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

The legend for this graph must be wrong.
I can't see AP being better that Str and Stam still giving us any threat.

culhag wrote:The legend for this graph must be wrong.
I can't see AP being better that Str and Stam still giving us any threat.

Yeah, that legend is definitely wrong... I have no idea how that one got screwed up but the rest were fine.

I'll have to wait until tomorrow to fix it though, my code is at work.

tlitp wrote:In order to expand the MATLAB code to properly assess combat situations versus trash mobs, we need the base armor values of 80-82 elites. Anyone that has a hunter is asked to provide the said data by using Beast Lore on some easily accessible elites :

• level 80 - Frostworg Denmother, Jotunheim Proto-Drake (outdoor)
• level 81 - Dread Creeper (Naxxramas)
• level 82 - Lavanthor, Hadronox, King Dred (heroic dungeons)

Thanks in advance.

Wish you'd asked yesterday, since I've had Dred, Levanthor and Hadronox in daily heroic groups since then.

But for:
80 elites (Jotunheim Proto-Drakes, Battlescarred Frostworg, Frostworg Denmother): 9729 armor
81 elites (Unyielding Constrictor): 10033 armor

Apparently Saurfang's Bloodbeasts are beasts too (untameable ), so I'll try to snag a shot of them for you tomorrow.

Actually, wouldn't an beast bosses in lowbie 5 mans count as level 82s? Or are those actually 72 instead of 5 man skull mobs?

culhag wrote:The legend for this graph must be wrong.
I can't see AP being better that Str and Stam still giving us any threat.

Legendairy.

Just like my future tauren Paladin.

Thalastor82 wrote:

Eredor wrote:
Where do I find the equations to calculate block value?

Summing all block value on my armory I have 829.
Rawr tells me I have 2273.
The block value you mention are way way bigger than mine.

Thanks,
Eredor

the block value of your items is only part of the total.

part comes from strenght (1 block value per 2 force), plus you have Redoubt (+30%) and possibly the metagem (+5%) that increase the total.

In the block value set I use for instancing, I have around ~1k block value coming from items, the same coming from strenght (~2k force, full red gemmed) and after kings, meta, redoubt and buffs I come to ~3k blocking. In raid it would be even bigger, but in raid I usually don't use the blocking set (with few exceptions).

If you want to increase the block value gem force and put the meta. A greath trinket for this is the noble deck, it gives 390 force (195 block value) during uptime. Also, you can make use of low lvl items that are perfectly ok for instance even if already unused in new raids. Many drop from ulduar25, for instance.

In any case, the DR mentioned in the previous posts concerns only the treath contribution of the blocking value. In effect, the SotR has diminishing returns, probably to avoid huges slams in pvp. The effectivenes of the blocking value against white non-bleeding attacks is not affected by diminishing returns and, the more you have, the more you block

theckhd wrote:
Rawr should be correct, or if you want an in-game source, Tankadin2 will calculate it for you. It's not surprising that the values I gave are large, since they're near the levels of the ShoR damage cap, which most people don't reach in regular gear.

If you sum your BV from gear, the formula is

Code: Select all

block_value=floor((floor(STR.*0.5) - 10 + Gear_BV + T84pc).*(Redoubt + BV_Meta));

Assuming 3/3 Redoubt:
STR is character sheet strength * 1.1 for kings, plus 291 for raid buffs
Gear_BV is whatever you summed it to be
T84pc = 225 if you have 4-piece T8 equipped
Redoubt = 1.3 (or 1.2 for 2/3, 1.1 for 1/3, etc)
BV_Meta = 0 if you don't have it gemmed, 0.05 if you do

Thanks & thanks.

Saving in my files for future reference

theckhd wrote:

culhag wrote:The legend for this graph must be wrong.
I can't see AP being better that Str and Stam still giving us any threat.

Yeah, that legend is definitely wrong... I have no idea how that one got screwed up but the rest were fine.

I'll have to wait until tomorrow to fix it though, my code is at work.

Legend is fixed now, apparently I hardcoded all of the legends for these plots, and failed to update the BV-TPS one in 3.2. Hardcoding legends is something I don't tend to do anymore (most of my plots are more dynamically generated now), but had to because of the line style choices in these plots. I may re-do the plotting section of this m-file in the future when I have some time.

fafhrd wrote:Wish you'd asked yesterday, since I've had Dred, Levanthor and Hadronox in daily heroic groups since then.

But for:
80 elites (Jotunheim Proto-Drakes, Battlescarred Frostworg, Frostworg Denmother): 9729 armor
81 elites (Unyielding Constrictor): 10033 armor

Apparently Saurfang's Bloodbeasts are beasts too (untameable ), so I'll try to snag a shot of them for you tomorrow.

