Weapon Specialization (de)Mystified

Over the past few weeks/months/years of rogue forum trolling at work, the question of how Fist/Dagger weapon specialization works have never been directed answered, documented, or even tested, despite the well known fact that Mace/Sword spec will work only if you ahve mace/sword equipped even in offhand only.

IMHO, the source of the confusion in Fist/Dagger spec is that, paperdoll's crit rate will increase by 5% if and only if you have the respective weapon equipped in Main-hand. Paperdoll crit rate will not receive the benefit of Fist/Dagger Spec if you only equip the respective weapon in Off-hand. Thus the 2 school of thoughts.

1. Fist/Dagger Spec will be in effect as long as you equip the respective MH, and OH will receive the benefit of +5% crit rate disregarding of the weapon type. e.g., Dagger Spec rogue with dagger in MH but sword in OH, should receive the same +5% crit chance increase for its OH sword.
   
2. Fist/Dagger Spec weapon spec will be in effect if and only if the respective weapon type is equipped, similar to Mace/Sword Spec.

My intuitation has always points to #1 as it is easier for the programmers to code the actual weapon spec mechanics, but I have not conduct any test to verify until today. In the past weekend of grinding Consortium rep (finally exalted btw), I have use recap to collect some sets of data from about 1000 melee swings with different weapons equipped.

The data collection is done using 13/41/7 combat daggers spec, with Dagger Specialization.

Set 1: Whispering Blades of Slaying (dagger) + Stormreaver Warblade (fist)

Set 2: Reflex Blade (fist) + Warp Splinter's Thorn (dagger)

My preliminary conclusion from the test data coheres to #2 argument, which argues for that fist/dagger specialization will be in effect as long as the respective weapon is equipped, ignoring actual paper doll crit rate.

I am at work right now, but the recorded numbers are at home. I will try to make an update soon.

Patch 2.0: Combat Potency

Combat Potency is a 35 points combat talent that gives, at 5/5, 20% chance to regen 15 energy on successful OH attacks. It is quite easy to model the amount of energy regen.

Energy Regen as a function of Weapon Speed and Mitigation, without any speed mods.
ER (S, M)
= (1/S) * (1 - M) * 20% * 15
= 3 * (1-M) / S

Grahpically depict, ER (S, M) looks like:
To maximize ER, take partial derivative on S:
d ER / d S = -3 * (1 - M) / S^2

No minimum or maximum function can be obtained as this is an negative squared function, but the graph indicates that any weapon speed 2.0 or under offers higher marginal value than those with speed 2.0 or above. Doubling OH weapon speed will reduce the rate of energy regen by 50%.

Combat potency has proc quite often during PvE fights with my 1.8 speed Anbisath Warhammer, and I would have to adjust/micro manage my PvE cycles because of the energy regen. Instead of a steady 5/5 SnD cycles, I could actually throw in a few cp worth of rupture when I got lucky on procs.

In summary:

• ER (S, M) = 3 * (1-M) / S, without any speed mods such as BF/SnD. To factor BF into account, multiply everything by 1.2; SnD, 1.3; both, 1.5.
  
• Combat potency benefits much more from fast OH weapons than slow ones.

P.S. I am currently working through a backlog of emails, and I will be updating/reviewing every post to fix errors and fit them for expansion.

Patch 2.0: Day 1, Blade Twisting

Patch 2.0 finally arrived yesterday and I log on right after getting home from work. The spec of choice is 10/41/0 Combat Mace stun/daze build. I have tried 41/3/7 mutilate build on test servers for couple of hours, but I figures that its time for me to change. I have been in the various SF builds for majority of my time in WoW, or at least 100 days out of the 130 days played, including new and old builds like 30/0/21, 30/8/12, 31/8/12, 30/20, 31/15/5. Misplaced Servo Arm remains to be the weapon of choice as it is currently the second hardest hitting SS weapon besides Gressil. Despite I have access to Kingsfall but the chance of me getting it before expansion is very slim. :(

The focus of the build is to annoy the shit out of people in PvP with Mace Spec Stun (5% chance) and Blade Twisting (20% chance) while maintain a certain degrees of PvE/farming viability with Combat Potency (20% chance to gain 15 energy per OH attack). I also want to investigate what weapon skills have become after the nerf with my decent +8 mace skills (5 from mace spec, 3 from Anubisath).

