Theck's MATLAB TPS analysis  WotLK/3.x
Moderators: Fridmarr, Worldie, Aergis, theckhd
Re: SoV Stack Stability and Ramp Time
theckhd wrote:Fivestack Stability
For our approximation that we can keep a 5stack indefinitely to be a good one, we want to make sure that the probability of that 5stack dropping off is very low.
We make an attack that triggers a debuff application roughly every 1/(1/1.3+1/6)=1.0685 seconds, not counting parry haste. So let's use one application attempt per second as a ballpark estimate. The probability of an application being successful is p, and the probability of failure (it gets avoided) is q=1p.
The probability of the stack falling off is then q^N, where N is the number of attacks we get in the time it takes to fall off. In this case, 15 attacks, since we have 15 seconds. In the worstcase scenario, we have an 8% chance to miss, 6.5% chance to dodge, and 14% to parry, for a total q of 0.285.
My understanding of Holy Vengence/Blood Corruption application is that a successful autoattack or HotR generates another melee attack to determine the success of application that can Miss/Dodge/Parry. Based on this, you are calculating q and p incorrectly for this two roll system.
 gibborim
 Posts: 282
 Joined: Sun Nov 02, 2008 12:13 am
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
agreed, it should be (1p^2)^N instead of (1p)^N

tlitp  Posts: 556
 Joined: Mon Jul 27, 2009 3:25 pm
Re: SoV Stack Stability and Ramp Time
gibborim wrote:My understanding of Holy Vengence/Blood Corruption application is that a successful autoattack or HotR generates another melee attack to determine the success of application that can Miss/Dodge/Parry. Based on this, you are calculating q and p incorrectly for this two roll system.
That is indeed how it works. To keep the calculation simple I sort of handwaved over this in the post, in that I assumed all of the autoattacks and HotRs were successful. If you include the possibility that they miss, you get tlitp's formula (which, given the values in my post, ends up being a 1 in 46,000 chance, or once every 12 hours or so  still long enough that the approximation is a good one).
If I find some time I'll rewrite the post to reflect the proper model.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
Completely OT:
My Calc professor evidently plays a Prot Paladin, as evidenced by his using this forum as an example of Math in Real Life (otherwise known as wake the students up mondays). I knew the lecture looked familiar.....
My Calc professor evidently plays a Prot Paladin, as evidenced by his using this forum as an example of Math in Real Life (otherwise known as wake the students up mondays). I knew the lecture looked familiar.....

sfrog  Posts: 219
 Joined: Tue Apr 01, 2008 1:16 am
 Location: Anchorage, Alaska
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
sfrog wrote:Completely OT:
My Calc professor evidently plays a Prot Paladin, as evidenced by his using this forum as an example of Math in Real Life (otherwise known as wake the students up mondays). I knew the lecture looked familiar.....
Ooh, what example did he use? Am I famous now?
Also: since when does WoW count as real life?
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
To answer a rhetorical question, the specific example of the use of math here is just the use of math in a hobby, which is really what WoW boils down to for a lot of us. A very time consuming hobby.
And I am curious, Theck, about the use of [Relentless Gladiator's Longblade] as a tanking weapon. I don't know that I'll get it anytime soon but am mostly just curious.
And I am curious, Theck, about the use of [Relentless Gladiator's Longblade] as a tanking weapon. I don't know that I'll get it anytime soon but am mostly just curious.

Petrus  Maintankadonor
 Posts: 940
 Joined: Wed Feb 06, 2008 3:45 am
 Location: St. Paul, Minnesota
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
Petrus wrote:And I am curious, Theck, about the use of [Relentless Gladiator's Longblade] as a tanking weapon. I don't know that I'll get it anytime soon but am mostly just curious.
I'll plug it into the Weapon Analysis when I get some time.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
If you're running your analysis again for weapons, might you include the updated versions of Quel'Serrar that we will soon have access to? 2.00 speed but no threat stats should make it an interesting specimen.
 Modal
 Posts: 557
 Joined: Thu Jan 24, 2008 1:36 am
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
Modal wrote:If you're running your analysis again for weapons, might you include the updated versions of Quel'Serrar that we will soon have access to? 2.00 speed but no threat stats should make it an interesting specimen.
Will do.
