Elitist Jerks Cat DPS Rotation

 12/02/08, 11:36 PM #31 Silverstorm Piston Honda   Racionen Night Elf Druid   Azjol-Nerub 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) ----------------------- 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.
 12/03/08, 1:28 AM #32 Marauding Master Glass Joe     Viviènne Night Elf Druid   The Maelstrom (EU) As my Balance DPS only sits around 2600(Surprisingly still topping everyone else, great guild) I'm going to try Feral as soon as the servers are up to see if it increases my DPS. Because I never played Feral before, I don't have any tiered pieces so this would make a Shred build more effective, right? I'm currently planning to play the following build: Talent Calculator - World of Warcraft With 4 points left where I've got no clue where to spend them on. I'm planning to become a pure DPS kitty.
12/03/08, 9:50 AM   #33
Carlos
Piston Honda

Night Elf Druid

Eredar (EU)
 Originally Posted by Marauding Master As my Balance DPS only sits around 2600(Surprisingly still topping everyone else, great guild) I'm going to try Feral as soon as the servers are up to see if it increases my DPS. Because I never played Feral before, I don't have any tiered pieces so this would make a Shred build more effective, right? I'm currently planning to play the following build: Talent Calculator - World of Warcraft With 4 points left where I've got no clue where to spend them on. I'm planning to become a pure DPS kitty.
I usually go for this: Talent Calculator - World of Warcraft
plus NI

I don't take Master Shapeshifter because the 3 points in Nautral Shapshifter are very expensive to get those 4% crit. I will do a test run in Naxx 10 as soon as I can for this specc above and the one with Master Shapeshifter as soon as my gear has stabilized a bit.

Last edited by Carlos : 12/04/08 at 11:53 AM.

12/03/08, 10:58 AM   #34
Glass Joe

Tauren Druid

Eonar (EU)
 Originally Posted by Carlos I usually go for this: Talent Calculator - World of Warcraft plus NI
Why take Feral Instinct for PvE raiding? If you skip it you can get 4% more crit like this. 4% crit is going to do a lot more for your DPS than improved stealth.

12/03/08, 11:46 AM   #35
charriu
Piston Honda

Tauren Druid

Gorgonnash (EU)
 Originally Posted by Nadir_Eonar Why take Feral Instinct for PvE raiding? If you skip it you can get 4% more crit like this. 4% crit is going to do a lot more for your DPS than improved stealth.
Well, I always found that bear form + swipe spam is much nicer than hurricane in cat gear. So, those talent points aren't really wasted, given the amount of trash in current raids.

12/03/08, 12:23 PM   #36
Glass Joe

Tauren Druid

Eonar (EU)
 Originally Posted by charriu Well, I always found that bear form + swipe spam is much nicer than hurricane in cat gear. So, those talent points aren't really wasted, given the amount of trash in current raids.
True I guess if you are worried about trash DPS. Still i'd rather lose points in feral aggression than the 4% crit for a DPS spec myself - 4% crit is a whole lot of free crit considering how much agility is required to get 1% crit nowadays. So when swipe (cat) arrives (can't wait) I'll probably go for something like this, assuming feral instinct also buffs the catform version of swipe.

Improved FB through feral aggression is a nice talent to have on trash and when soloing but I rarely find myself able to fit Ferocious Bites in on bosses myself, and 5 talent points for a 15% buff to an infrequently used ability doesn't seem worth it when you can get 4% crit on white dps, shreds and mangles (and also theh extra crit provides synergy with Predatory Instincts and Primal Fury).

12/03/08, 5:15 PM   #37
ErrantSpark
Glass Joe

Tauren Druid

Ner'zhul
 Originally Posted by Marauding Master As my Balance DPS only sits around 2600(Surprisingly still topping everyone else, great guild) I'm going to try Feral as soon as the servers are up to see if it increases my DPS. Because I never played Feral before, I don't have any tiered pieces so this would make a Shred build more effective, right? I'm currently planning to play the following build: Talent Calculator - World of Warcraft With 4 points left where I've got no clue where to spend them on. I'm planning to become a pure DPS kitty.
With regards to spec I'd try out the one Kazanir is using (first post in the thread), and in terms of mangle v.s. shred I would start out with a mangle rotation simply because you probably won't have enough crit to keep up a steady rotation using shred. Additionally, it's a lot more difficult to keep track of things if using a shred rotation so and I think the vast majority of people will get better results using mangle as they first try feral because there is more room for error and it's actually possible to keep up a rotation with nearly 100% savage roar, rake and rip uptime.

