My druid (see signature) is leveling up right now, and while I got to raid a little bit at 70, I didn't get into T6 instances, therefore I don't have 2t6 available unless I drag some people back through BT or Hyjal or Sunwell. I've watched the Shred/Mangle debate, so I decided to try some math and figure out what the deal is. Here's what I did (note, this is theory, I haven't figured out if there's an actual rotation that makes this work):
- Assume Rake (9 seconds), Glyphed Rip (no T7, 16 seconds), 5p SR (34 seconds), 3/3 King of the Jungle with Tiger's Fury used on cooldown. Assume Ferocity, Shredding Attacks, Improved Mangle, Predatory Instincts (standard cat DPS talents)
- For Shred calculation, assume Glyphed Mangle (18 seconds)
- Energy regen is 10 energy/second. Tiger's Fury adds 2 energy/second.
- Calculate minimum time required to finish all cycles at the same time, using Least Common Multiple
- Determine the inflow and outflow of Energy/second (since we're energy bound)
- Assume 6% proc rate on Omen of Clarity on white attacks, and assume those are all Shreds (or Mangles). Wowhead comments indicate OoC procs only on white attacks.
- Compute damage done by all attacks in terms of DPS
Step 1 is pretty self explanatory. I intend to run the numbers with T7 as well, but I want to make sure my methods are sound first.
Step 2 is another assumption, but a fair one, I think.
Step 3 is basic game mechanics. I know the Tiger's Fury adds 60 energy all at once, but this doesn't alter the average energy flows because we're already energy bound. 60 energy at once shouldn't waste any energy once we get into steady state of attacking.
Step 4
Rake = 9 seconds = 3^2
Glyphed Rip = 16 seconds = 2^4
Savage Roar = 34 seconds = 2 * 17
Glyphed Mangle = 18 seconds = 2 * 3^2
LCM = 2^4 * 3^2 * 17 = 2448
Keep in mind, that's nearly 41 minutes.
Step 5
Rake = -35 energy / 9 seconds = -3.889 e/s
Rip = -30 energy / 16 seconds = -1.875 e/s
Savage Roar = -25 energy / 34 seconds = -0.735 e/s
Improved Mangle = -34 energy / 18 seconds = -1.889 e/s
Shred = -42 energy / x seconds = y e/s
White Attack = 10 energy / 1 second = 10 e/s (natural regen)
Tiger's Fury = 60 energy / 30 seconds = 2 e/s (talented regen)
Y is relatively simple to find due to the law of conservation of energy. Energy in + energy out = 0 e/s. Therefore,
Y = -3.612 e/s.
As a result,
X = -42 / -3.612 = 11.628 seconds per shred due to the energy requirements of debuff maintenance.
Step 6
2448 white attacks at 6% proc rate gives about 146.9 OoC procs. This adds 2/3 more Shreds, since these would occur every 16.667 seconds.
Step 7
Damage calculations assume Ferocity, Naturalist, Savage Fury, Mangle debuff (self-applied), Predatory Instincts, and Rend and Tear.
AP and Crit are the variables used below. AP includes Savage Roar, Crit include Predatory Instincts. Rip calculation is extended to 16 seconds by scaling the damage up from 6 ticks to 8 ticks, assuming same tick strength for all 8 ticks.
Rake = ((AP/100+190)*(1+Crit)+(0.18*AP+1161)*Mangle)*Naturalist*SavageFury
Rip = (0.05*AP+534)*6*Mangle*Naturalist*(16/12)
Mangle = (AP/14*2+638)*(1+Crit)*Naturalist*SavageFury
White = AP/14*(1+Crit)
Shred = (AP/14*2.25+742.5)*(1+Crit)*Mangle*Naturalist*RendTear
Plugging in base AP of 5200 and Crit of 43%, Savage Roar and Predatory Instincts give 7280 AP and 47.3% extra damage on crits. I think 5200 was a reasonable AP from a high-end T6, and I chose 43% crit to minimize excess combo points. Anything higher built up CP faster than energy was available to use them. I'm not sure if a Ferocious Bite just before a Tiger's Fury would be possible, since the calculations I did were based on zero net energy.
Rake = 4751.9 / 9 = 528.0 DPS
Rip = 10273.1 / 16 = 642.1
Mangle = 3262.6 / 18 = 181.3
White = 766.0 / 1 = 766.0
Shred = 4834.2 / 11.628 = 415.7
Shred = 4834.2 / 16.667 = 290.0 (Omen of Clarity procs)
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Total = 2823.1
When I repeat steps 5-7 for Mangle (29 and 34 energy), the results indicate Shred is still better DPS (for this combination of AP/crit at least). Once my calculations are checked over, I plan to run a quick program to compute for a variety of AP/crit combos.