Actually, wouldn't an beast bosses in lowbie 5 mans count as level 82s? Or are those actually 72 instead of 5 man skull mobs?

Thanks. The lowbie 5-mans are 72 elites, so they won't work. But Saurfang blood beasts will be fine. However, I can already guess what they'll be from your data.

Code: Select all

level   armor
80   9729
81  10033
82      ?
83  10643

If you plot those three, you get a straight line of the form:
armor = 305*level - 14672

So a level 82 should be around 10338 armor based on the fit.

I actually suspect the fit is off slightly, as the lvl 80 value differs by 1 armor and the intercept is negative. In all likelihood it's a nonlinear function, but we're looking at a small enough level range that it's locally linear.

theckhd wrote:

Code: Select all

level   armor
80   9729
81  10033
82      ?
83  10643

If you plot those three, you get a straight line of the form:
armor = 305*level - 14672

So a level 82 should be around 10338 armor based on the fit.

I actually suspect the fit is off slightly, as the lvl 80 value differs by 1 armor and the intercept is negative. In all likelihood it's a nonlinear function, but we're looking at a small enough level range that it's locally linear.

It's worth noting that the equation for the C constant in the armor DR equation is in the same form:

value*enemy_level - value

I wouldn't be surprised if the enemies armor was exactly like that.

EDIT:
armor DR equation:
DR_armor = AC/(AC+C)

C = 467.5 * EnemyLevel - 22167.5

EDIT:
Also, those armor values you see could be after rounding. Given that the DR equation uses 0.5's in its values, that might be why one of the values is off by one.

Thanks for helping us out, Faf. Theck and Jere are right, the slight numerical discrepancies we see between the linear model of the base armor values and the observed ones are an effect of integerization.

3.3 Weapon Analysis, round 2

Now that most of the Icecrown loot table is available, let's look at the weapon analysis again. First, let's look at what we don't have.

We don't have most of the loot from the lich king encounter, but we know there's an axe that drops from the heroic 10-man encounter. So it's fairly likely that there's a non-heroic 258 version on his normal-mode loot table. There's also the possibility that the 25-man lich king encounter drops a tanking weapon on either difficulty, which would add two more potential weapons in the 271 and 284 ilvl slots. And of course, there might be a juicy slow dps weapon in any of those four loot tables that could be good for threat.

Once we have confirmed loot tables for the lich king encounter, I'll post the final wrap-up of this analysis. In the meantime, you can estimate the positions of these weapons based on the others of the same ilvl that we already have stats for.

I've also made one change to the simulation since last time - I'm now artificially forcing the expertise and hit from gear to be 0. This way each weapon will get the full benefit of its stat contributions. There are arguments for and against doing this, but gear will be so variable this tier that I'm not sure it's fair to artificially choose a particular hit and expertise level as a baseline.

----------------------------------------

Quick overview of what we know about weapons and their effect on our threat:

• Slow weapons are good thanks to SoV 5-stack procs (see past calculations).
• The only spec-related choice that can change the outcome is Reckoning.
• Higher-DPS weapons tend to trump lower-DPS weapons
• Threat stats make only a minor difference (generally less than a 13-ilvl upgrade in weapon dps)

Since 53/18 will be the de-facto tank spec for Icecrown, we'll calculate threat for the 1V+3C and 3R+1V+3C specs. There are notes at the end on how to modify this if you pick up more or less points in Reckoning.

Thanks to Blizzard's inane "lets make identical items with different names" policy for Coliseum, I've generated tables and plots for both Alliance and Horde versions of the weapons.

I've included all of the 2.6-speed melee DPS weapons from Coliseum and ICC. 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.

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: T10 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 ICC.

This time around, there are simply too many weapons to fit on one graph that isn't excessively long. I've broken down the plots a bit to make it more manageable. The first three plots will be tanking weapons only, and the fourth plot will show DPS weapons and a few representative tanking weapons.