 12/04/08, 4:25 AM #38 Fauxpаw Banned   Fauxpaw Blood Elf Paladin   No WoW Account (EU) 2Silverstorm Thank you for a very good post. But having in mind how little the difference in DPS between mangle/feral spam is, shouldn't you take finishers into account? Even if it is 17-25 points only for 4-6 minutes fight, that's up to 5 FBs (about 10k on avg each? Sorry, I am still confused with cats multipliers, given 7280 SRed AP, avg non-crit non multiplied FB is about 4200, I assume it translates into about 10k with crit bonus and 20% bonus from "something" (assuming FB always crits given 70% base crit + 43% from gear)) Thats roughly 50000 dmg over 360 seconds => about 140'extra" dps, which is roughly twice as much as the difference between shred/2t6 mangle spam. (!) (but yes, I've ignored 175 energy that one would need to 5xFB as well that the fact that it would be quite hard to perfectly time FBs, but it still shows that finishers shouldn't be ignored in calculations)
 12/04/08, 9:39 AM #39 Monedula Piston Honda     Monedula Tauren Druid   Defias Brotherhood (EU) I also wondered about the use of mangle vs shred. I did some calculations on the shred vs mangle per energypoint story depending on some AP I guess I have; I did not calculate in the 2t6 part because, 1 I don't have that in feral, 2 WotLK gear is better and if not at this point it will be finally replaced. ```White hits of 594: Shred: ((594 * 2.25) + 742) * 1.3 * 1.2 = 3242 / 42 = 77.1 = 100% Mangle ((594 * 2) + 634) * 1.2 = 2186.4 / 34 = 64.3 = 83%``` ```Somewhat raidbuffed; white hits of 875: Shred: ((875 * 2.25) + 742) * 1.3 * 1.2 = 4228.8 / 42 = 100.6 = 100% Mangle: ((875 * 2) + 634) * 1.2 = 2860.8 / 34 = 84.1 = 83.6%``` Conclusion: it looks like shred and mangle scale about the same way. However this doesn't mean shred is the best option by definition. This is because the use of mangle generates more CP per energy, thus making Mangle better then DPE values state. I think somewhere (don't have the time to look it up) there are calculations on how many actions are needed depending on crit percentage. Then there should be some kind of calculation what that means for druids, how much more damage... Instead of spending a lot of thinking and calculation on what the perfect rotation would be, I agree with a previous post saying we should not talk about rotation but of appropriate use of abilities at the best time. I don't know how it is for others but I at least have had some periods when I lacked energy and some periods (berserk, tigers fury) when I had too much energy. I would suggest the following use of mangle/shred: Berserk: Shred only! Tigers fury: Shred, but use mangle if you are about to replace both savage fury and rip soon. Tigers fury's 30 second cooldown fits nicely with savage roar's 34 second duration. Use that to your advantage (if the fight allows it). All of the other time: Mangle.  Counting in cooldowns, refresh time and stuff I did some calculations on energy availability. Having 2t7 and glyph of Rip your rip lasts 19 seconds. (though it seems 20 seconds effectively). so every 34 second cycle (SR length) you will get: ```34/2 x 20 = 340 energy 60 * 34/30 = 68 energy (Tigers Fury) = 408 energy. During that time you need to (assuming 30% crit on bosses): keep rake up: 34/9 * 40 = 151 energy (3.8 hits * 1.3 = 4.9 CP) do 1 savage roar: 25 energy (-5 CP) Keep rake up: 34/20 * 30 = 51 energy (-5 * 34/20 = -8.5 CP) Total energy consumed: 227 Combopoints consumed: 8.6 Within this timeframe you have the choice to mangle/shred. Energy left over: 408 - 227 = 181 Combopoints needed: 8.6 (30% crit): 8.6/1.3 = 6.6 hits Energy available per hit: 27.3``` That is less then mangle and shred costs. So if it was a steady flat fight mangle would still be the best option (not counting berserk). Lets do a slightly different calculation: Using SR at less combo points: 3 CP sR = 24 seconds so every 24 second cycle (SR length) you will get: ```24/2 x 20 = 240 energy 60 * 24/30 = 48 energy (Tigers Fury) = 288 energy. During that time you need to (assuming 30% crit on bosses): keep rake up: 24/9 * 40 = 106.7 energy (2.7 hits * 1.3 = 3.5 CP) do 1 savage roar: 25 energy (-5 CP) Keep rake up: 24/20 * 30 = 31.1 energy (-5 * 24/20 = -6 CP) Total energy consumed: 162.8 Combopoints consumed: 7.5 Within this timeframe you have the choice to mangle/shred. Energy left over: 288 - 162.8 = 125.2 Combopoints needed: 7.5 (30% crit): 7.5/1.3 = 5.7 hits Energy available per hit: 21.7``` So the 5CP use of SR is preferred always. In some circumstances like Malygos this does of course not apply. Malygos is not in melee range long enough for a 5 CP SR to run out. Better to use a shorter one. For instance: Hit > SR, Hit till 5 points > Rip, 1 hit > SR Hit till 5 points and rip again if possible. Meanwhile using your Tigers Fury asap. Thus the statement above is not changed: Only shred when you have way too much energy (Berserk and Omen of Clarity proc or a miscalculated tigers Fury). Last edited by Monedula : 12/05/08 at 4:48 AM. Reason: Energy availablity taken into the picture
 12/04/08, 1:12 PM #40 HengeMaker Glass Joe   HengeMaker Night Elf Druid   Skullcrusher Sorry if this is something that's common knowledge, I just came back to WoW after a 3 or 4 month hiatus. I noticed that the mangle tooltip no longer says that it gives a 30% bonus to shred(just bleeds). Is this a misprint? I notice people in this thread keep using the 1.3 multiplier in their calculations.
 12/04/08, 1:23 PM #41 Pharmacon Von Kaiser   Pharmacon Undead Rogue   Scilla Shred Changed due to Trauma being the same debuff as Mangle/Mangle Last edited by Pharmacon : 12/04/08 at 1:24 PM. Reason: mislink
 12/04/08, 4:57 PM #42 Syra Glass Joe   Northfist Blood Elf Death Knight   Bleeding Hollow I'm not 80 yet so keep that in mind. I also started my druid a month ago so I have zero raid gear, I'm in all northrend blues and greens. That said, I'm specced for tanking, because I want that experience while leveling up. However, occasionally I go to an instance in a dps role. I found my cat dps was pretty gimpy compared to other classes with all the AOE talents. Not to mention, trash mobs die in seconds, so rip is a waste. I decided cat dps wasn't enough and experimented with the following approach: Pounce > Shred > TF > Shred > Mangle > FB > Bear > Enrage > Maul(w/glyph) > Swipe > Swipe, throw in a maul when you've got the energy for it. Rinse and repeat for the next pull. Throw in a bash for a caster. My DPS went up and my overall damage output moved me up to place number 2 on the meters.
12/04/08, 5:31 PM   #43
Silverstorm
Piston Honda