Here's the Mangle steps:
Step 5 (Mangle)
Rake = -35 energy / 9 seconds = -3.889 e/s
Rip = -30 energy / 16 seconds = -1.875 e/s
Savage Roar = -25 energy / 34 seconds = -0.735 e/s
Improved Mangle = -34 energy / x1 seconds = y e/s
Improved Mangle = -29 energy / x2 seconds = y e/s
White Attack = 10 energy / 1 second = 10 e/s (natural regen)
Tiger's Fury = 60 energy / 30 seconds = 2 e/s (talented regen)
Y is relatively simple to find due to the law of conservation of energy. Energy in + energy out = 0 e/s. Therefore,
Y1 = -5.501 e/s.
As a result,
X1 = -34 / -5.501 = 6.181 seconds per mangle due to the energy requirements of debuff maintenance.
As a result,
X2 = -29 / -5.501 = 5.272 seconds per mangle due to the energy requirements of debuff maintenance.
Step 6 (Mangle)
2448 white attacks at 6% proc rate gives about 146.9 OoC procs. This adds 1/3 more Shreds, since these would occur every 16.667 seconds.
Step 7 (Mangle)
Damage calculations assume Ferocity, Naturalist, Savage Fury, Mangle debuff (self-applied), Predatory Instincts, and Rend and Tear.
AP and Crit are the variables used below. AP includes Savage Roar, Crit include Predatory Instincts. Rip calculation is extended to 16 seconds by scaling the damage up from 6 ticks to 8 ticks, assuming same tick strength for all 8 ticks.
Rake = ((AP/100+190)*(1+Crit)+(0.18*AP+1161)*Mangle)*Naturalist*SavageFury
Rip = (0.05*AP+534)*6*Mangle*Naturalist*(16/12)
Mangle = (AP/14*2+638)*(1+Crit)*Naturalist*SavageFury
White = AP/14*(1+Crit)
Plugging in base AP of 5200 and Crit of 43%, Savage Roar and Predatory Instincts give 7280 AP and 47.3% extra damage on crits. I think 5200 was a reasonable AP from a high-end T6, and I chose 43% crit to minimize excess combo points (and it's easy to confirm identical formulas between Shred/Mangle sheets). Anything higher built up CP faster than energy was available to use them. I'm not sure if a Ferocious Bite just before a Tiger's Fury would be possible, since the calculations I did were based on zero net energy.
Rake = 4751.9 / 9 = 528.0 DPS
Rip = 10273.1 / 16 = 642.1
White = 766.0 / 1 = 766.0
Mangle = 3262.6 / 6.181 = 527.9
Mangle = 3262.6 / 16.667 = 195.8 (Omen of Clarity procs)
-----------------------
Total = 2659.6
Or, for 2t6 + Imp:
Rake = 4751.9 / 9 = 528.0 DPS
Rip = 10273.1 / 16 = 642.1
White = 766.0 / 1 = 766.0
Mangle = 3262.6 / 5.272 = 618.9
Mangle = 3262.6 / 16.667 = 195.8 (Omen of Clarity procs)
-----------------------
Total = 2750.6
I should mention that 43% base crit (47.3% with PI) leaves 0.031 CP/second with Imp Mangle and 0.072 CP/second with 2t6/Imp Mangle. That turns into 75.4 and 176 extra combo points over the course of ~41 minutes. For a reasonable 4-6 minute fight, this is only 7-10 or 17-25 CP depending on presence of 2t6.
Results
Mangle (Imp): 2659.6
Mange (2t6/Imp): 2750.6
Shred: 2823.1
Since Shred scales marginally better than Mangle, I believe it would continue to outperform Mangle.
Increasing Base AP to 7800 gives this:
Mangle (Imp): 3529.8
Mangle (2t6/Imp): 3649.0
Shred: 3741.0
These results extend the gap between each combination, which indicates a somewhat linear relationship based on AP. More crit just means extra CP, or perhaps more timely CP, since none of this includes the actual ability rotation that makes this possible.
Comments?
I'm fairly new to the cat DPS world, so I'd appreciate if those more experienced and knowledgeable would review the above calculations. I hope it's straightforward to follow, if not, I'll be happy to clarify anything.