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    8810    9151 
Peacekeeper Blade                 219    8527    8747 
Stoneguard                        219    8569    8802 
Legacy of Thunder                 219    8605    8851 
Last Laugh                        226    8632    8869 
Titanguard                        232    8674    8914 
Shiver                            232    8682    8921 
Sorthalis                         239    8755    8998

Lucky Old Sun                     219    8607    8841 
Gleaming Quel'Serrar              232    8687    8978 
Crusader's Glory                  232    8687    8916 
Falric's Wrist-Chopper            232    8765    9007 
Rimefang's Claw                   232    8757    9010 
Burnished  Quel'Serrar            245    8798    9097 
Crusader's Glory (245)            245    8813    9048 
Honor of the Fallen               245    8850    9096 
The Facelifter                    251    8861    9110 
Bonebreaker Scepter (251)         251    8886    9148 
Silverwing Defender               258    8997    9251 
The Facelifter (264)              264    8985    9242 
Bonebreaker Scepter (264)         264    9036    9308 
Last Word                         264    9008    9297 
Last Word (277)                   277    9167    9467 
Troggbane, AotFK                  271    9282    9600 

Ghoulslicer                       219    8911    9272 
Hate-Forged Cleaver               219    8925    9286 
Singed Vis'kag the Bloodletter    232    8890    9256 
Vulmir, the Northern Tempest      232    9019    9388 
Nighttime                         232    9059    9431 
The Grinder                       232    9066    9437 
Black Icicle                      232    9083    9456 
The Lion's Maw                    232    9084    9456 
Caress of Insanity                232    9104    9488 
Tempered Vis'kag the Bloodletter  245    9008    9383 
Raging Deathbringer               245    9043    9431 
Stormpike Cleaver                 245    9172    9553 
The Grinder (245)                 245    9208    9591 
The Lion's Maw (245)              245    9230    9614 
Gutbuster                         251    9288    9678 
Frost Giant's Cleaver             251    9289    9680 
Cudgel of Furious Justice         251    9294    9683 
Soulbreaker                       251    9304    9694 
Quel'Delar, CotS                  251    9317    9720 
Relentless Gladiator's Longblade  258    9300    9696 
Stormpike Cleaver (258)           258    9312    9704 
Remorseless                       258    9374    9769 
Black Bruise                      264    9295    9693 
Bloodvenom Blade                  264    9385    9786 
Gutbuster (264)                   264    9460    9864 
Frost Giant's Cleaver (264)       264    9464    9869 
Soulbreaker (264)                 264    9467    9870 
Black Bruise (277)                277    9434    9846 
Bloodvenom Blade (277)            277    9564    9979 

Horde List
                                             TPS       
Weapon                           ilvl   1V+3C  3R+1V+3C
Broken Promise                    213    8810    9151 
Peacekeeper Blade                 219    8527    8747 
Stoneguard                        219    8569    8802 
Legacy of Thunder                 219    8605    8851 
Last Laugh                        226    8632    8869 
Titanguard                        232    8674    8914 
Shiver                            232    8682    8921 
Sorthalis                         239    8755    8998 
Lucky Old Sun                     219    8607    8841 
Gleaming Quel'Serrar              232    8687    8978 
Ardent Guard                      232    8687    8916 
Falric's Wrist-Chopper            232    8765    9007 
Rimefang's Claw                   232    8757    9010 
Burnished  Quel'Serrar            245    8798    9097 
Ardent Guard (245)                245    8813    9048 
Blood and Glory                   245    8850    9096 
The Facelifter                    251    8861    9110 
Bonebreaker Scepter (251)         251    8886    9148 
Orgrim's Deflector                258    8997    9251 
The Facelifter (264)              264    8985    9242 
Bonebreaker Scepter (264)         264    9036    9308 
Last Word                         264    9008    9297 
Last Word (277)                   277    9167    9467 
Troggbane, AotFK                  271    9282    9600 
Ghoulslicer                       219    8911    9272 
Hate-Forged Cleaver               219    8925    9286 
Singed Vis'kag the Bloodletter    232    8890    9256 
Vulmir, the Northern Tempest      232    9019    9388 
Nighttime                         232    9059    9431 
Blackhorn Bludgeon                232    9066    9437 
Black Icicle                      232    9083    9456 
Frostblade Hatchet                232    9084    9456 
Caress of Insanity                232    9104    9488 
Tempered Vis'kag the Bloodletter  245    9008    9383 
Raging Deathbringer               245    9043    9431 
Hellscream Slicer                 245    9172    9553 
Blackhorn Bludgeon (245)          245    9208    9591 
Frostblade Hatchet (245)          245    9230    9614 
Gutbuster                         251    9288    9678 
Frost Giant's Cleaver             251    9289    9680 
Cudgel of Furious Justice         251    9294    9683 
Soulbreaker                       251    9304    9694 
Quel'Delar, CotS                  251    9317    9720 
Relentless Gladiator's Longblade  258    9300    9696 
Hellscream Slicer (258)           258    9312    9704 
Cudgel of the Damned              258    9374    9769 
Black Bruise                      264    9295    9693 
Bloodvenom Blade                  264    9385    9786 
Gutbuster (264)                   264    9460    9864 
Frost Giant's Cleaver (264)       264    9464    9869 
Soulbreaker (264)                 264    9467    9870 
Black Bruise (277)                277    9434    9846 
Bloodvenom Blade (277)            277    9564    9979 

Horde Names

Last Word and The Facelifter are new additions this round, in both normal and heroic varieties. The Facelifter is a pretty solid contender, falling just below Bonebreaker Scepter in both categories, and marginally ahead of the 245-ilvl tanking weapons from ToGC10. There's not much else to say about this weapon though, it's sort of boring.

