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

[Oldpappa]

I have been playing with talent calculators this morning

1-5 Seals of the Pure
1-2 Vindication
1-5 Conviction

To take Spiritual Attunement or not - or 1 vs. 2 points...

Or what about a nice Lay of Hands build - 20% damage reduction is nice...

Man, Theck - stop being busy and give some conclusions

[Minarva]

The conclusion is already there, look through the thread. 53/18 is the best for the new instance due to Crusade being 6% on all the mobs there, where as SoTP specs are better for Ulduar. Never take 2 points in SA, that would not change with the patch. You should probably also always want 2/2 vindication - its in my opinion as mandatory as thunderjudge.

[NYRIN1]

I can't veiw and wowhead links (or much else for that matter) at work, but im assuming 53/18 spec has 2 vintication, 3 conviction, 3 crusade.

[theckhd]

I can't veiw and wowhead links (or much else for that matter) at work, but im assuming 53/18 spec has 2 vintication, 3 conviction, 3 crusade.

Or 2 Vindication, 2 PoJ, 1 Conviction, 3 Crusade. There are a couple other variations as well.

[theckhd]

Before starting in with the simulations, I'd like to bring everyone up to speed on the current state of the code. I've made a lot of changes in the past week, the majority of it thanks to someone who offered to proofread my code and do most of the legwork of checking it against the latest information from EJ. Most of the changes are simple bug-fixes, but there are a few noticeable improvements/additions:

• The avoidance code now works properly, incorporating the DR formulas found in avoid_dr.m. This means that the code will properly calculate all avoidance percentages as well as block percent, which makes the Holy Shield DPS calculations more accurate. This also means that I can start looking into serious survival simulations in the future, for example to compare agility against pure dodge rating.
• The effects of parry haste have been implemented for both boss and player.
• Player base stats have been updated for 3.2
• Several buffs that had been previously overlooked/ignored have been added to buffs_debuffs.m. These include:
  
  • Winter's Chill
  • Arcane Intellect
  • Moonkin Aura
  • Thorns
  • Retribution Aura
  • Blessing of Sanctuary
  • Divine Plea
  • Replenishment
  • Bloodlust (disabled by default)
  • Insect Swarm
  • Avenging Wrath support is coming soon as well.
• Code has been added to help support mana recovery mechanisms, though this is still a work in progress.
• The code has been cleaned up a little bit - in particular, a lot of things that were "bolted on" to the ability_recalc module have now properly been consolidated into the stats_recalc module.

Anyway, while the contributor would like to remain anonymous, their help has been greatly appreciated.

[Awyndel]

Survival simulations...

Awesome work on the code guys, looks impressive. Good to know its been rechecked to see if its up to date etc. I know how much work that can be.

[theckhd]

Patch 3.2 - Paladin Ability Damage/DPS/Threat/TPS Breakdown

As always, the first simulation we post is the one that gives us the damage values for each ability. The gear set we'll be using as "default" for starting the Crusader's Coliseum raid instance (CC from here on) will be an updated version of my WTF Double Vanq again?? gear set. Here's the exact load-out:

Head: Helm of the Faceless
Neck: Shard of the Crystal Forest
Shoulder: Shoulderplates of the Deconstructor
Back: Cloak of the Makers
Chest: Conqueror's Aegis Breastplate
Bracers: Mimiron's Inferno Couplings
Gloves: Conqueror's Aegis Handguards
Belt: Indestructible Plate Girdle
Legs: Saronite Plated Legguards
Boots: Spiked Deathdealers
Rings: Platinum Band of the Aesir and The Leviathan's Coil
Trinkets: Heart of Iron and Royal Seal of King Llane
Weapon: Shiver (Accuracy)
Shield: The Boreal Guard
Libram: Libram of Obstruction

All gem slots are filled with epic gems. 30 Stam for blue/prismatic, 10 Agi / 15 Stam for red, and 10 Def / 15 Stam for yellow. I realize these may not be optimal choices in all cases (i.e. Boreal Guard should probably get two blue gems), but I stuck with them for consistency. The difference in threat should be small enough that swapping gems isn't going to change the outcome anyway.

