shuffling code around from one file to another, I can handle this part easily enough.  The other requirement is updated equations that accurately reflect the abilities post3.1. A lot of things are changing with this patch, but luckily we have a lot of time to play with them on the PTR. Unfortunately, I don't have the free time to do all of it myself. If people would be willing to post updated formulas for abilities as we discover the changes, that would cut down the workload significantly. It doesn't have to be in the same code structure as the matlab program, just in a pseudocode format that I can read.
As it stands, I can imagine translating this into an addon eventually, though I'm not sure I'll have the time to do that part personally. All it would require for a proofofconcept is to be able to grab the information provided in the "base stats" module though, once you have that everything else is just algebra crunching.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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So, I had some time today and I rearranged the code into a more modular format. The basic idea is that you build a master simulation file that calls the different modules. For example, PallyTPS is now a master file that looks like this:
Each of the lines in here is calling a module by the same name, which applies the appropriate modifiers as explained by the code comments.
The files can be found here for anyone that wants to peruse them. Here are the direct links for the modules:
base_stats
talents
glyphs
gear
buffs_debuffs
stats_recalc
ability_recalc
rotation_969
ability_recalc now calculates the total damage done by the ability so that it's more portable across different rotation modules (more on that in a minute). rotaiton_969 models the 969 rotation by taking the ability damage values and weighting them appropriately.
To demonstrate the usefulness of this rework (and to justify spending the last hour or two on it), let's take a look at something that people have been asking about a lot lately  How does Exorcism fit into our normal rotation? I've added Exorcism to the ability_recalc module as:
I based this off of Consecrate and Holy Shield, neither of which can crit, but can resist. Since the "boss spell resistance" line in each of those spells mimics the format of the hit/crit lines for the melee skills, I assumed that format but substituted spell_crit for melee_crit, boss_spell_resist for boss_miss, and boss_scrit_supp for boss_mcrit_supp (crit suppression).
Since I'm not sure if this is entirely correct, all of the calculations are preliminary, once I get confirmation that this is right (or someone corrects it) we'll have more confidence in the numbers the script puts out.
 Code: Select all
clear %clears workspace
base_stats %loads base stats into memory
talents %loads talent spec modifiers
glyphs %loads glyph modifiers
gear %loads gear statistics
buffs_debuffs %loads buff and debuff modifiers
stats_recalc %calculates the net character statistics required for ability calcs
ability_recalc %calculates the Damage of each ability
rotation_969 %calculates DPS and TPS based on a 969 rotation
[DPS TPS] %spit the DPS and TPS out to workspace
Each of the lines in here is calling a module by the same name, which applies the appropriate modifiers as explained by the code comments.
The files can be found here for anyone that wants to peruse them. Here are the direct links for the modules:
base_stats
talents
glyphs
gear
buffs_debuffs
stats_recalc
ability_recalc
rotation_969
ability_recalc now calculates the total damage done by the ability so that it's more portable across different rotation modules (more on that in a minute). rotaiton_969 models the 969 rotation by taking the ability damage values and weighting them appropriately.
To demonstrate the usefulness of this rework (and to justify spending the last hour or two on it), let's take a look at something that people have been asking about a lot lately  How does Exorcism fit into our normal rotation? I've added Exorcism to the ability_recalc module as:
 Code: Select all
Exorcism = (1087 + 0.15.*AP + 0.15.*SP).* ... %inherent
(100+(spell_crit + HotC).*Crit_Meta  boss_spell_resist  boss_scrit_supp)./100 * ... %hit, crit, HotC
(OHWS.*Crusade.*SU.*Exor).* ... %talents/glyphs
(CoE.*SanctRet) ... %buffs/debuffs
.*boss_resist_reduce; %boss resist
I based this off of Consecrate and Holy Shield, neither of which can crit, but can resist. Since the "boss spell resistance" line in each of those spells mimics the format of the hit/crit lines for the melee skills, I assumed that format but substituted spell_crit for melee_crit, boss_spell_resist for boss_miss, and boss_scrit_supp for boss_mcrit_supp (crit suppression).
Since I'm not sure if this is entirely correct, all of the calculations are preliminary, once I get confirmation that this is right (or someone corrects it) we'll have more confidence in the numbers the script puts out.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty

theckhd  Moderator
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Exorcism Rotation Testing
For the moment, let's assume a cookiecutter 5/59/6 spec (so no ret dps talents outside of 1/2 Imp Judgment). For the first pass, we'll only use the glyphs for Judgment and SoV, but we'll add the Exorcism glyph in later for good measure.
To test this, we'll have to write a new rotation module to model weaving Exorcism into the 969. That file is rotation_969_with_Exor. All of what I'm about to write is summarized in the comments of that file, but I'll repeat it here so you don't need to dig through the files if you don't want to.