So far, Last Word is the only 25-man tanking weapon we know of, and its proc makes it hard to gauge performance. I've modeled the proc as 30% uptime, which is a completely random guess. Once we have more details, we'll have a better idea where it falls in the rankings. If you increase the uptime to 100%, it pulls ahead of everything in its category by a decent margin, including Troggbane.

If I had to guess (which I did, hence the arbitrary 30%), I'd say that Last Word will end up in the 30-50% uptime range, which will put it slightly ahead of its peers, but leave the heroic version slightly behind Troggbane.

Troggbane is the first slow tanking weapon we've seen since Broken Promise, and that 2.0 speed really shows in these simulations. However, it's going to be a few months before we see it.

More pertinently, the Bonebreaker Scepter is a pretty impressive weapon. Its 1.7 speed nearly catches it up to Silverwing Defender in threat output. The fact that Bonebreaker drops from the first boss of 10-man ICC means that it should be far more available to tanks thank the previous tier's tanking weapons were.

In addition, we have three new weapons from the new 5-man instances. Lucky Old Sun drops from normal mode, while Rimefang's Claw and Falric's Wrist-Chopper drop from heroic mode. The 232 weapons are a very competetive boon for players who haven't had luck with Anub'arak drops.


The next plots are just sorted differently, by TPS and by ilvl respectively.

Horde Names

Horde Names


Here's the plot with the slow DPS weapons, along with the "upper tier" tanking weapons (ToC/ICC). Again, this one is sorted by instance, then ilvl, then TPS.

Horde Names

Nothing particularly amazing here in terms of insight, but the plot reveals a few interesting options for the new tankadin. The new 219 DPS weapons actually perform as well as the 245-ilvl tanking weapons. Black Icicle from one of the new heroic 5-man instances actually out-threats any tanking weapon available pre-heroic ICC.

If you can get your hands on one of the slow dps weapons from the 10-man instance, that's probably your best bet for a threat weapon at this point, as it will probably take a month or two until the dps weapons from 25-man go to off-spec.

Finally, I've run the numbers for a few spell damage weapons as well. We all know that spell damage weapons are inferior, but now we have a place to point to with numbers to prove it.

Code: Select all

                                             TPS       
Weapon                           ilvl   1V+3C  3R+1V+3C
The Turning Tide                  226    8419    8653 
Seethe                            232    8540    8819 
Hammer of Purified Flame          251    8582    8825 
Frost Needle (251)                251    8566    8807 
Quel'Delar, LotM                  251    8700    8978 
Lockjaw (251)                     251    8684    8971 
Frost Needle (264)                264    8678    8924 
Lockjaw (264)                     264    8861    9156 

The take-home message from this plot is that even the best spell damage weapons in the game are inferior to tanking weapons available two tiers of content ago. The only exception here is the heroic version of Lockjaw, and even that one is weaker than the tanking weapon from the first boss of 10-man normal mode.

We can use the rotation_AoE file to see whether this changes at all for aoe threat, using the limited skill set:


Not a whole lot of change here. What we gain in Consecration damage, we lose in HotR and Seal of Command procs. Given the relative availability of tanking weapons this tier (from both raids and the heroic 5-man instance), there's no good reason a tankadin should be rolling on spell damage weapons.



TLDR version:

• Slow weapons are good for threat. A quick check of the numbers from this analysis shows:
  
  • Going from a 1.6 speed to a 2.6 speed weapon of equal DPS nets you around 450 TPS.
  • Each point in Reckoning will add about 80 TPS for a 1.6 speed weapon, while it will add about 130 TPS for a 2.6 speed weapon.
  • The combination of these two things means that a 2.6 speed weapon will be ahead of a 1.6 speed weapon of equal dps by 450+50*(# points in Reckoning), as a rule of thumb.
• If your tanking weapon is growing long in the tooth, head to the heroic 5-man to pick up one of the 232-ilvl weapons (tanking or dps), or better yet to normal 10-man ICC to pick up Bonebreaker Scepter.
  