Here's some thoughts:

Blade Twisting - 20% chance per SS/BS/Shiv/Gouge to daze target for 8 seconds; targets will have a daze debuff when it procs. Sounds perfect on paper but it doesnt deliever. Assumes all SS lands, it should proc:

(SS / 40 energy) * (20 energy / 2 second) * (60 second / minute) * (1 proc / 5 SS) = 3 ppm.

Compare to my Crusader MH (1 ppm):

(1 proc / min) * (min / 60 sec) * (2.8 sec / swing) * (swing / 0.80 hit) = 5.8% proc / hit

which translate into (0.058 * (60/4 + 60/(2.8/0.8))) = 1.86 ppm.

Compare to Mace Spec stun (5% proc/hit)
(5% proc/hit ) * (2.8/0.8 + 1.8/0.8 + 4 hit/s) * (60s / m) = 2.94 ppm

So theoritically, Blade Twisting should proc as much as Mace Spec and a lot more than Crusader. However, from 4 hours of PvP and PvE, it's proc rate is definitely less than either of them. The problem with it is it proc only off special attacks, which has a 4 second cooldown, so the larger interval offsets some of the proc chances.

So in summary:

• With 2.8s MH, 1.8s OH, SS, +5% hit, Blade Twisting will proc roughly 3.00 ppm, compare to Crusader's of 1.86 ppm and Mace Spec Stun of 2.94ppm.
• Despite similar theoratical proc rates to Mace Spec, Blade Twisting will proc less than Mace Spec and even Crusader due to the large time intervals between special attacks (4 second cooldown for SS, 6 second cooldown for BS).
• My feeling is that Blade Twisting procs less than Crusader after 4 hours of PvP/PvE.
• Blade Twisting needs to be buffed, to roughly 30% proc chance to offset the large time interval between specials.

EDIT: Oh and btw, the Crit Scaling post is still TBC...

BC Talent Preview: Surprise Attacks

Suprise Attacks
Requires 1 point in Adrenaline Rush
Requires 40 points in Combat Talents
Your Sinister Strike, Backstab, and Gouge can no longer be dodged.

Melee attack ruleset explained here
Energy regen explained here

Assuming a typical melee attack table of a well equiped rogue and a backstab damage of B. Energy loss for miss/dodge/parried backstab is 11.

00-04 Dodge (5%)
05-09 Parry (5%)
10-44 Crit (35%)
45-99 Hit (55%)

Damage WITHOUT Surprise Attacks

Total damage = 1.355B
Total Energy Cost = 55.1
Total CP gain (without SF) = 0.9

DPE = 0.0246B
CP per Energy = 0.01633

With Surprise Attacks, it effectively move Dodge out of the melee roll table, so now the table will look like:

00-04 Parry (5%)
05-39 Crit (35%)
40-99 Hit (60%)

Damage WITH Surprise Attacks

Total damage = 1.405B
Total Energy Cost = 57.55
Total CP gain (without SF) = 0.95

DPE = 0.0244 B
CP per Energy = 0.01652

Surprise Attacks thus in decrease your DPE by 0.8% and increase your CPE by 1.1%. The slight decrease in DPE will be offset by the slight increase in CPE. In other words, your white DPS will be flat.

The only time it will be useful is when you are fighting at the Crit cap. Consider an target with 90% dodge (a rogue with evasion).

Before -> Target
00-04 Dodge (5%) -> 00-89 Dodge (90%)
05-09 Parry (5%) -> 90-94 Parry (5%)
10-44 Crit (35%) -> 95-99 Crit (5%)
45-99 Hit (55%) -> 99-99 Hit (0%)

Your Crit is capped by the high dodge andd parry of your target. Now if we are to remove dodge from the table, it will look like:

00-89 Dodge (90%) -> 00-00 Dodge (0%)
90-94 Parry (5%) -> 00-04 Parry (5%)
95-99 Crit (5%) -> 05-39 Crit (35%)
99-99 Hit (0%) -> 40-99 Hit (60%)

Surprise Attacks will be extremely benefitial at this situation.