The relevant threat stats are as follows:

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STR          1027
STA          2304
AGI            82
Hit Rating    209
Crit Rating    25
Exp Rating     42
BV            643

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 8.5 Progression Set, given above
File: calc_ability_dmg.m

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Ability  Damage   Glyphed   Threat   Glyphed
ShoR      3984        0     11041         0
HotR      2950        0      8175         0
Cons      3437        0      9525         0
JoV       2264     2490      6274      6901
AS        2562     5124      7100     14200
HoW       2525        0      6998         0
SoV        435        0      1206         0
VDoT      4810        0     13330         0
HS         933        0      2586         0
Melee      697        0      1017         0

Threat graph
Unsurprisingly, ShoR, Cons, and HotR are still our top 3 damage abilities, followed by Avenger's Shield (unglyphed), HoW, and JoV (unglyphed). Glyphing AS boosts it to our highest-damage ability, while glyphing Judgement doesn't quite catch it up to HoW. Nothing changes on the threat graph, outside of the relative value of a melee attack.

Now that Exorcism is gone, our options for substitution rotations are nearly nonexistent. We gain nothing by substituting anything but glyphed AS for our top damage abilities (ShoR, Cons, HotR). Judgement is still the weak link, and we gain around 300 damage by substituting either unglyphed AS or HoW for it. That's about it as far as options go, though.

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 1.32 seconds in the absence of Reckoning). The SoV proc gets divided by the proc rate, which is calculated to include procs from melee attacks, Judgements, and HotR. This works out to
(1/1.32 + 1/6 + 1/9)^(-1)=0.95.
The first term is the contribution from melee swings, the second from HotR, and the third from Judgements.

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 0.161 pps in this gear set for a boss swing speed of 2.4 (2.0 base), or an average of 1.4 procs every 9 seconds (or a proc every 6.23 seconds).

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Ability   DPS   Glyphed    TPS   Glyphed
ShoR      664       0     1840       0 
HotR      492       0     1363       0 
Cons      382       0     1058       0 
JoV       252     277      697     767 
AS         71     142      197     394 
HoW       281       0      778       0 
SoV       459       0     1273       0 
VDoT      321       0      889       0 
HS        149       0      414       0 
Melee     736       0     1073       0 

Nothing terribly amazing here, but it's worth noting that the SoV 5-stack proc is now a huge component of our threat. Thanks to the fact that it procs off of melee attacks, HotR, and Judgement, we're getting a proc every 0.95 seconds or so. As a result, it's actually causing more raw threat than the DoT component. This will have ramifications for the stat analysis, since it gives us extra incentive to connect with our attacks.

Talent comparison coming up later this afternoon, hopefully.

[theckhd]

Back to the talent analysis. Not a lot has changed here, so I'll mostly be repeating myself.

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. no threat talents
2. 3/3 One-Handed Weapon Specialization (OHWS)
3. OHWS + 3/3 Touched By The Light (TBTL)
4. OHWS+TBTL + 3/3 Crusade
5. OHWS+TBTL + 5/5 Conviction
6. OHWS+TBTL + 5/5 Seals of the Pure (SotP)
7. OHWS+TBTL + 5/5 Reckoning
8. OHWS+TBTL + 0/5 Divine Strength
9. OHWS+TBTL + 0/3 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. There are really only two differences from previous analyses here:

Setup:
Rotation: 969
Seals: SoV
Glyphs: V only
Talents: Various, in combinations to isolate the benefit of each talent individually.
Gear: Theck's 8.5 Progression Set
File: calc_talent_analysis.m

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Talent     DPS      TPS   (both per point)
Reck      13.2     25.4                   
Conv      19.2     46.9                   
Crus      30.8     78.7                   
SotP      28.8     79.8                   
Red       37.2    103.1                   
DivStr    41.7    106.3                   
TbtL      51.5    142.7                   
C(6%)     61.7    157.5                   
1HWS      88.8    225.6   

The addition of a SoV 5-stack proc to Judgement has tipped the scales in favor of SotP once again, letting it sneak ahead of Crusade by just over 1 TPS per point for "no-DUH" mobs.