• Spellpower Weapons are bad. Don't use them if you have any other option whatsoever.
  
• Troggbane is the sex.

Solved.

I'd like to re-do the Mongoose uptime calculation before continuing on to the Enchant analysis. For one thing, the old one is slightly incorrect, which I'll explain in this post. More importantly though, with ShoR becoming a melee attack, we need to know whether it does or does not proc PPM-based effects like Blade Ward and Mongoose.

If anyone has some spare time and a weapon enchanted with Blade Ward or Mongoose, and wouldn't mind checking for me, I'd appreciate it. If nobody gets to it, then I'll test it myself later this week.


Anyway, as to the error in the Mongoose calculation. Let's consider a sequence of events that can cause a proc of some sort - I'm keeping this generic since it's applicable to both Redoubt and Mongoose. We'll say that each event is identical, and has a probability of success s. If the event does succeed, it has a probability t of triggering a proc. Thus, the possible outcomes of any one event, along with their probabilities, are:

Code: Select all

Event   Probability   Note
00      (1-s)         event fails, no chance for a proc
10      s(1-t)        event succeeds, but no proc
11      st            event succeeds, proc occurs

Each event is an independent event, or a Bernoulli trial. A sequence of such trials gives you a Binomial distribution. In other words, the probability of having k successes in n trials is:

where p here is our st for a successful event that leads to a proc. In functional notation, this is

P(k,n)=f(k;n,st).

What we want to know is what's the chance of getting 0 procs in T seconds, where T is the duration of the proc effect. If we say there are N events in time T, that's simply

P(0,n) = f(0;N,st) = 1*(st)^0*(1-st)^N
P(0,n) = (1-st)^N

This result is the downtime of the effect, so the uptime is just:

Uptime = 1 - (1-st)^N

This is exactly the form of the Reckoning code - the success chance is s = (1-player_avoid) corresponding to not avoiding an incoming attack, the a proc chance is t = 0.02 per point in Reckoning, and N is the number of attacks we take from the boss in the time it takes to make 4 weapon swings or 8 seconds, whichever's less.

Now look back at the mongoose calculation. Since we're dealing with different event types, it's a little more complicated. I calculated N as the number of successful attacks in the buff duration. For a single event type, this would end up being:

Uptime = 1 - (1-t)^(sN)

... Oops. Of course, for many event types, it looks more like this:

Uptime = 1 - (1-t)^(s1*N1 + s2*N2 + ...)

It's pretty obvious why I made this mistake - I already had an expression for sum(si*Ni), and it was easy to trick myself into formulating the problem by saying that the Bernoulli trial was just the proc itself. It turned out to be a pretty good approximation, as the error was less than 1%, but it's still slightly wrong. The error becomes much more apparent when t grows larger and s becomes smaller.

In any event, the proper way to calculate the uptime of mongoose is to calculate the product of the different event type contributions:

Uptime = 1 - [(1-s1*t)^N1] * [(1-s2*t)^N2] * [(1-s3*t)^N3] * ....

Which is what the code is doing now. What we need to know is whether to include a term in this expression for ShoR.

winsonlim wrote:Crusader's Glory's tps seems to be different in these 2 graphs...

Yup, part of the new code I added to split the tanking weapons into three instance groups messed up the labels on the axis. They should be fixed now.

This calculation file really needs a complete overhaul to make it easier to work with. I already know what I want to do, but it will take a decent bit of time. It will probably go on my "Cataclysm Beta To-Do list."

theckhd wrote:

winsonlim wrote:Crusader's Glory's tps seems to be different in these 2 graphs...

Yup, part of the new code I added to split the tanking weapons into three instance groups messed up the labels on the axis. They should be fixed now.

This calculation file really needs a complete overhaul to make it easier to work with. I already know what I want to do, but it will take a decent bit of time. It will probably go on my "Cataclysm Beta To-Do list."

Its no problem. Post removed.

And also just to tell you that I'm a huge fan of your formulas. Just that I'm not so active in contributing to the forums. Great work, appreciate it a lot!

winsonlim wrote:And also just to tell you that I'm a huge fan of your formulas. Just that I'm not so active in contributing to the forums. Great work, appreciate it a lot!

No problem, and thanks for catching that error. Pointing out mistakes like that one counts as contributing - you're doing a favor to all the other players who would read the graph and take away the wrong conclusion.

One extra feature I'd be keen to see in your analysis Theck is to account for the various racial benefits for different weapon types.

As a dwarf paladin, I have always tried to find tanking maces to get the free +5 expertise bonus, but obviously increased weapon damage from higher iLevel non-mace weapons will outpace the benefits of the additional expertise at some point.