Theck's MATLAB thread - Cataclysm/4.x

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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby theckhd » Mon Oct 11, 2010 6:41 am

I don't know. But I should have answers to that and most other questions soon(TM).
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby Klaudandus » Mon Oct 11, 2010 2:47 pm

I guess I'll add Insight to the things to make a parse on.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby theckhd » Mon Oct 11, 2010 4:49 pm

Default Gear Set

This is the default gear set I'm using for the calculations on this page. It's loosely based off of the gear I had on Theck this past summer, which should still adequately represent an average tank progressing on ICC25 hard modes (i.e. able to kill early hard modes, but probably still working on PP/Sindra/LK).

Sanctified Lightsworn Plate (Heroic)
Bile Encrusted Medallion (Heroic)
Sentinel's Winter Cloak
Gargoyle Spit Bracers (Heroic)
Verdigris Chain Belt
Grinning Skull Greatboots (Heroic)
Deviums Eternally Cold Ring (Heroic)
Ashen Band of Endless Courage
Corroded Skeleton Key
Sindragosa's Flawless Fang
Last Word (Heroic)
Icecrown Glacial Wall (Heroic)
Libram of the Eternal Tower

I've left the socketing alone for the most part, since the socket bonuses haven't changed. That means 30 stam in every blue or yellow socket, but instead of agi/stam in red sockets I've used parry/stam (assuming they give 9 or more stamina per red gem).

Each item has had its highest avoidance stat (dodge or parry) reforged into mastery in an attempt to reach block cap. I managed to get to around 100% but no further without swapping armor items out for more avoidance.

Enchants are:
Arcanum of the Stalwart Protector
Greater Inscription of the Pinnacle
Enchant Cloak - Mighty Armor
Enchant Chest - Super Health
Enchant Bracer - Major Stamina
Heavy Borean Armor Kit
Frosthide Leg Armor
Enchant Boots - Tuskarr's Vitality
Enchant Ring - Stamina x2
Enchant Weapon - Accuracy
Enchant Shield - Major Stamina

Net stats
Most of these are recognizable enough to be understandable, but until I get them into the glossary feel free to ask. We've used "ph" and "sp" as shorthands for physical and spell, "dr" for damage reduction
str: 2178
sta: 5625
agi: 290
int: 102
armorystr: 1830
hitpoints: 63279
armor: 2.9026e+004
phdr: 0.6357
resistance: 0
spdr: 0
phhit: 4.8448
sphit: 11.6801
exp: 23.0294
phhaste: 10.0000
sphaste: 5.0000
effhaste: 0
phgcd: 1.5000
spgcd: 1.4286
phcrit: 6.9757
spcrit: 11.4940
aacrit: 6.9757
sp: 1398
hsp: 1398
mast: 18.2819
miss: 4.4000
dodge: 20.3412
parry: 20.0368
block: 55.2221
avoid: 44.7779
avoidpct: 0.4478
VengAP: 6.0115e+003
ap: 11646
wdamage: 1.9483e+003
ndamage: 2.4475e+003
swing: 1.6364
reck: 0.3007
wswing: 1.2100
wdps: 1.6103e+003
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Postby theckhd » Mon Oct 11, 2010 5:00 pm

Ability damage

Setup:
Talents: 0/31/5 with all prot damage talents + Crusade
Glyphs: N/A
Seal: N/A
Gear: T10 sample set

Code: Select all
                Damage
Ability    Raw    Net  Glyph
ShoR     15546  14324  15756
CS        4063   3743   3912
JoT       5177   5363   5899
AS        8888   9044  11757
HW        3329   3806      0
HoW       3492   4516      0
Exor      3141   3145   3774
SoT        388    415      0
SoR        356    356      0
SoJ        162    162      0
Cens      9635  10307      0
Cons      6629   6637      0
HotR       606    559    615
HaNova    4912   4321      0
Melee     1296   1132      0


Raw is the damage one would expect on a regular hit without target damage reduction. Net incorporates damage redux, hit/miss, and crit factors. Glyph is the same as net, but with that ability's glyph active. Censure damage is for a 5-stack over 15 seconds, and Consecration is a full 10 ticks. "HaNova" is HotR's AoE "holy nova" component.

