Math by Murmurs

Enjoy the math! Don't read when half awake, you may hurt yourself! (all math done by murmurs)

There have been a lot of whining lately over the changes that Balance Druids have seen, in this thread, I am going to present the math related to all of those concerns. I am doing this in a separate thread in order to keep the main post less cluttered and shorter. If you have questions concerning the validity of the math, please post them here and I will do my best to address them. If you have questions or comments about the general conclusion of the topic, then please post them in the other thread. I will do my best to monitor both.

2T9/T8 compared to 4T9.

It was requested that I do these comparisons based on actual gearing numbers and not based upon theoretical values that these gearing sets might have. I agree that this is an important factor, and so I went and built item sets for each one. Each set will use no item with a higher ilevel than 245 though some of which might be from ToGC 10. I did my best to find as optimal a gear set up for each one as a possibly could, but I won't say that they are exactly perfect. For instance, I know that both are slightly over the hit cap. I did try and switch one of the Hit items and gem for Hit instead, but I found that the overall loss of stats seen by doing this simply wasn't worth it. In general, the set would gain far less Haste than it would lose in Crit to do this while Spell Power would remain approximately unchanged. The professions I used were Enchanting and Inscription. They are arguably not the best, but all professions are approximately the same in value, and these are easy to configure. For gemming, I ignored socket bonuses if I felt they weren't an on-par gain, I only used 2 Purple gems for the Meta and choose the best socket bonus for doing so. I also chose to gem yellow sockets for SP/Crit, you could argue for SP/Haste, but that's a different topic really, and since both are pretty much the same in terms of yellow gems, it doesn't really matter.

Again, please note, I am not saying that these are BiS lists for these gear sets, you can argue different gearing set ups for lots of things, but these are really good ones.

Also note, WoWhead automatically calculates the gains from talents such as Improved Moonkin Form, so the only difference in stats from those talents is due to raid buffs which alter stats. I will also be using ToW values even those Demonic Pact is actually better, this is because it is a set value and not a theoretical one that could be different. Oh, and since Intellect does increase Crit values, I added in 1% Crit to adjust the values for raid buffs which increase Intellect, the actual value is just slightly over that, since the 0.XX% additional Crit won't effect scaling too much, I don't care to figure out the exact value.

Glyphs will be the standard Starfire, Moonfire, Insect Swarm.

2T9/T8 Gearing
http://www.wowhead.com/?profile=18655158

Stats once raid buffed:
Intellect: 1386
Spirit: 648
Spell Power: 3428
Crit: 44.68 (47.68 for Starfire, 54.68 for Moonfire)
Haste: 14.52% (Raid buffs effecting Haste are embedded into the calculations. Celestial Focus removed from base value displayed as it is not additive(Stupid WoWhead))

Insect Swarm:
(215 + (3428 * 0.2)) * (1.03) * (1.04) * (1.13) * (1.03) * (1.3) = 1459.69301 per tick

(1.5 / 1.11400) / (1 + (14.52 / 100)) = 1.1757

Moonfire: Direct Damage ignored due to insignificance
(200 + (3428 * .13)) * (1.85) * (1.03) * (1.04) * (1.13) * (1.03) * (1 + ((.5468 * 1.09) * 1)) = 2376.75569 per tick

(1.5 / 1.11400) / (1 + (14.52 / 100)) = 1.1757

Wrath (nonEclipse):
(592 + (3428 * .671)) * 1.1 * 1.03 * 1.04 * (1 + ((.4468 * 1.09) * 1)) * 1.13 * 1.03 * 1.03 = 6075.15181

((1.5 / 1.114) / ((1 + (14.52 / 100))) = 1.1757

(1 -(1-.4468)^3)) = 0.830704071

(1 * 0.8307) + (1.1757 * 0.1693) = 1.0297

Wrath (Eclipse):
(592 + (3428 * .671)) * 1.55 * 1.03 * 1.04 * (1 + ((.4468 * 1.09) * 1)) * 1.13 * 1.03 * 1.03 = 8560.44119