Night Elf Druid

Azjol-Nerub
Clarifying FB damage from excess energy

 Originally Posted by Fauxpаw 2Silverstorm Thank you for a very good post. But having in mind how little the difference in DPS between mangle/feral spam is, shouldn't you take finishers into account? Even if it is 17-25 points only for 4-6 minutes fight, that's up to 5 FBs (about 10k on avg each? Sorry, I am still confused with cats multipliers, given 7280 SRed AP, avg non-crit non multiplied FB is about 4200, I assume it translates into about 10k with crit bonus and 20% bonus from "something" (assuming FB always crits given 70% base crit + 43% from gear)) Thats roughly 50000 dmg over 360 seconds => about 140'extra" dps, which is roughly twice as much as the difference between shred/2t6 mangle spam. (!) (but yes, I've ignored 175 energy that one would need to 5xFB as well that the fact that it would be quite hard to perfectly time FBs, but it still shows that finishers shouldn't be ignored in calculations)
You're correct that you have enough CP for 3-5 FB. However, as you mentioned, you wouldn't have the energy for both FB and keeping Rip and SR rolling. The main problem with my theoretical stuff is actually having the CP ready at the right times for SR and Rip. I haven't had a chance to play with actual possible rotations, but given the 16s of Rip and 34s of SR, you wind up having to refresh both at about the same time. Spacing them further apart means you either overwrite Rip ticks, or can't apply due to a "stronger effect" on the target. Neither are optimal for DPS.