A stark change from the Wrath model of paladin tanking, our abilities now cover a wide range of damage values. I'm going to come back to this post and address DPS values/plots once we have our rotation nailed down (more on that later).

In the meantime, here's a plot of net damage for each ability, to give you some feeling of the damage range we're talking about:
Image
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Postby theckhd » Mon Oct 11, 2010 5:45 pm

Rotation Simulations

The rotation simulation code is available on the matlabadin project page, as are the priority models used.

Setup:
Talents: 0/31/5 with all prot damage talents + Crusade
Glyphs: CS/Jud/ShoR for Prime, AS for Major
Seal: SoT
Gear: T10 sample set

There are some subtleties here that I want to discuss before addressing the data. The simulation works by simulating a limited combat environment. It keeps track of ability cooldowns, holy power, and the GCD, iterating in user-definable time steps. At each time step, it checks the priority queue in order and casts the first thing for which the conditionals are true.

While it's capable of incorporating haste effects (by working in time steps of 0.1s or less), that leads to some weird situations. For example, since Holy Wrath is a spell it has a shorter GCD than a melee attack like Crusader Strike. Thus, you can end up in a situation that looks like this:

CS-HW-????

If your Holy Wrath GCD is shorter than 1.5 seconds by at least one full timestep, CS still won't be off of cooldown. However, if something else is (Judgement perhaps, or Consecration) it'll try and cast that instead. That pushes CS back by almost a full GCD, inevitably causing a massive drop in DPS.

Because of this, I've simulated in time steps of 0.5 seconds, which is essentially throwing out haste as far as our spellcast choices are concerned. Since we are unlikely to want to deviate from casting CS on every alternate cooldown, this shouldn't be an issue.

In the queues below, there are some non-standard abbreviations:

SD stands for Sacred Duty, and means that in a case where you have 3 Holy Power, no Sacred Duty buff, and Judgement is off of cooldown, you prioritize Judgement (instead of just casting ShoR) to "fish" for a Sacred Duty proc.

J# stands for "Judgement #," and means that we treat Judgement as having an effective cooldown of #. "J8" would be the "standard" mode, and is implicit anywhere that a lone "J" is encountered. "J9" treats Judgement as having a 9-second effective cooldown, which is mostly irrelevant for us, but can cause strange things to happen when you prioritize AS over Judgement.

#ShoR stands for an #-point ShoR. If the number is omitted, it's assumed to be a 3-pointer.

2SDShoR stands for an 2-point ShoR if and only if Sacred Duty is up.

The simulation is run for 90k time steps, which is 30k GCDs, or roughly 12 and a half hours of combat. That's a long time, but random procs are random, and it's still entirely possible to get variations of 10-20 DPS from sim to sim. This is pretty evident from rotations #2 and #10, which are functionally identical queues because the cooldown clashes make SD prioritization irrelevant. However, #2 has 38 more AS casts than #10 due to lucky GC procs, which gives it an edge of about 30 DPS.

Code: Select all
Q#         Priority                              DPS   Empty    E%
1   SD>ShoR>CS>J>AS>Cons>HW                    7837     32   0.1
2   SD>ShoR>CS>J>AS>HW                         7776     43   0.1
3   SD>ShoR>CS>AS>J8>HW                        7694    833   1.5
4   SD>ShoR>CS>AS>J9>HW                        7336   2195   7.3
5   SD>ShoR>CS>AS>J8>HW>Cons                   7703    525   0.7
6   SD>ShoR>CS>AS>J9>HW>Cons                   7426   1403   4.7
7   SD>ShoR>AS>CS>J>HW>Cons                    7637   1114   2.3
8   SD>AS>ShoR>CS>J>HW>Cons                    7640    982   2.1
9   AS>SD>ShoR>CS>J>HW>Cons                    7636   1036   2.2
10   ShoR>CS>J>AS>HW                            7767      0   0.0
11   ShoR>CS>AS>J>HW                            7695    144   0.5
12   ShoR>AS>CS>J>HW                            7609   1268   3.0
13   AS>ShoR>CS>J>HW                            7573   1487   3.4
14   SD>3ShoR>2SDShor>CS>J>AS>HW                6728   2041   3.1
15   Inq>3ShoR>CS>J>AS>HW (Inq model)           7258      0   0.0
16   Inq>3ShoR>CS>AS>J>HW (Inq model)           7421    155   0.5
17   Inq>3ShoR>2SDShoR>CS>J>AS>HW (Inq model)   6412   1207   1.5


