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

[gibborim]

Five-stack Stability
For our approximation that we can keep a 5-stack indefinitely to be a good one, we want to make sure that the probability of that 5-stack 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=1-p.

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 worst-case 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 auto-attack 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.

[tlitp]

agreed, it should be (1-p^2)^N instead of (1-p)^N

[theckhd]

My understanding of Holy Vengence/Blood Corruption application is that a successful auto-attack 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 hand-waved over this in the post, in that I assumed all of the auto-attacks 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 re-write the post to reflect the proper model.

[sfrog]

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.....

[theckhd]

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?

[Petrus]

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.

[theckhd]

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.

[Modal]

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.

[theckhd]

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)

[theckhd]

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 end-game goal at the moment, but I figure it should reasonably represent a player trying to progress through ToGC-25. 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 25-man 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/stam-heavy).

If anyone wants to suggest a more well-rounded 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

[Jonesy]

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 96-exorcism-69 a tps gain? Is it also a dps gain?

[theckhd]

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 "no-DUH" 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 low-BV 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 highest-damage 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 6-second cooldowns, it gets treated as a 9-second 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 9-second ability every 4th rotation.

Melee swings get divided by the player's raid-buffed 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:

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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 block-capped).

In practice, this works out to 0.181 pps in this gear set (42.7% block) for a boss swing speed of 2.4 (2.0 base), or an average of 1.63 procs every 9 seconds (or a proc every 5.52 seconds).

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.

[theckhd]

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 96-exorcism-69 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 push-back 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 push-back.

[Petrus]

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.

[theckhd]

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 auto-attacks 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 five-stack on your target.