Starfire (nonEclipse):
(1130 + (3428 * 1.2)) * 1.1 * 1.03 * 1.04 * (1 + ((.4768 * 1.09) * 1)) * 1.13 * 1.03 = 10928.7317

((3 / 1.114) / ((1 + (14.52 / 100))) / (1 + (.2 * (1 -(1-.4768)^2)) = 2.0533

Starfire(Eclipse):
(1130 + (3428 * 1.2)) * 1.1 * 1.03 * 1.04 * (1 + ((.9268 * 1.09) * 1)) * 1.13 * 1.03 = 14456.073

((3 / 1.114) / ((1 + (14.52 / 100))) / (1 + (.2 * (1 -(1-.9268)^2)) = 1.9613

Each Wrath cast has a 26.808% chance to proc Eclipse. On average, it should take 5 Wrath casts to proc Eclipse. An additional Wrath cast is added for reaction time. Lunar Eclipse lasts for 13.9703 and allows for 7 Starfire casts. Insect Swarm will not be refreshed during Lunar Eclipse, Moonfire will unless there is minimal time remaining. On average, it should take 3 Starfire casts to proc Eclipse. An additional Stafire cast is added for reaction time. Solar Eclipse lasts for 13.0404 seconds and allows for 12 Wrath casts. Insect Swarm and Moonfire will be refreshed during Solar Eclipse.

IS - 14 (IS)
MF - 12.8243 (IS) 15 (MF)
Wrathx6 - 6.6461 (IS) 8.8218 (MF)
Starfire(E)x7 - Both DoTs drop (IS half way, MF during last SF cast.)
IS - 14
MF - 12.8243 (IS) 15( MF)
Starfirex3 - 6.6644 (IS) 17.8401(MF)
Wrath(E)x6 - 11.6619 (MF) 6.8622 (E)
IS - 10.4862 (MF) 5.6865(E)
Wrath(E)x5 - 8.8515 (IS) 5.3377 (MF)
Wrathx6
Starfire(E) x2

Normally I would have ended the rotation after the last Wrathx6 to proc Eclipse since this should represent when the damage gained from Eclipse has balanced back to the standard average, but adding in the last two Starfires would allow for IS to fall off while Moonfire fell off just after the last Wrath cast. In total, the rotation has 2 Insect Swarms, 2 Moonfires, 12 Wraths, 11 Wraths(E), 3 Starfires, and 9 Starfires(E) and takes 52.1975 seconds to complete.

(1459.69301 * 14) + (2376.75569 * 16) + (6075.15181 * 12) + (8560.44119 * 11) + (10928.7317 * 3) + (14456.073 * 9) = 388421.32

388421.32 / 52.1975 = 7441.37784 DPS

4T9 Gearing:
http://www.wowhead.com/?profile=18671025

Stats once raid buffed:
Intellect: 1430
Spirit: 645
Spell Power: 3505
Crit: 45.66 (48.66 for Starfire, 55.66 for Moonfire)
Haste: 14.39% (Raid buffs effecting Haste are embedded into the calculations. Celestial Focus removed from base value displayed as it is not additive(Stupid WoWhead))

Insect Swarm
(215 + (3505 * 0.2)) * (1.03) * (1.04) * (1.13) * (1.03) * (1.3) = 1484.65333 per tick

(1.5 / 1.11400) / (1 + (14.39 / 100)) = 1.1771

Moonfire
(200 + (3505 * .13)) * (1.85) * (1.03) * (1.04) * (1.13) * (1.03) * (1 + ((.5566 * 1.09) * 1)) = 2429.75899

(1.5 / 1.11400) / (1 + (14.39 / 100)) = 1.1771

Wrath (nonEclipse):
(592 + (3505 * .671)) * 1.14 * 1.03 * 1.04 * (1 + ((.4566 * 1.09) * 1)) * 1.13 * 1.03 * 1.03 = 6454.5774

((1.5 / 1.114) / ((1 + (14.39 / 100))) = 1.1771

(1 -(1-.4566)^3)) = 0.839542913

(1 * 0.8395) + (1.1771 * 0.1605) = 1.0284

Wrath (Eclipse):
(592 + (3505 * .671)) * 1.44 * 1.03 * 1.04 * (1 + ((.4566 * 1.09) * 1)) * 1.13 * 1.03 * 1.03 = 8153.1504