Since 3.2.2 is going live today, I'll be trying to update and post the relevant calculations throughout the day as I can fit them in. Some may have to wait until tomorrow though. I'll try and get the Weapon Analysis updated sooner rather than later though, since I expect a bunch of us to be killing Ony tonight. (It had to be today, of course, when I have an important deadline this afternoon and can't waste the whole morning posting theorycraft)
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
For the first round of simulations, I plan on using my current gear set. You can check my armory, but for posterity's sake I'm saving it as a chardev template:
http://chardev.org/seven/?profile=300035
Theck's "Thank the Light there's no Vanquisher this tier" set:
Turalyon's Faceguard of Triumph (245)
Endurance of the Infernal (232)
Turayon's Shoulderguards of Triumph (245)
Cloak of the Makers (226)
Chestplate of the Towering Monstrosity (245)
Saronite Swordbreakers (245)
Turalyon's Handguards of Triumph (245)
Girdle of the Nether Champion (245)
Legguards of Feverish Dedication (245)
Dawnbreaker Greaves (245)
Fate's Clutch (239)
Clutch of Fortification (245)
Heart of Iron (226)
Satrina's Impending Scarab (245)
Crusader's Glory (245)
The Boreal Guard (232)
Libram of Defiance (245)
This is obviously not my endgame goal at the moment, but I figure it should reasonably represent a player trying to progress through ToGC25. Mostly ilvl 245's, with a few legacy items that haven't been upgraded yet. The weapon might be a tad OP, but if your guild is working on 25man hard modes then you're likely already able to reach the tribute chest.
The only liberty I've taken here is that I've switched the weapon enchant from Blood Draining to Accuracy. Otherwise, the enchants are all identical to what's in the chardev profile (very EH/stamheavy).
If anyone wants to suggest a more wellrounded set, please feel free. I can always recalculate later.
The net stat allocation is:
http://chardev.org/seven/?profile=300035
Theck's "Thank the Light there's no Vanquisher this tier" set:
Turalyon's Faceguard of Triumph (245)
Endurance of the Infernal (232)
Turayon's Shoulderguards of Triumph (245)
Cloak of the Makers (226)
Chestplate of the Towering Monstrosity (245)
Saronite Swordbreakers (245)
Turalyon's Handguards of Triumph (245)
Girdle of the Nether Champion (245)
Legguards of Feverish Dedication (245)
Dawnbreaker Greaves (245)
Fate's Clutch (239)
Clutch of Fortification (245)
Heart of Iron (226)
Satrina's Impending Scarab (245)
Crusader's Glory (245)
The Boreal Guard (232)
Libram of Defiance (245)
This is obviously not my endgame goal at the moment, but I figure it should reasonably represent a player trying to progress through ToGC25. Mostly ilvl 245's, with a few legacy items that haven't been upgraded yet. The weapon might be a tad OP, but if your guild is working on 25man hard modes then you're likely already able to reach the tribute chest.
The only liberty I've taken here is that I've switched the weapon enchant from Blood Draining to Accuracy. Otherwise, the enchants are all identical to what's in the chardev profile (very EH/stamheavy).
If anyone wants to suggest a more wellrounded set, please feel free. I can always recalculate later.
The net stat allocation is:
 Code: Select all
STR 1122
STA 2775
AGI 78
INT 0
SPI 0
Hit 99
Crit 25
Exp 270
AP 0
SP 0
Haste 0
ArP 0
Def 777
Dodge 775
Parry 251
BV 412
BR 33
Armor 23742
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
I had a crack at this but didn't get an answer I was satisfied with. Occasionally it's appropriate to absolutely prioritise dps/tps at the total expense of mitigation. In that situation is using 96exorcism69 a tps gain? Is it also a dps gain?
 Jonesy
 Posts: 418
 Joined: Fri Jul 13, 2007 1:23 am
Patch 3.2.2  Paladin Ability Damage/DPS/Threat/TPS Breakdow
3.2.2 Paladin Ability Damage/DPS/Threat/TPS Breakdown
Setup
Rotation: 969
Seals: SoV
Glyphs: V only, VJ and VA for glyphed Judgement and AS calculations
Talents: 1V+3C build, on a "noDUH" mob type
Gear: Theck's 9.245 Progression Set
File: calc_ability_dmg.m
Threat graph
Interestingly, in a lowBV set like this, ShoR and HotR are nearly neck and neck for damage. Consecration is a very close third place. JoV, Avenger's Shield (unglyphed), and HoW are all fairly close as well. Glyphing AS still boosts it to our highestdamage ability, while glyphing Judgement edges it ahead of HoW.
