Going Arcane, Part 3 - Spell Rotations

by Tachyon on Fri. 20. February 2009, 00:22

Filed under: arcane, spec, raiding, dps, patch, theorycrafting

UPDATE FOR 3.2.2:
For an updated spell rotation analysis for patch 3.2.2+ see 3.2.2 Arcane Mage Changes or Tachyon's Arcane Mage Guide for 3.2.2.
In part 2 of this series, we introduced the theorycrafting basics to calculate the average DPS for the single target arcane spells, as well as the DPM. Now let's look into possible spell rotations.

The arcane spec allows to dynamically tweak the DPS/DPM depending on how many subsequent Arcane Blasts are cast.

The Arcane Blast debuff

Remember that Arcane Blast applies a stackable debuff (up to 3 times), which increases the damage of the next arcane spell by 15% (18% with the Arcane Blast glyph) per stack, but also increases the mana cost of the next Arcane Blast by 200%.
Casting Arcane Missiles or Arcane Barrage will consume that buff and thus reset the stack. Note also that those spells will profit from the increased damage, but will not get a mana penalty.
  • Arcane Blast, 1 stack: increases damage by 18%, next AB costs 3x its base mana
  • Arcane Blast, 2 stacks: increases damage by 36%, next AB costs 5x its base mana
  • Arcane Blast, 3 stacks: increases damage by 54%, next AB costs 7x its base mana

Being to lazy to do all the calculations in a spreadsheet, I wrote a small simulation program in Java instead. Here's the outcome:

DPS/DPM for arcane cast sequences
RotationDamageTimeDPSManaDPMMana/sec
ABx14968.0002.1552305.150245.00020.280113.680
ABx210830.0004.3102512.560980.00011.050227.360
ABx317586.0006.4662719.9702205.0007.980341.040
ABx425236.0008.6212927.3803920.0006.440454.720
ABx532886.00010.7763051.8205635.0005.840522.928
ABx1071136.00021.5523300.71014210.0005.010659.344
ABx100000764994636.000215517.2413549.580171497060.0004.460795.746
ABx0, ABarr3762.0001.2932909.280553.0006.800427.653
ABx1, ABarr9407.0003.4482728.030798.00011.790231.420
ABx2, ABarr15946.0005.6032845.7501533.00010.400273.582
ABx3, ABarr23379.0007.7593013.2902758.0008.480355.476
ABx4, ABarr31029.0009.9143129.8804473.0006.940451.190
ABx5, ABarr38679.00012.0693204.8306188.0006.250512.720
ABx0, Mbarr8812.0002.1554088.770952.0009.260441.728
ABx1, Mbarr15367.0004.3103565.1401197.00012.840277.704
ABx2, Mbarr22815.0006.4663528.7201932.00011.810298.816
ABx3, Mbarr31157.0008.6213614.2103157.0009.870366.212
ABx4, Mbarr38807.00010.7763601.2904872.0007.970452.122
ABx5, Mbarr46457.00012.9313592.6706587.0007.050509.395
ABx0, AM8812.0004.3102044.380952.0009.260220.864
ABx1, AM15367.0006.4662376.7601197.00012.840185.136
ABx2, AM22815.0008.6212646.5401932.00011.810224.112
ABx3, AM31157.00010.7762891.3703157.0009.870292.970
ABx4, AM38807.00012.9313001.0704872.0007.970376.768
ABx5, AM46457.00015.0863079.4406587.0007.050436.624

(AB = Arcane Blast, ABxN = N subsequent AB casts (max. 3 stacks), ABarr = Arcane Barrage, AM = Arcane Missiles, MBarr = AM cast on Missile Barrage)

A first approach towards a new cast sequence

According to these results, you get the highest DPS cycle when using Missile Barrage procs as early as possible. Arcane Missiles however should never be cast without Missile Barrage procs, the DPS is just not competitive without it.