Second data set, to give you an idea of the variance:
Code: Select all
1   SD>ShoR>CS>J>AS>Cons>HW                    7812     40   0.1
2   SD>ShoR>CS>J>AS>HW                         7770     39   0.1
3   SD>ShoR>CS>AS>J8>HW                        7710    849   1.6
4   SD>ShoR>CS>AS>J9>HW                        7321   2285   7.6
5   SD>ShoR>CS>AS>J8>HW>Cons                   7695    553   0.8
6   SD>ShoR>CS>AS>J9>HW>Cons                   7433   1392   4.6
7   SD>ShoR>AS>CS>J>HW>Cons                    7629   1064   2.2
8   SD>AS>ShoR>CS>J>HW>Cons                    7651    976   2.1
9   AS>SD>ShoR>CS>J>HW>Cons                    7649   1033   2.2
10   ShoR>CS>J>AS>HW                            7758      0   0.0
11   ShoR>CS>AS>J>HW                            7671    160   0.5
12   ShoR>AS>CS>J>HW                            7579   1291   3.1
13   AS>ShoR>CS>J>HW                            7558   1496   3.4
14   SD>3ShoR>2SDShor>CS>J>AS>HW                6735   2025   3.1
15   Inq>3ShoR>CS>J>AS>HW (Inq model)           7252      0   0.0
16   Inq>3ShoR>CS>AS>J>HW (Inq model)           7459    143   0.5
17   Inq>3ShoR>2SDShoR>CS>J>AS>HW (Inq model)   6427   1126   1.5


There are lots of observations to be made here, and I hope to come back to this post and discuss some of the more subtle ones in more detail. But for now, here are the big ones that matter:

  • Cons>HW (#1 vs #2) at the end of the queue is a slight DPS increase, if we can afford the mana. Note that this sim already includes Hallowed Ground, so if you don't spec that it's basically dead even (i.e. not worth the mana cost).
  • Despite being our "signature" move, Avenger's Shield is relatively low priority.
    • Putting it above Judgement inevitably causes empty GCDs and a drop in DPS, no matter what else you try and fill the rest of the queue with.
    • That said, the difference between #10 and #11 is relatively small, so it won't hurt you much to prioritize AS>J.
    • Putting it above CS or higher is always a significant DPS loss.
  • Given that there isn't a significant difference between #2 and #10, Sacred Duty prioritization isn't worth bothering with. It causes empty GCDs thanks to ShoR misses that offsets any benefit it might convey. It can help in a few situations with high AS priorities, but those are always sub-optimal anyway.
  • 2-point ShoR's are always a DPS loss even if you only use it on a guaranteed crit.
  • Inquisition is always a DPS loss. Interestingly, with Inq up you actually start to see AS>J pull ahead of J>AS, but neither are as good as using that Holy Power on ShoR.


TLDR Summary
  • Our new queue is ShoR>CS>J>AS>HW. Feel free to slip Cons in above HW if the boss is stationary and mana isn't an issue.
  • This is equivalent to the following (dubbed "939") rotation: CS-J-CS-X-CS-ShoR, where X is filled with AS if it's available, or HW otherwise.
  • Yes, this is bad news for Grand Crusader. More on that soon.
Last edited by theckhd on Tue Oct 12, 2010 7:01 am, edited 1 time in total.
Reason: corrected data
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Postby theckhd » Mon Oct 11, 2010 7:26 pm

Talent Comparison

Setup:
Talents: 5/38/10 with all relevant damage talents (see analysis)
Glyphs: CS/Jud/ShoR for Prime, AS for Major
Seal: SoT
Gear: T10 sample set


To do this analysis, we use a reduction strategy. We start with an unpossible spec that contains every relevant damage talent we have access to in all 3 trees, and record the simulated and modeled DPS output.

We then set each talent to 0 points spent one at a time and repeat the sim/model. The difference was the effect of that talent, and the difference per point is simply that value divided by the number of points we dropped.