There are 3 obvious ways to weave Exorcism into the 969. The first is to replace every other Consecration with Exorcism, which reduces Consecration's contribution to your sustained DPS by half, but adds one Exorcism every 18 seconds. This is modeled in the program as:
(Side note, why did it take me until just now to realize I misspelled Judgment in the MATLAB code. Oops. How embarrassing)
The next obvious choice is to replace every other Judgment with Exorcism. Again, this is done fairly trivially in the code:
The third way is to use Exorcism on cooldown in a 9 slot. It will always fall in a 9slot if used this way in a 9slot the first time, due to the 15 second cooldown. Unfortunately, this complicates the rotation quite a bit. From the code:
At this point the pattern emerges (though you might have guessed it ahead of time). At 45.0 we have Holy Shield followed by Exorcism on the 9's, which is how we started the rotation. The 6's are flipped though, we have a ShoR there. However, if we continue this pattern for another 45 seconds (4590), we'll end up where we started, since the 6's will flip again.
What does this mean? Well, the 9's work on a 45second cycle that's the same for 045 as 4590. In this cycle, we get off:
Thus, the DPS calculation would be
I wrote a quick master file (Exorcism_rotation_testing) to calculate the DPS for all of these systems. With the Judgment and SoV glyphs (but not the Exorcism one), we have:
Regular 969  DPS = 3162, TPS = 8181
Cons replace  DPS = 3113, TPS = 8046
Jud replace  DPS = 3149, TPS = 8145
Exor on c/d  DPS = 3170, TPS = 8202
If we include the Exorcism Glyph without removing Judgment, we get:
Regular 969  DPS = 3162, TPS = 8181
Cons replace  DPS = 3140, TPS = 8120
Jud replace  DPS = 3176, TPS = 8219
Exor on c/d  DPS = 3202, TPS = 8291
Finally, if we drop the Judgment glyph, but keep SoV and Exorcism, we have:
Regular 969  DPS = 3135, TPS = 8107
Cons replace  DPS = 3113, TPS = 8046
Jud replace  DPS = 3162, TPS = 8182
Exor on c/d  DPS = 3180, TPS = 8231
We see a few things here:
I'm going to quickly whip up some stats for a Holy Shield replacement rotation, and maybe for a 6's substitution rotation, just to see how those compare
For the moment, let's assume a cookiecutter 5/59/6 spec (so no ret dps talents outside of 1/2 Imp Judgment). For the first pass, we'll only use the glyphs for Judgment and SoV, but we'll add the Exorcism glyph in later for good measure.
To test this, we'll have to write a new rotation module to model weaving Exorcism into the 969. That file is rotation_969_with_Exor. All of what I'm about to write is summarized in the comments of that file, but I'll repeat it here so you don't need to dig through the files if you don't want to.
There are 3 obvious ways to weave Exorcism into the 969. The first is to replace every other Consecration with Exorcism, which reduces Consecration's contribution to your sustained DPS by half, but adds one Exorcism every 18 seconds. This is modeled in the program as:
 Code: Select all
DPS1=((1player_avoid)./swing_timer).*Holy_Shield + ... %Holy Shield
Shield_of_Righteousness./6 + ... %ShoR every 6 seconds
Judgement_of_Vengeance./9 + ... %Judgment every 9 seconds
Vengeance_DOT./15 + ... %Vengeance DOT  total damage for a 5stack done over 15 seconds
Hammer_of_the_Righteous./6 + ... %Hammer every 6 seconds
Consecrate./18 + ... %Consecrate every 18 seconds
Exorcism./18 + ... %Exorcism every 18 seconds
Melee_Swing_DPS; %DPS done by melee swings
(Side note, why did it take me until just now to realize I misspelled Judgment in the MATLAB code. Oops. How embarrassing)
The next obvious choice is to replace every other Judgment with Exorcism. Again, this is done fairly trivially in the code:
 Code: Select all
DPS2=((1player_avoid)./swing_timer).*Holy_Shield + ... %Holy Shield
Shield_of_Righteousness./6 + ... %ShoR every 6 seconds
Judgement_of_Vengeance./18 + ... %Judgment every 9 seconds
Vengeance_DOT./15 + ... %Vengeance DOT  total damage for a 5stack done over 15 seconds
Hammer_of_the_Righteous./6 + ... %Hammer every 6 seconds
Consecrate./9 + ... %Consecrate every 18 seconds
Exorcism./18 + ... %Exorcism every 18 seconds