So my first approach (RotationTachyon)was following:
  • Cast AM when MBarr procs, no mater how many stacks of AB you have
  • Otherwise cast AB, stack maximally to 3, then use ABarr if MBarr didn't proc
Running the simulation with this rotation (1'000'000 spells cast) resulted in:
RotationTachyon: 3279.46 DPS, 9.58 DPM

Then I wanted to compare this to the classic rotation:
  • Cast AB until you have 3 stacks
  • Cast AM if MBarr procced, otherwise cast ABarr
RotationClassic: 3351.04 DPS, 9.27 DPM

To my surprise, the classic rotation still had slightly more DPS. This is confusing, as the rotation involved less MBarr procs than the first rotation. I'd have expected to see higher DPS when using more of the high DPS sequences, but obviously that was not the case. To explain this effect, it's crucial to know how to calculate the DPS/DPM of mixed rotations.

Spell rotation: DPS/DPM of mixed cast sequences

The best cast sequence above, ABx0,Mbarr is only sustained for a very short time, so it contributes less to the overall DPS than other rotations which have a longer run time.

The total DPS contribution of a cast sequence is therefore to be weighted by the length of the sequence, the DPS during that lenght, and the probability you are casting it.
DPS := sum(DPS[i]*t[i]*p[i]) / sum(t[i]*p[i])
where DPS[i] is the DPS of Sequencei, t[i] is the cast time of Sequencei, and p is the probability (or percentage of times) we use Sequencei.

To determine the probabilities, the simulation comes to aid again. Results:
RotationTachyon:
ABx3, ABarr 46.5139%
ABx1, MBarr 18.0682%
ABx2, MBarr 14.4659%
ABx3, MBarr 11.6308%
ABx0, MBarr 9.3213%
RotationClassic:
ABx3, MBarr: 53.5976%
ABx3, ABarr: 46.4024%
The calculated weighted DPS matches the results of the simulated DPS, so you can take that formula along with the probabilities as given fact for your own theorycrafting calculations.

In conclusion, the best approach is to use the longest cast sequences that give you good DPS without wasting too much mana, as they often contribute more to the effective DPS than short cast sequences with slightly higher DPS.

Generic pattern of arcane rotations

Basically, every arcane rotation follows the same pattern:
  • If Missile Barrage procced, use it after at least A subsequent Arcane Blast casts
  • If Missile Barrage didn't proc after B subsequent Arcane Blast casts, cast Arcane Barrage instead

There are two paramenters in there, A and B. My suggested rotation was A=0,B=3, while the classic rotation is A=3,B=3.

Using the simulation, I calculated the DPS and DPM for the configurations A=0..6, B=0..6, and here's the result:

.A=0A=1A=2A=3A=4A=5
B=0 3204 DPS
7.43 DPM		 3171 DPS
8.62 DPM		 3219 DPS
8.86 DPM		 3312 DPS
8.44 DPM		 3343 DPS
7.55 DPM		 3366 DPS
6.98 DPM
B=1 3028 DPS
11.66 DPM		3029 DPS
12.21 DPM		3095 DPS
11.8 DPM		3196 DPS
10.56 DPM		 3238 DPS
8.99 DPM		 3271 DPS
8.06 DPM
B=2 3136 DPS
10.93 DPM		3132 DPS
11.23 DPM		3165 DPS
11.09 DPM		3262 DPS
10.08 DPM		 3296 DPS
8.67 DPM		 3321 DPS
7.84 DPM
B=3 3278 DPS
9.58 DPM		 3272 DPS
9.75 DPM		3286 DPS
9.78 DPM		3351 DPS
9.27 DPM		 3374 DPS
8.13 DPM		 3394 DPS
7.43 DPM
B=43371 DPS
8.36 DPM		 3363 DPS
8.47 DPM		3370 DPS
8.56 DPM		3417 DPS
8.34 DPM		 3432 DPS
7.6 DPM		 3445 DPS
7.02 DPM
B=5 3428 DPS
7.78 DPM		 3422 DPS
7.85 DPM		3425 DPS
7.96 DPM		3462 DPS
7.83 DPM		 3470 DPS
7.27 DPM		 3479 DPS
6.82 DPM
B=6 3467 DPS
7.44 DPM		 3462 DPS
7.49 DPM		 3462 DPS
7.59 DPM		3493 DPS
7.52 DPM		 3498 DPS
7.07 DPM		 3503 DPS
6.68 DPM
B=7 3493 DPS
7.22 DPM		 3489 DPS
7.26 DPM		 3488 DPS
7.36 DPM		3516 DPS
7.32 DPM		 3518 DPS
6.92 DPM		 3521 DPS
6.58 DPM
B=8 3513 DPS
7.08 DPM		 3510 DPS
7.1 DPM		 3508 DPS
7.21 DPM		3532 DPS
7.17 DPM		 3534 DPS
6.83 DPM		 3535 DPS
6.51 DPM
B=9 3527 DPS
6.97 DPM		 3525 DPS
6.99 DPM		 3521 DPS
7.08 DPM		3545 DPS
7.06 DPM		3546 DPS
6.76 DPM		3546 DPS
6.46 DPM