Next, let's look at DPS and TPS.
DPS/TPS
To plot each ability's DPS and TPS contributions, we divide by the cooldown for a realistic 969 scenario. For ShoR, HotR, Consecration, and Judgement this is easy: just divide by 6 or 9 depending on what slot it fills in the rotation. Since HoW would be a net threat loss if used in place of one of our 6second cooldowns, it gets treated as a 9second cooldown for this plot. For Avenger's Shield, we divide by 36, since the most likely way to weave it in is to substitute for a 9second ability every 4th rotation.
Melee swings get divided by the player's raidbuffed swing speed (which for a 1.6 speed weapon comes out to 1.26 seconds after parry haste (19.19% parry) but in the absence of Reckoning). The SoV proc gets divided by the proc rate, which is calculated to include procs from melee attacks, HotR, and Judgement. This works out to
(1/1.26 + 1/6 + 1/9)^(1)= 0.9333 seconds
The first term is the contribution from melee swings, the second from HotR.
Holy Shield gets multiplied by its average procs per second, which is a slightly more complicated function:
This works out to whichever's smaller:
This plot should look familiar as well. Not much has changed since last time.
The rest of the calculations should be ready for posting tomorrow morning.
Setup
Rotation: 969
Seals: SoV
Glyphs: V only, VJ and VA for glyphed Judgement and AS calculations
Talents: 1V+3C build, on a "noDUH" mob type
Gear: Theck's 9.245 Progression Set
File: calc_ability_dmg.m
 Code: Select all
Ability Damage Glyphed Threat Glyphed
ShoR 3502 0 9014 0
HotR 3478 0 8952 0
Cons 3413 0 8785 0
JoV 2319 2550 5969 6564
AS 2512 5024 6466 12932
HoW 2476 0 6373 0
SoV 464 0 1194 0
VDoT 4605 0 11853 0
HS 927 0 2386 0
Melee 776 0 1110 0
Threat graph
Interestingly, in a lowBV set like this, ShoR and HotR are nearly neck and neck for damage. Consecration is a very close third place. JoV, Avenger's Shield (unglyphed), and HoW are all fairly close as well. Glyphing AS still boosts it to our highestdamage ability, while glyphing Judgement edges it ahead of HoW.
Next, let's look at DPS and TPS.
DPS/TPS
To plot each ability's DPS and TPS contributions, we divide by the cooldown for a realistic 969 scenario. For ShoR, HotR, Consecration, and Judgement this is easy: just divide by 6 or 9 depending on what slot it fills in the rotation. Since HoW would be a net threat loss if used in place of one of our 6second cooldowns, it gets treated as a 9second cooldown for this plot. For Avenger's Shield, we divide by 36, since the most likely way to weave it in is to substitute for a 9second ability every 4th rotation.
Melee swings get divided by the player's raidbuffed swing speed (which for a 1.6 speed weapon comes out to 1.26 seconds after parry haste (19.19% parry) but in the absence of Reckoning). The SoV proc gets divided by the proc rate, which is calculated to include procs from melee attacks, HotR, and Judgement. This works out to
(1/1.26 + 1/6 + 1/9)^(1)= 0.9333 seconds
The first term is the contribution from melee swings, the second from HotR.
Holy Shield gets multiplied by its average procs per second, which is a slightly more complicated function:
 Code: Select all
avg_HS_pps=min([8/9.*ones(size(boss_swing_speed)); (max([(player_block./100) 0])./boss_net_swing_speed)]);
This works out to whichever's smaller:
 8/9 (if all charges are used up, 8 procs every 9 seconds) or
 (player_block./100)./boss_net_swing_speed (chance to block divided by time between incoming attacks, assuming blockcapped).
 Code: Select all
Ability DPS Glyphed TPS Glyphed
ShoR 584 0 1502 0
HotR 580 0 1492 0
Cons 379 0 976 0
JoV 258 283 663 729
AS 70 140 180 359
HoW 275 0 708 0
SoV 445 0 1144 0
VDoT 307 0 790 0
HS 168 0 432 0
Melee 744 0 1063 0
This plot should look familiar as well. Not much has changed since last time.
The rest of the calculations should be ready for posting tomorrow morning.
Last edited by theckhd on Wed Sep 23, 2009 10:52 am, edited 7 times in total.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
Jonesy wrote:I had a crack at this but didn't get an answer I was satisfied with. Occasionally it's appropriate to absolutely prioritise dps/tps at the total expense of mitigation. In that situation is using 96exorcism69 a tps gain? Is it also a dps gain?