The other issue (energy) forces you to ignore finishers like FB. The only time the ability actually maximizes DPE (and thus DPS indirectly) is when used at exactly 35 energy (or less with OoC proc). The additional damage added by excess energy lowers the efficiency of FB. The base damage for a 35 energy FB is 0.35*AP + 1640 (average). For 5200 AP (ignoring all multipliers for now), that's 3460 or nearly 100 DPE. For 36 energy, you add (36-35)*(9.4 + AP/410), which is 22.1 DPE. The additional damage from excess energy is purely linear, so you start lowering the ~100 DPE with every additional point of energy you have. All that said, if I did the math right, specced FB (5/5 Feral Aggression + Rend/Tear) surpasses a Glyphed Rip in DPE at about 16.5k AP if you have 43% crit (possibly attainable in T8/T9?). Without the Rip Glyph, FB surpasses at roughly 4k AP, which is easily attainable in Northrend greens once you get Savage Roar.

Calcs:

Rip: (0.3*AP+3204)*1.3*1.1
GRip: (0.3*AP+3204)*1.3*1.1*(16/12) (extended duration)
FB: (0.35*AP+1640)*1.15*1.1*(1+0.5+0.43) (0.5 from Rend/Tear assuming a bleeding target, 0.43 from crit percentage)

Adding the 2t7 bonus, FB doesn't pass a Glyphed/2t7 Rip in DPE until past 30k AP if you have 43% crit. The [almost] exact number is 38686.7, which we might see someday.

12/04/08, 5:38 PM   #44
Baggles
Von Kaiser

Night Elf Druid

Hyjal
 Originally Posted by Syra I'm not 80 yet so keep that in mind. I also started my druid a month ago so I have zero raid gear, I'm in all northrend blues and greens. That said, I'm specced for tanking, because I want that experience while leveling up. However, occasionally I go to an instance in a dps role. I found my cat dps was pretty gimpy compared to other classes with all the AOE talents. Not to mention, trash mobs die in seconds, so rip is a waste. I decided cat dps wasn't enough and experimented with the following approach: Pounce > Shred > TF > Shred > Mangle > FB > Bear > Enrage > Maul(w/glyph) > Swipe > Swipe, throw in a maul when you've got the energy for it. Rinse and repeat for the next pull. Throw in a bash for a caster. My DPS went up and my overall damage output moved me up to place number 2 on the meters.
I really have no idea why you would ever shred prior to using mangle. Moreover, you'd probably get a lot more out of using pounce -> SR -> rake -> mangle -> TF -> shred. Not for nothing, but there's so much information across a multitude of cat dps threads, I'm pretty sure there's no more groundbreaking rotations to discover.

12/04/08, 5:47 PM   #45
Baggles
Von Kaiser

Night Elf Druid

Hyjal
 Originally Posted by Silverstorm You're correct that you have enough CP for 3-5 FB. However, as you mentioned, you wouldn't have the energy for both FB and keeping Rip and SR rolling. The main problem with my theoretical stuff is actually having the CP ready at the right times for SR and Rip. I haven't had a chance to play with actual possible rotations, but given the 16s of Rip and 34s of SR, you wind up having to refresh both at about the same time. Spacing them further apart means you either overwrite Rip ticks, or can't apply due to a "stronger effect" on the target. Neither are optimal for DPS.
While this is accurate, I find that it's not necessarily bad for a dps rotation to just use SR when it's down. For example, if you roar at 1 or 2 cp at the beginning of a cycle, rip at 5 cp, at ~48%ish crit, you should be able to reapply a roar at ~2-3 cp. Going from there, generally I find I'm able to work it into a cycle where I'm simply keeping roar, rake, a 5-pt rip, and still able to bite in-between. The problem is that it is absolutely not static and requires what amounts to total concentration (look out for void zones lolz). Still, having topped meters in a very competitive guild, it does appear to be the best cycle I can muster.

 Elitist Jerks Cat DPS Rotation