In the table above, I grayed out every rotation for which there is a better (more DPS and more DPM) alternative rotation in the table. The remaining rotations have either better DPS or better DPM than any other rotation in the table.

To put the result in a more relative context, let's take the classic rotation (A=3, B=3) as a base (100%) and compare the relative differences:

.A=0A=1A=2A=3A=4A=5
B=0 -4.4% DPS
-19.8% DPM		 -5.4% DPS
-7.0% DPM		 -3.9% DPS
-4.4% DPM		 -1.2% DPS
-9.0% DPM		 -0.2% DPS
-18.6% DPM		 +0.5% DPS
-24.7% DPM
B=1 -9.6% DPS
+25.8% DPM		 -9.6% DPS
+31.7% DPM		 -7.6% DPS
+27.3% DPM		 -4.6% DPS
+13.9% DPM		 -3.3% DPS
-3.0% DPM		 -2.4% DPS
-13.1% DPM
B=2 -6.4% DPS
+17.9% DPM		 -6.5% DPS
+21.1% DPM		 -5.5% DPS
+19.6% DPM		 -2.6% DPS
+8.7% DPM		 -1.6% DPS
-6.5% DPM		 -0.9% DPS
-15.4% DPM
B=3 -2.2% DPS
+3.3% DPM		 -2.4% DPS
+5.2% DPM		 -1.9% DPS
+5.5% DPM		+0.0% DPS
+0.0% DPM		 +0.7% DPS
-12.3% DPM		 +1.3% DPS
-19.8% DPM
B=4 +0.6% DPS
-9.8% DPM		 +0.4% DPS
-8.6% DPM		 +0.6% DPS
-7.7% DPM		 +2.0% DPS
-10.0% DPM		 +2.4% DPS
-18.0% DPM		 +2.8% DPS
-24.3% DPM
B=5 +2.3% DPS
-16.1% DPM		 +2.1% DPS
-15.3% DPM		 +2.2% DPS
-14.1% DPM		 +3.3% DPS
-15.5% DPM		 +3.6% DPS
-21.6% DPM		 +3.8% DPS
-26.4% DPM
B=6 +3.5% DPS
-19.7% DPM		 +3.3% DPS
-19.2% DPM		 +3.3% DPS
-18.1% DPM		 +4.3% DPS
-18.9% DPM		 +4.4% DPS
-23.7% DPM		 +4.5% DPS
-27.9% DPM
B=7 +4.3% DPS
-22.1% DPM		 +4.1% DPS
-21.7% DPM		 +4.1% DPS
-20.6% DPM		 +5.0% DPS
-21.0% DPM		 +5.0% DPS
-25.4% DPM		 +5.1% DPS
-29.0% DPM
B=8 +4.9% DPS
-23.6% DPM		 +4.8% DPS
-23.4% DPM		 +4.7% DPS
-22.2% DPM		 +5.4% DPS
-22.7% DPM		 +5.5% DPS
-26.3% DPM		 +5.5% DPS
-29.8% DPM
B=9 +5.3% DPS
-24.8% DPM		 +5.2% DPS
-24.6% DPM		 +5.1% DPS
-23.6% DPM		 +5.8% DPS
-23.8% DPM		 +5.8% DPS
-27.1% DPM		 +5.8% DPS
-30.3% DPM

Again, the grayed out rotations are to be avoided since there is a better alternative rotation with higher DPS and DPM.
The blue colored rotations are the ones with higher DPS, and the green colored rotations have a higher DPM ratio that the classic rotation. The red ones have less DPS and less DPM, so they should be avoided at any cost.

As a comparison, that's what you get with chain-spamming Arcane Blasts: 3549.58 DPS, 4.46 DPM.