I've done this three ways - first with the simulator, and then twice with the analytical model (see the post on the next page). The first model covers ShoR>CS>J>AS>HW, the second covers ShoR>CS>J>AS>Cons>HW (for hallowed ground handling). Note that I haven't glyphed Consecration here, but you could conceivably do so to get a 20% increase to the effect per talent point of Hallowed Ground.

Code: Select all
                           DPS per point
Talent                     Sim  Model   w/Cons
SotP                      43.4   43.4    ---
Hallowed Ground            0.0    0.0   18.0
WotL                     284.4  277.6  272.1
Reckoning                 97.8   97.8    ---
Arbiter of the Light      23.2   22.7    ---
JotP                      30.6   30.6    ---
Crusade                   76.5   74.8    ---
Rule of Law               40.5   39.5    ---
Grand Crusader            53.9   46.7    ---
Sacred Duty              287.3  283.4    ---


Image

The first thing to notice is that Sacred Duty and WotL are head and shoulders above our other talents. Those four points alone are responsible for over 1000 DPS.

The next big talent is Reckoning. Yes, I said it. Reckoning. Oh Reckoning, how we have pined for you to some day grow up and become a real, viable DPS talent. Well, the devs must have listened, because that day is now here.

Reckoning clocks in at almost 100 DPS because of the heavy reforging into mastery. This will drop down to around 40-50 DPS per point at very low mastery, but since we'll want to be nearly block-capped the larger value is more relevant.

Continuing down the line, we have Crusade clocking in at around 75 DPS per point. A far cry from the Crusade we knew and loved in Wrath, but still one of the more potent choices we have.

Then we reach a slight plateau of three talents: Grand Crusader, SotP, and Rule of Law. All three of these talents are pretty good, but Rule of Law isn't accessible to us at 80. Interestingly, GC is better than SotP by a tiny bit, and has the additional benefit of giving you an interrupt and a ranged ability that much earlier. So despite the fixed rotation that 939 has shackled us with, Grand Crusader didn't turn out to be as terrible as it could have been.

Judgements of the Pure sits somewhere in-between the Grand Crusader tier and the "Lolwut you specced that" tier. It's only worth 30 DPS per point, which for comparison is about what Reckoning was (per point, when points were "cheaper") in Wrath. JotP (and by extension AotL and HG) are probably beneath the threshold of efficiency for anything other than a pure "max DPS" spec.

Arbiter of the Light and Hallowed Ground bring up the rear. It's worth noting that Hallowed Ground is a minor DPS increase on paper, but the mana efficiency that the talent gives you could translate into a slightly better value (because you might not be able to cast consecration without it!). It's also helpful for AoE tanking, which will likely become a concern in the next few weeks.

TLDR Summary:
  • Sacred Duty and Wrath of the Lightbringer are mandatory threat talents.
  • Reckoning now kicks ass. It's Reckommended (see what I did there?)
  • Crusade is also quite potent, and worth the 3 points if you have them.
  • Grand Crusader and Seals of the Pure are about equal and "decent" choices.
  • JotP, AotL, and Hallowed Ground are all "optional" from a single-target perspective.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby tlitp » Mon Oct 11, 2010 11:39 pm

What's the rush ? Why are the ephemeral level 80 values important ? When we still have a lot of implementations/tweaks/cleanup ahead, spending time on level 80 computations is, in fact, wasting time. We've managed to port a good chunk of the 3.0 code in about 100 commits, what's the reason to divert the "war effort" ?
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby seigert » Mon Oct 11, 2010 11:44 pm

theckhd wrote:No time to make this pretty, as I need to get to bed. However, here's the talent sim output:

Code: Select all
Talent            DPS per point
JotP                      30.6
RoL                       40.5
Grand Crusader            53.9



Theckhd, could you please later simulate impact of 1/2 point GrCr and 2/3 points JotP & RoL? I'm pretty sure it's a linear function, but...

P.S.: Well, seems like i didn't saw 'DPS per point' column name...
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby daiceman » Tue Oct 12, 2010 2:32 am

I'm not sure if this belongs in here, but at level 80 at least on the ptr, you currently gain (x-66)*.25 parry rating per strength ROUNDED to the nearest integer. I find this really weird that its rounded, maybe I made some error, but equipping multiple sets of gear shows me that it is correct.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby knaughty » Tue Oct 12, 2010 3:24 am

tlitp wrote:What's the rush ? Why are the ephemeral level 80 values important ?