To find out for how much dodge, crit, etc will Surprise Attacks actually increase DPS, we have to solve some fucking nasty equation:

Assuming special attack damage of SAD, crit rate of C, dodge rate of D, parry rate of P, miss rate of M.

No SA:
Crit damage = MIN [(100 - M - D - P), C] * 2.3 SAD
Non Crit damage = MAX [(100 - M - D - P - C), 0] * SAD
Energy Cost = 100 * 60 + (M+D+P)*11

SA:
Crit damage = MIN [(100 - M - P), C] * 2.3 SAD
Non Crit damage = MAX [(100 - M - P - C), 0] * SAD
Energy Cost = 100 * 60 + (M+P) * 11

DPE WITH SA > DPE WITHOUT SA
(MIN [(100 - M - D - P), C] * 2.3+ MAX [(100 - M - D - P - C), 0] ) / [100 * 60 + (M+D+P) * 11] > (MIN [(100 - M - P), C] * 2.3 + MAX [(100 - M - P - C), 0] ) / [100 * 60 + (M+P) * 11]

Yay for a massive 4 variable inequality equation. Take out block and parry if you believe Blizzard fixed the bloc/parry from behind bug.

Simplifying by assuming you won't miss or parry:
(MIN [(100 - D), C] * 2.3+ MAX [(100 - D - C), 0] ) / [100 * 60 + 11D] > (MIN [100, C] * 2.3 + MAX [(100 - C), 0] ) / (100 * 60)
(MIN [(100 - D), C] * 2.3+ MAX [(100 - D - C), 0] ) > (2.3C + 100 - C) / (6000) * (6000 + 11D)
(MIN [(100 - D), C] * 2.3+ MAX [(100 - D - C), 0] ) > (1.3C + 100) * (6000+ 11D) / (6000)

(MIN [(100 - D), C] * 2.3+ MAX [(100 - D - C), 0] ) > 1.3C + 100 + 14.3CD/6000 + 1100D/6000

Alright. I gave up here. Something is wrong here. There is no way in hell for me to crunch through this and I probably made thousands of errors up to this point, but if anyone could please plot this simple 2D piece of shit on Excel or Matlab, I would helluva appreciate it.

EDIT: fucking bloggers killed my work, but I have simplified the equation into 3 cases and done some math.

Summary:
SA will increase your DPS only at the shaded region of the below graph, with Dodge being the y-axis and Crit being the x-axis. The boundry condition will be dodge + crit = 100. What does it all mean? SA is FUCKING USELESS under most conditions.
EDIT 2: Disregard the above graph. Somehow my brute force calculation is just a brain fart. Need to do something on Excel once I figure out how do. The equations are true.

More to come: BC Talent Preview: Mutilate

New Combat Dagger Build

Taken directly from an email conversation:

If you want to own DM up, the most important thing, beside l2p, is spec all the high DPS buffing talents. So lets look at the DPS gained from the arguable talents (raid buffed DPS, using Tier 3 gears. Numbers roughly got from Chalon's current DPS calculators):

Adreline Rush (Direct-scaling):
Assuming you are doing 1400 expected/average backstabs, AR is 150 energy, or 150 / 60 * 1400 = 3500 damage, over 300 seconds, or a mere 11.7 DPS per talent point.

Murder (Direct-caling):
Assuming you are doing 750 DPS, murder adds straight 15 DPS when it applies, or 7.5 DPS per talent point.

Ruthlessness (Semi-scaling):
Assuming you are using SnD only, every 30 seconds, the actual CP/s = 0.6 / 30 = 0.02 CP/s
SnD DPS is around 110 of the overall 750 DPS, so each CP is worth 110/5 * 30s = 22 DPS/CP * 30s = 660 D/CP

0.02 CP/s * 660 D/CP = 13.2 DPS, or 4.4 DPS per talent point

Relentless Strikes (Direct-scaling):
Assuming you are using SnD only, every 30 seconds, so its an extra 25 energy every 30 seconds.

25/60 * 1400 = 583 damage, over 30 seconds = 19.4 DPS per talent point

Lethality (Semi-scaling):
Assuming 40% Crit, and Backstab DPS assumed to be 233. Working backwards, Backstab DPS is 122 ( 0.3 * 122 + 0.7 * 122 * 2.3 = 233).