Looks like the optimal path is to use the Missile Barrage proc only with the maximum Arcane Blast (3) stack, and to cast at least one Arcane Blast before using Arcane Barrage. The more subsequent Arcane Blast casts you can afford to wait hoping for a Missile Barrage proc, the higher the DPS, but the lower the DPM.
This path is always efficient, because there is no other alternative path that would yield more DPS for a higher DPM ratio.

So here's my recommended rotation:

DPS/Burst:
  • If Missile Barrage procced, use it only with a full Arcane Blast (3) stack
  • Otherwise keep casting Arcane Blast, hoping for a Missile Barrage proc. Use Arcane Barrage to reset your stack as soon as you think you're using too much mana.
DPM/Recovering:
  • If Missile Barrage procced, use it not before having stacked the Arcane Blast debuff to 2-3
  • Cast no more than 3 subsequent Arcane Blasts. Reset the stack with Arcane Barrage if Missile Barrage don't procs.
That's all folks, I hope my calculations aren't too far off, and remember that your mileage may vary, as always

LXj wrote:

posted on Wed. 25. February 2009, 16:47

Seems like B above 6 or 7 gets too much diminishing returns. And A>3 can be just dismissed by definition.

But I can't understand why do you suggest A=3 B=3 as a DPM rotation. A=1 B=1 clearly has 30% more DPM, right? Why not to use it as a recovery rotation?

I would say A=3 B=3 is a "balanced" rotation, and A=1 B=1 is a "recovery" rotation

zupa wrote:

posted on Thu. 09. April 2009, 03:37

Awesome series of posts, thanks!

I think it's about time to try an arcane spec, and these articles have all the info I could want,

Cheers,

spocket wrote:

posted on Thu. 09. April 2009, 21:48

Very nice write up. Easier to understand than some of the previous things I have read.

Metsanielle wrote:

posted on Tue. 14. April 2009, 18:37

Amazing analysis. I've been playing a mage religiously for almost 4 years. So I feel like I know the class pretty well. I was somewhat intuitively performing your recommendation before having read it. Good to know I haven't been wasting my mana.

Kiku wrote:

posted on Thu. 30. April 2009, 10:20

Interesting numbers but you lack the solid testing put into the spec on elitist jerks. Primarily in the form of abx3am yields better results in real world raiding situations, especially with the longer fights in ulduar the dps vs dpm trade off is marginal and helps alot.

Tachyon wrote:

posted on Thu. 30. April 2009, 15:42

@Kiku:

I just run the simulation for ABx3AM (or ABx3(ABarr|AM)):
ABx3AM: 3204.46 DPS, 9.87 DPM

That's less DPS than the 'classic' rotation (3351 DPS, 9.27 DPM), but has a little better DPM ratio.

But in this theorycrafting scenario, it's clearly subpar to the A=3, B=2 recovery rotation, which has both better DPS and DPM:
A=3, B=2: 3262 DPS, 10.08 DPM
Hence I sincerely doubt that ABx3AM should be used ever.

For completeness, here are the simulated numbers:
Classic (A=3,B=3):
3350.62 DPS
9.27 DPM
ABx3, MBarr 53.5256%
ABx3, ABarr 46.4744%

Tachyon A=3,B=2:
3260.37 DPS
10.08 DPM
ABx2, ABarr 56.7647%
ABx3, MBarr 43.2353%

ABx3AM:
3204.26 DPS
9.87 DPM
ABx3, AM 51.1756%
ABx3, MBarr 48.8244%[/code]

Kiku wrote:

posted on Fri. 01. May 2009, 04:59

again you are only looking at numbers and not real world raiding. good luck with arcane and ulduar trying that.

Tachyon wrote:

posted on Wed. 06. May 2009, 14:08

Kiku, I can't really see you point. Yes I'm raiding with the rotations I suggested, and the A=3,B=2 rotation serves very well as a recovery rotation.

If you think my observations are plain rubbish to use in 'real world raiding' (apart from the fact that there's no such thing, and all effects in the game can well be simulated), then please tell where you think my assumptions are wrong.
Just pointing to Elitist Jerks and reciting their 'we need to ABx3AM all day' psalm doesn't help much.