Because people (including me) want some sort of basis for working out how to spec tomorrow.

The numbers Theck's provided are driving my 4.0 Basic FAQ.
Last edited by knaughty on Tue Oct 12, 2010 5:24 am, edited 1 time in total.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby theckhd » Tue Oct 12, 2010 4:47 am

tlitp wrote:What's the rush ? Why are the ephemeral level 80 values important ? When we still have a lot of implementations/tweaks/cleanup ahead, spending time on level 80 computations is, in fact, wasting time. We've managed to port a good chunk of the 3.0 code in about 100 commits, what's the reason to divert the "war effort" ?


As Knaughty said, 4.0 comes out today. The deluge of PM's, whispers, and e-mails asking "What's the best X?" have already started.

That's part of the reason I was so concerned that the code was functional at 80. In some senses, it's more important than the 85 code right now, because we still have two months before anyone will actually be 85.

At this point, I'm mostly working on calc files anyway, which would be done exactly the same way for the 85 code.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby theckhd » Tue Oct 12, 2010 4:49 am

daiceman wrote:I'm not sure if this belongs in here, but at level 80 at least on the ptr, you currently gain (x-66)*.25 parry rating per strength ROUNDED to the nearest integer. I find this really weird that its rounded, maybe I made some error, but equipping multiple sets of gear shows me that it is correct.

I believe it's actually FLOOR()'ed rather than rounded. That's pretty standard though, blizzard does that a lot for things like stats, ratings, etc.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby Klaudandus » Tue Oct 12, 2010 5:00 am

The logs you were requesting have been posted. I'll try to get some on live but I don't think I'll have time before the raid, maybe till tomorrow.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby tlitp » Tue Oct 12, 2010 5:17 am

theckhd wrote:
tlitp wrote:What's the rush ? Why are the ephemeral level 80 values important ? When we still have a lot of implementations/tweaks/cleanup ahead, spending time on level 80 computations is, in fact, wasting time. We've managed to port a good chunk of the 3.0 code in about 100 commits, what's the reason to divert the "war effort" ?

As Knaughty said, 4.0 comes out today. The deluge of PM's, whispers, and e-mails asking "What's the best X?" have already started.

Ignore them.
Look, if we'd only have "aesthetic" changes at this point, it would be OK. Things like :
  • comments/wiki
  • improving layout/readability
  • cleanup

But we don't. We still have a lot of functional tasks. Few examples :
  • damage taken
  • vengeance
  • dynamic effects
  • new calcs (mind you, I'm emphasizing the implementation here, not the results)
  • checking and double-checking the input args (functions)

Finally, do remember that moving to a public repository was a decision also driven by the need to minimize the spoonfeeding. Conveniently enough, it is something that should free your schedule (as a developer). Knaughty says : "people (including me) want some sort of basis for working out how to spec tomorrow. The numbers Theck's provided are driving my 4.0 Basic FAQ". Fine. Then again, the repository is public.
People that desperately need level 80 values should simply download the source and work with it directly. Incessantly bugging Theck (one of the grand total total of 3 devs) is not helpful in any fucking way.
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Re: Theck's MATLAB thread - Cataclysm/4.x

Postby Eredor » Tue Oct 12, 2010 5:19 am

tlitp wrote:What's the rush ? Why are the ephemeral level 80 values important ? When we still have a lot of implementations/tweaks/cleanup ahead, spending time on level 80 computations is, in fact, wasting time. We've managed to port a good chunk of the 3.0 code in about 100 commits, what's the reason to divert the "war effort" ?


I'm playing 3 classes and 6 specs on a regular basis for my guild and I am rapidly panicking as I thought changes would come nearer to cataclysm.
I really don't have time to study everything for tomorrow, I just need quick summaries, such as Theck's recommended rotations and when I have more time I will study more in-depth.

I am extremely grateful to Theck and the maintankadin community for helping a lot for this 4.01, as it always did for previous iterations.
Any decency in my paladin tanking is strictly thanks to your work guys.
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