So Lethality = 122 * 0.3 = 36.6 DPS per 5 talent points, or 7.3 DPS per talent point

Improved Poison (Non-scaling):
Assuming no VP, 15% Hit, 2.0 speed MH and OH, Backstabbing rogue.
20% * 130 * (90% * 1 + 95% / 4) = 29.575 ~ 30 DPS per 20% proc rate.

30 DPS per 20% proc rate => 3 DPS per 2% proc rate, or 3 DPS per talent point

Conclusion:

1. (Assasination Tier 2) 3/3 SnD is absolutely needed for combat daggers. Murder produces better DPS/talent point compare to Ruthlessness, so 2/2 Murder.
2. (Assasination Tier 3) Lethality is 7.3 DPS per talent point vs. Relentless Strikes' 19.4 DPS per talent point. 1/1 Relentless Strikes + 4/5 Lethality.
3. (Assasination Tier 3, Combat Tier 7) AR is 11.7 DPS/talent point, but would require 3 talent points investment (2 fillers), so its actually 11.7 DPS/ 3 talent points. The other choice is 1/5 Lethality @ 7.3 DPS + 2/3 Ruthlessness @ 4.4 DPS each, netting you 16.1 DPS/ 3 talent points.

The resulted build is:
http://www.worldofwarcraft.com/info/classes/rogues2/talents.html?005223105000000005325000055010020005000000000000000

Overall efficiency: 2/2 Imp SS, 3/3 Imp Gouge, 2/2 Imp Sprint as fillers (total of 7). The rest are all DPS producing talents, vs. 15/31/5 build with total of 9 fillers.

Hope this helps. Feel free to correct my errors.

More on Sword Spec Modeling

There has been some discussion and validation of Sword Specialization mechanics on the Rogue forum recently, and the results are exactly the same as I stated in both 3/2/06 and 3/3/06 post.

1. Sword Spec proc off only swords.
   
2. OH sword spec proc triggers an instant extra MH attack.
3. Special attacks triggers an instant extra MH attack.
4. Sword spec proc is an normal mainhand attack and will cancel attack-in-motion and resets your MH attack timer.
5. Sword spec will NOT proc off enchant/weapon/poison procs.

There are 3 cases that will trigger a sword spec proc: 1. MH normal attack 2. OH normal attack 3. Special attack. And it will be the determining factor in modeling sword spec proc dps.

Case 1: MH normal attacks

MH attack triggers another instant normal attack from sword spec. No swing timer is "wasted" as the sword spec proc is instant. Thus you gain 100% of the damage.

Effective MH sword spec proc damage = 100% * MH damage.

Case 2: OH normal attacks

OH attack triggers an instant MH normal attack.

t=0: Attack initialized. Both MH and OH swing at the same time.
t=OH_Speed: OH attacks. Procs sword spec. MH attacks instantly and resets the swing timer.

Thus, swing timers will reset to initial engagement state everytime OH attack procs sword spec, with the wasted MH swing time equal to OH speed.

Effective OH sword spec proc damage = [1 - (OH Speed/MH Speed)] * MH damage

Yes, your OH sword spec proc will do less effective damage, as the only "time"/"damage" you gain is the part you get for free but not yet swung. i.e. MH speed minus OH speed.

Case 3: Special attacks

Similar to OH proc modeling, assuming you aint doing anything stupid like SnD/Evis/Rupture.

Effective MH sword spec proc damage = [1 - (MH Speed/4)] * MH damage

Example:

2.8 Speed MH, 1.8 Speed OH.

MH Sword Spec Proc = 100% of MH damage
OH sword spec proc = 36% of MH damage
Special sword spec proc = 30% of MH damage

The overall sword spec proc effective damage (weighted average) will be 54%.

I Slap Myself in the Fase. 1% Chance to Gain Extra Attack = 1.5% Hit

I retract my eariler statement that +2% Hit and +2% Chance for an Extra Attack have no material differences after some discussion with Pj. We have come to an agreement that 3% Hit = 2% Chance to Gain Extra Attacks. This is some logic flaw on my part. My apologies.