I didn't list it on the table, but Exorcism evaluates to 2634 damage and 6779 threat in this calculation. That would put it above Judgement, unglyphed AS, and HoW.
However, you also lose melee swings by casting Exorcism, which is doubly painful due to the loss of the accompanying SoV proc. Missing even one melee swing costs you 776 physical damage and 464 holy damage, which is far more than the 300 holy damage gained by subbing Exorcism in.
In addition, if you suffer pushback while casting Exorcism, it will lower your overall dps even further.
There's basically only one reason to sub Exorcism into your rotation if you're in melee range. Substituting it for Holy shield would net you 6779 threat at the cost of around 2300 to 4600 threat from melee swings and SoV procs. Substituting it for anything else is guaranteed to be a threat loss, even without pushback.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
What about a boss like Anub'arak or the Val'kyr where you are guaranteed an exorcism crit? I would never even THINK of using it in any situation except that one. If I'm guaranteed a crit, then is it worth using/subbing?
Is it worth using/subbing if it's a hybrid boss like Kel'Thuzad and you can cast while he casts? Guaranteed a crit and without worrying about mitigation loss, I could see situational use for it.
Is it worth using/subbing if it's a hybrid boss like Kel'Thuzad and you can cast while he casts? Guaranteed a crit and without worrying about mitigation loss, I could see situational use for it.

Petrus  Maintankadonor
 Posts: 940
 Joined: Wed Feb 06, 2008 3:45 am
 Location: St. Paul, Minnesota
Re: Theck's MATLAB TPS analysis (A Jonesy derivative work)
Well, again ignoring the mitigation aspect:
Exorcism is 3671 damage (9449 threat) against an Undead due to the guaranteed crit.
So you gain 1037 damage (2669 threat) by casting this instead of Judgement, for example.
However, casting it resets your swing timer, which given a 1.26s swing timer means you lose two melee attacks rather than the one I mentioned earlier. Each melee attack is worth 776 physical damage (1109 threat), and each SoV proc is 464 damage (1194 threat). So you lose 2303x2=4606 threat from autoattacks in the process.
More accurately:
Assuming you're equally likely to be at any particular point in your swing timer when you start casting Exorcism, you lose 1.26/2=0.63 seconds by starting to cast. You lose 1.5 seconds from casting, which resets your swing timer.
So you lose, on average, 1.5+0.63=2.13s, or 2.13/1.26=1.69 swings, by casting exorcism. That equates to 2303*1.69=3892 threat. Again, a fairly significant loss (3892  2669 = 1223 threat, every other judgement is 18 seconds, for a net TPS loss of 68 or so).
In other words, it's never going to be worth substituting Exorcism for anything but Holy Shield, provided you're in melee range and have SoV active with a fivestack on your target.
Exorcism is 3671 damage (9449 threat) against an Undead due to the guaranteed crit.
So you gain 1037 damage (2669 threat) by casting this instead of Judgement, for example.
However, casting it resets your swing timer, which given a 1.26s swing timer means you lose two melee attacks rather than the one I mentioned earlier. Each melee attack is worth 776 physical damage (1109 threat), and each SoV proc is 464 damage (1194 threat). So you lose 2303x2=4606 threat from autoattacks in the process.
More accurately:
Assuming you're equally likely to be at any particular point in your swing timer when you start casting Exorcism, you lose 1.26/2=0.63 seconds by starting to cast. You lose 1.5 seconds from casting, which resets your swing timer.
So you lose, on average, 1.5+0.63=2.13s, or 2.13/1.26=1.69 swings, by casting exorcism. That equates to 2303*1.69=3892 threat. Again, a fairly significant loss (3892  2669 = 1223 threat, every other judgement is 18 seconds, for a net TPS loss of 68 or so).
In other words, it's never going to be worth substituting Exorcism for anything but Holy Shield, provided you're in melee range and have SoV active with a fivestack on your target.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty
Simcraft 6.x, Call to Arms 6.0, Talent Spec & Glyph Guide 6.x, Blog: Sacred Duty

theckhd  Moderator
 Posts: 8001
 Joined: Thu Jul 31, 2008 3:06 pm
 Location: Harrisburg, PA
Return to Advanced Theorycraft and Calculations
Who is online
Users browsing this forum: No registered users and 1 guest