Melee_Swing_DPS; %DPS done by melee swings
The third way is to use Exorcism on cooldown in a 9 slot. It will always fall in a 9slot if used this way in a 9slot the first time, due to the 15 second cooldown. Unfortunately, this complicates the rotation quite a bit. From the code:
 Code: Select all
% 0.0  (9) Holy Shield #1
% 1.5  (6) Hammer of the Righteous #1
% 3.0  (9) Exorcism #1  next at 18
% 4.5  (6) Shield of Righteousness #1
% 6.0  (9) Judgment #1
% 7.5  (6) HotR #2
% 9.0  (9) Consecration #1 Holy shield drops off at 10.0 (2s gap)
%10.5  (6) ShoR #2
%12.0  (9) Holy Shield #2
%13.5  (6) HotR #3
%15.0  (9) Judgment #2
%16.5  (6) ShoR #3
%18.0  (9) Exorcism #2  next at 33
%19.5  (6) HotR #4
%21.0  (9) Consecration #2 Holy shield drops off at 22.0 (2s gap)
%22.5  (6) ShoR #4
%24.0  (9) Holy Shield #3
%25.5  (6) HotR #5
%27.0  (9) Judgment #3
%28.5  (6) ShoR #5
%30.0  (9) Consecration #3
%31.5  (6) HotR #6
%33.0  (9) Exorcism #3  next at 48, Holy shield drops off at 34.0 (2s gap)
%34.5  (6) ShoR #6
%36.0  (9) Holy Shield #4
%37.5  (6) HotR #7
%39.0  (9) Judgment #4
%40.5  (6) ShoR #7
%42.0  (9) Consecration #4
%43.5  (6) HotR #8
%45.0  (9) Holy Shield  refreshed before it expires
%46.5  (6) ShoR
%48.0  (9) Exorcism  next at 63
At this point the pattern emerges (though you might have guessed it ahead of time). At 45.0 we have Holy Shield followed by Exorcism on the 9's, which is how we started the rotation. The 6's are flipped though, we have a ShoR there. However, if we continue this pattern for another 45 seconds (4590), we'll end up where we started, since the 6's will flip again.
What does this mean? Well, the 9's work on a 45second cycle that's the same for 045 as 4590. In this cycle, we get off:
 3 Exorcisms  DPS=Exorcism*3/45 = Exorcism/15, as expected if we're using it on cooldown
 4 Judgments  DPS=Judgment*4/45
 4 Consecrations  DPS=Consecration*4/45
 4 Holy Shields  this one is trickier, since we also have 3 gaps of 2 seconds each between applications. The net uptime is 39/45.
Thus, the DPS calculation would be
 Code: Select all
DPS3=((1player_avoid)./swing_timer).*Holy_Shield.*39./45 + ... %Holy Shield
Shield_of_Righteousness./6 + ... %ShoR every 6 seconds
Judgement_of_Vengeance.*4./45 + ... %Judgment every 9 seconds
Vengeance_DOT./15 + ... %Vengeance DOT  total damage for a 5stack done over 15 seconds
Hammer_of_the_Righteous./6 + ... %Hammer every 6 seconds
Consecrate.*4./45 + ... %Consecrate every 18 seconds
Exorcism./15 + ... %Exorcism every 18 seconds
Melee_Swing_DPS; %DPS done by melee swings
I wrote a quick master file (Exorcism_rotation_testing) to calculate the DPS for all of these systems. With the Judgment and SoV glyphs (but not the Exorcism one), we have:
Regular 969  DPS = 3162, TPS = 8181
Cons replace  DPS = 3113, TPS = 8046
Jud replace  DPS = 3149, TPS = 8145
Exor on c/d  DPS = 3170, TPS = 8202
If we include the Exorcism Glyph without removing Judgment, we get:
Regular 969  DPS = 3162, TPS = 8181
Cons replace  DPS = 3140, TPS = 8120
Jud replace  DPS = 3176, TPS = 8219
Exor on c/d  DPS = 3202, TPS = 8291
Finally, if we drop the Judgment glyph, but keep SoV and Exorcism, we have:
Regular 969  DPS = 3135, TPS = 8107
Cons replace  DPS = 3113, TPS = 8046
Jud replace  DPS = 3162, TPS = 8182
Exor on c/d  DPS = 3180, TPS = 8231
We see a few things here:
 We actually lose DPS and TPS with the Consecration replacement rotation, regardless of glyph choices
 Judgment replacement is worse if Exorcism is unglyphed, of no benefit if Judgment is unglyphed (as compared to regular 969 with Judgment glyph), but about a 14 DPS upgrade if we have both glyphs
 Exorcism on cooldown is always better, and provides a 40 DPS improvement if we use both damage glyphs. Without the Judgment glyph, it's farther ahead of 969, but only about 20 DPS better than a regular 969 with the Judgment glyph
I'm going to quickly whip up some stats for a Holy Shield replacement rotation, and maybe for a 6's substitution rotation, just to see how those compare
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
MATLAB 5.x, Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty

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