Starfire (nonEclipse):
(1130 + (3505 * 1.2)) * 1.14 * 1.03 * 1.04 * (1 + ((.4866 * 1.09) * 1)) * 1.13 * 1.03 = 11606.7374

((3 / 1.114) / ((1 + (14.39 / 100))) / (1 + (.2 * (1 -(1-.4866)^2)) = 2.0519

Starfire (Eclipse):
(1130 + (3505 * 1.2)) * 1.14 * 1.03 * 1.04 * (1 + ((.7866 * 1.09) * 1)) * 1.13 * 1.03 = 14086.7544

((3 / 1.114) / ((1 + (14.39 / 100))) / (1 + (.2 * (1 -(1-.7866)^2)) = 1.9768

Each Wrath cast has a 27.40% chance to proc Eclipse. On average, it should take 5 Wrath's to proc Eclipse. An additional Wrath cast is added for reaction time. Lunar Eclipse lasts for 13.9716 and allows for 7 Starfire casts. Insect Swarm will not be refreshed during Lunar Eclipse, Moonfire will unless there is minimal time remaining. On average, it should take 3 Starfire casts to proc Eclipse. An additional Stafire cast is added for reaction time. Solar Eclipse lasts for 13.0404 seconds and allows for 12 Wrath casts. Insect Swarm and Moonfire will be refreshed during Solar Eclipse.

IS - 14 (IS)
MF - 12.8243 (IS) 15 (MF)
Wrathx6 - 6.6461 (IS) 8.8218 (MF)
Starfire(E)x7 - Both DoTs drop (IS half way, MF during last SF cast.)
IS - 14
MF - 12.8243 (IS) 15( MF)
Starfirex3 - 6.6644 (IS) 17.8401(MF)
Wrath(E)x6 - 11.6619 (MF) 6.8622 (E)
IS - 10.4862 (MF) 5.6865(E)
Wrath(E)x5 - 8.8515 (IS) 5.3377 (MF)
Wrathx6
Starfire(E) x2

Although there are slight cast time differences between the two sets, none of them were significant enough to alter the rotation. In total the rotation has 2 Insect Swarms, 2 Moonfires, 12 Wraths, 11 Wraths(E), 3 Starfires, and 9 Starfires(E) and takes 52.3085 seconds to complete.

(14 * 1484.65333) + (16 * 2429.75899) + (12 * 6454.5774) + (11 * 8153.1504) + (3 * 11606.7374) + (9 * 14086.7544) = 388401.875

388401.875 / 52.3085 = 7425.21531

2T9/T8
7441.37784 DPS

4T9
7425.21531


The Change to Eclipse

Eclipse has recently been buffed to 40% increases instead of 30%. Since we will now be using 4T9 without question due to the 2T8 nerf, here is how this change would impact the DPS of the above T9 rotation

Wrath (Eclipse):
(592 + (3505 * .671)) * 1.54 * 1.03 * 1.04 * (1 + ((.4566 * 1.09) * 1)) * 1.13 * 1.03 * 1.03 = 8719.3414

Starfire (Eclipse):
(1130 + (3505 * 1.2)) * 1.14 * 1.03 * 1.04 * (1 + ((.8866 * 1.09) * 1)) * 1.13 * 1.03 = 14913.4267

((3 / 1.114) / ((1 + (14.39 / 100))) / (1 + (.2 * (1 -(1-.8866)^2)) = 1.9660

The slight reduction in Starfire's cast time would reduce the total time of the rotation by 0.0756 seconds, not really significant, but it shouldn't have been expected to be, but still a slight change. This brings the total time down to 52.2329

(14 * 1484.65333) + (16 * 2429.75899) + (12 * 6454.5774) + (11 * 8719.3414) + (3 * 11606.7374) + (9 * 14913.4267) = 402070.027

402070.027 / 52.2329 = 7697.63936

7697.63936 - 7425.21531 = 272.42405

(272.42405 / 7425.21531) * 100 = 3.6689% gain