And just to reiterate what I said last time, 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 8.5 Progression Set
File: calc_talent_analysis.m

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Spec         DPS      TPS      TPS(e)   Util
3S           3080     7907     7907     12 
4S           3108     7983     7983     11 
5S           3135     8058     8058     10 
4S+3R        3146     8058     8058      8 
5S+3R        3174     8135     8135      7 
5S+5R        3199     8184     8184      5 
5S+3R+1V     3194     8184     8184      7 
5S+3R+3V     3234     8282     8282      5 
5S+1V        3155     8107     8107      9 
5S+3V        3194     8204     8204      7 
5V           3094     7911     7911     10 
1V+2C        3078     7880     8035     12 
1V+3C        3108     7958     8189     11 
3R+1V+3C     3146     8031     8265      8 
3V+3C        3147     8053     8288      9 
5V+3C        3187     8149     8386      7 
3R+5V+3C     3226     8225     8465      4 
5V+2C        3156     8070     8228      8 
5V+3C-1T     3141     8023     8257      8 

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





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:

• It's a good time to be a paladin, threat will be strong no matter which way you go (SotP or Crusade).
• 0/53/18 providesthe 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.

[jere]

http://www.tankspot.com/forums/f64/42643-judgement-light-3-0-8-a.html

One of the changes in 3.0.8 that we may or may not have announced is that we changed Judgment of Light to do no threat in order to fix some of this seemingly random behavior. We aren't trying to nerf Prot paladin threat overall with this change.

The topic came up again recently when Protadin OTs were accidentally pulling off the MT with huge threat spikes while tanking adds etc.

By the way, since 3.2 is coming out today, I'll be posting the finalized 3.2 calculations throughout the day. Unfortunately, I'll be really busy today as well, so it may take until later this afternoon or evening to get all of the important ones up.

As an additional note. Testing I did yesterday (prior to 3.2 obviously) indicated that the following do NOT cause threat:
JoW mana procs
BoSanc mana procs
SoW mana procs
SA mana procs

As far as I could see, none of them were returning threat, at least according to the ingame threat API functions. I sent you a PM on the matter Theck, incase you were interested. I will try to retest for 3.2 sometime this week for verification.

Mind you those findings are different for when I tested right after WotLK came out. Back then, they were providing 0.5 threat unmodified per mana gained, but somewhere between then and now (I am guessing when JoL got changed), they stopped providing threat.

[Arees]

What about Divine Plea mana procs?

[theckhd]

As far as I could see, none of them were returning threat, at least according to the ingame threat API functions. I sent you a PM on the matter Theck, incase you were interested. I will try to retest for 3.2 sometime this week for verification.

Yeah, I saw that message. The question arose when the mana regen mechanics were added to the code. Which is a moot point due to your findings, it seems.


Also, interesting note: Retribution Aura (Improved) is worth 52 DPS (144 TPS), and Thorns is worth 34 DPS (49 TPS), according to the code. So the presence or absence of Thorns is worth almost two points in Reckoning.

[jere]

Is that accounting for the "extra threat" they were supposed to have baked into it? Back when they announced the Retribution Aura change, they mentioned giving it an extra threat modifier. I honestly forgot to test it though while on the PTR.

[theckhd]

Is that accounting for the "extra threat" they were supposed to have baked into it? Back when they announced the Retribution Aura change, they mentioned giving it an extra threat modifier. I honestly forgot to test it though while on the PTR.

No, that was just the standard Holy modifier I used. Apparently the threat modifier was just a factor of 2, so it should be double what I posted.

[Candiru]

theckhd, are you assigning the Judgement and HotR the extra threat from the resulting SoV proc? It wasn't clear from your post if you were. If you aren't adding them already, then that would push HoW back to only be worth replacing HolyShield with.

[theckhd]

Now that we've reviewed abilities and specs, let's take a look at how stats will affect our threat in 3.2.

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: 100./DivStr
STA: 100
AGI: 10./BoK
AP: 10./UnRage
BV: 1./(Redoubt + BV_Meta)
Everything else is just one point worth

In the end, the plots look the way they did in the past; 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 8.5 Progression set
File: calc_stat_tps.m

As usual, we'll look at STR first. For a point of reference, I have around 1300 STR on my character sheet, so that's about the level of an Ulduar geared tank.

DPS plot
For those who have been following this thread, this should look familiar. STR is still tops, followed closely by BV, then Hit and Expertise. Expertise gained some ground thanks to the SoV proc, and BV gained ground due to blizzard halving it's itemization budget.

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.

Next we'll look at hit.

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:

DPS plot
Pretty much identical to the Hit graph, expertise loses effectiveness when you hit the soft and hard caps, and damage-increasing stats scale differently above and below those caps.

Block Value:

DPS plot
Here we see the effects of the ShoR diminishing returns formula. Copying and Pasting from last time:

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 2952 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, 2600, 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.