Yes I read the Arcane thread there, especially p.81/82 where my article was mentioned, and the user mentioning it getting a short forum ban. That's just silly, EJ never even considered the A=3,B=2 rotation, but that's their problem not mine

Zpyrox wrote:

posted on Sat. 23. May 2009, 09:40

Your critical analysis is astounding ! you really manage to simplify and break down the arcane spec and rotations for mages i thank you and keep it going !!!

Iambuckets wrote:

posted on Sat. 06. June 2009, 18:43

Nice work, Tachyon. Thanks for doing all this research.

Dave wrote:

posted on Wed. 17. June 2009, 09:37

Great information, what is the mod you are using for showing the buffs and targets ?

thanks

Tachyon wrote:

posted on Wed. 17. June 2009, 11:21

The addon which shows the buffs/debuffs around my unit frames is called TellMeWhen. I wrote about it in another article: blogArticle.do?action=view&id=21889024

Ravcik wrote:

posted on Fri. 03. July 2009, 12:17

Hello, i saw your UI on thr raid movie, can you tell me what addons you have installed ??

Pellex/Hyjal wrote:

posted on Mon. 20. July 2009, 18:52

I'm a little confused by this bit:

Basically, every arcane rotation follows the same pattern:

* If Missile Barrage procced, use it after at least A subsequent Arcane Blast casts
* If Missile Barrage didn't proc after B subsequent Arcane Blast casts, cast Arcane Barrage instead

I'm not sure of the meaning of "subsequent." Do you mean "subsequent to the time when Arcane Blast is fully charged"? I.e., if A=3 and B=2, does that mean that in a typical rotation, you'd cast 6 and 5 Arcane blasts, respectively?

To put it another way, in a typical rotation, how many times do you cast Arcane Blast before you give up on the Missile Barrage and cast Arcane Barrage instead?

Tachyon wrote:

posted on Tue. 21. July 2009, 14:45

I'm not sure of the meaning of "subsequent.

n subsequent Arcane Blast means n Arcane Blasts in a row (n=3: AB, AB, AB)

I generally use A=3, B=3 (cast 3x AB, then MBarr if it procced, else ABarr).
That's two cycles: AB/AB/AB/MBarr or AB/AB/AB/ABarr.

My mana saving cycle is A=3, B=2 (cast 2x AB, when MBarr didn't proc: ABarr, else another AB and then MBarr).
Thats also two cycles: AB/AB/ABarr or AB/AB/AB/MBarr.

On burst phases (e.g. during Arcane Power and Icy Veins), I use A=3, B=4 (cast 3xAB, then MBarr if it procced, otherwise cast anther AB, then MBarr if it procced, else cast ABarr).
That's three cycles: AB/AB/AB/MBarr or AB/AB/AB/AB/Mbarr or AB/AB/AB/AB/ABarr.

Madameastra wrote:

posted on Tue. 21. July 2009, 15:22

I love to reasearch my class and with the many hours i spend doing so i has been frustrating at times. I come here and evrything I need is alrdy done here. YOU ARE A GOD AMONGST MERE MORTALS !!!

Pachuk wrote:

posted on Thu. 13. August 2009, 21:04

Here is a macro I use with the Burst Phase you mention.

/cast Icy Veins
/cast Arcane Power
/use Living Flame (Or any other trinket you have with an "Use" abiity to increase your spellpower)
/cast Mirror Image
/use Mana Gem (the one at lvl 80)
/use Potion Of Wild Magic or /use Potion of Speed

by using this macro + Burning Phase A=3, B=4 in a BG you will confuse your enemies and burn them really fast.

by using this macro + Burning Phase A=3, B=4 + Raid Buffs + Totems + another trinket buff like Dying Curse or maybe a tailor emboid + Heroism + maybe another source of power like Rune of Power from Iron Council in ulduar (just to mention one), you will become GOD! believe me!

Enjoy the real meaning of power...

Dmzor wrote:

posted on Fri. 06. November 2009, 01:48

This guide is awesome, Just one question with regards to fights when you have to move around and dont have time to stack AB 4 times then AM your face off. Atm im just improvising rotations it seems to effect overall damage done quite abit is theyre anything you could suggest to help with this or is it the same for all ?