So 5/5 Sword Spec is effectively 6.5% Hit. HoJ is effectively 3% Hit + 20 AP.

My 03.03.06 post regarding my calculation assumptions still holds true, except flawed logic in interpreting the results.

On a side note, grats to my guild Eminence on Twin Emp kill. Gate opened 02/27/06. Twin Emperor down on 03/03/06. Good progress. Now where the fuck is me on the group shot. :S

My Excel Calculator v0.4.3 is well in progress. Now I just have to make the Data Table work so they display the correct value. > <

HoJ/Sword Spec Procs? Pfft. Get +Hit

First of all, I've shown a 0.5% increase in DPS from 2% hit to 2% for an extra attack. That's far from 50% improvement from the comment.

1. 2.4 MH and OH Speed Assumption I assumed 2.4 speed for both MH and OH. Most MH sword speed ranges from 2.6 to 2.9. There are only 4 epic sword that has speed less than 2.4: Blackguard(craftable), Ravencrest's Legacy(AQ Gate Quest), Maladath, Runed Blade of the Black Flight(BWL), Warblade of the Hakkari(ZG). Most uses Brutality Blade(MC) for OH. 2.4 speed for both hands is a fairly reasonable assumption.
   
2. Sword Spec or HoJ procs are additive and will slightly decrease total number of MH attacks as they cancel out attack-in-motion. And although you gain more chance to proc extra MH attacks through HoJ/Sword Spec, but you also have less chance to miss on BOTH your MH and OH attacks for +2% Hit.
3. Aggression won't change the results. Extra 6% damage on SS does not have anything to do with extra MH attacks gained through +Hit or +Chance to attack.
4. Slice and Dice won't change the results either as it benefit both the same way. Neither will Blade Flurry skew the results.
   
5. Duel Wield spec will only reinforce my argument further. OH DPS weights 75% instead of 50% of the white DPS, thus the damage from MH extra procs will be reduced as a % of overall damage.

Extremely minor details I should say.

+2% Chance for an Extra Attack Has No Material Benefit Over +2% Hit

Known Facts:
HoJ procs off both special attacks and normal attacks.
HoJ can proc on another HoJ proc.
HoJ proc triggers an extra Main Hand attack.

Now assume a normal 5% hit 30% crit rogue (20% miss rate on normal attacks, 0% miss rate on special attacks) SS spamming over the course of 100 seconds using two 2.4 speed weapons. Further assume 250 non-crit white attacks and 318 non-crit SS for simplicity.

Default:
Total # of white attacks = (2*100/2.4)*(100%-20%) = 66.7
Damage from white attacks = 66.7 * (250+250*0.5) /2 * 1.3 = 16,258
Total # of SS = 25
Damage from SS = 25 * 318 * (0.7+0.3*2.3) =11,051
Total # of attacks = 91.7
Damage Total = 27,309

2% Hit:
Total # of white attacks = (2*100/2.4)*(100%-20%+2%) = 68.3
Damage from white attacks = 68.3 * (250+250*0.5)/2 * 1.3 = 16,648
Total # of SS = 25
Damage from SS = 25 * 318 * (0.7+0.3*2.3) =11,051
Total # of attacks = 93.3, or 1.74% more attacks than the original.
Damage Total = 27,699, or 1.43% improvement over the original.

2% Chance for an Extra Attack:
Total # of white attacks = (2*100/2.4)*(100%-20%) *1.02 + 25 * 0.02 = 68.5
Damage from white attacks = 16,258 + (68-66.7+25*0.02)*250*1.3 + = 16,843
Total # of SS = 25
Damage from SS = 25 * 318 * (0.7+0.3*2.3) =11,051
Total # of attacks = 93.5, or 1.96% more than the original, or 0.2% over +2% Hit.
Damage Total = 27,894, or 2.14% improvement over the original, or 0.7% over +2% Hit.

I have ignored proc on proc since those have very marginal benefit (2% for proc, 2.04% for proc on proc, 2.0408% for proc on proc on proc, etc).

Conclusion:

• Is +2% chance for an extra attack better than +2% hit? Yes.
• Is the difference significant? No, unless you consider 0.2%/0.7% more swings/damage material.
• For modeling purposes, it's easier to proximate +2% chance for an extra attack to +2%