Math for deciding whether to cast Earth Shock 6 seconds before Flame Shock falls off to avoid wasting Fulmination procs or clip Flame Shock.
TL;DR: don't clip Flame Shock, it's not worth it.
Situation: You already have some Lightning Shield charges (LScharges), your Shock cooldown is free, and you have some time (not more than 6 seconds) Flame Shock dot remaining (dotrem). You have two choices: (1) cast Earth Shock, letting Flame Shock fall of for a small amount of time (0-6 seconds), but not wasting any Rolling Thunder procs, or (2) cast Flame Shock, losing some ticks of the old dot, maybe wasting some Rolling Thunder procs but keeping Flame Shock running.
I'm using my gear for reference here (4079 spell damage, 36,76% haste, 44,03% crit, 30% overload chance)
(1) cast Earth Shock, letting FS drop (if dotrem < 6 seconds), not wasting any Rolling Thunder charges
You gain:
Earth Shock: 3475 (2348 * (1 + 1.09) * crit))
Fulmination: 2211 * max(0,(LScharges - 3)) [max(0,(LScharges - 3)) * 1491 * (1 + 1.09 * crit)]
Flame Shock is still ticking for dotrem seconds:
Flame Shock dot for dotrem seconds: 547 * dotrem [0.46 * dotrem * 803 * (1 + 1.09 * crit)]
Number of ticks: dotrem / time_between_ticks = dotrem / (3 / (1 + haste)) = dotrem * (1 + haste) / 3 = 0.46 * dotrem
After that, we have 6 sec - gcd = 4.90sec left of the Shock cooldown in which we can cast other spells. You only have dotrem seconds left of your Flame Shock dot.
If you are somewhere in your rotation, there's a chance of (dotrem - lvb_cast) / 8 that Lava Burst will come off cooldown naturally and can be finished casting while Flame Shock is still ticking. There's also a 20% chance for every Flame Shock tick to reset the Lava Burst cooldown, but if the last tick resets Lava Burst, we can't finish casting before the Flame Shock dot falls off. So we get another 0.2 * (0.46 * dotrem - 1) = (9.2% * dotrem - 20%) chance that we can finish casting Lava Burst before the Flame Shock dot falls of.
So on average, we will cast 0.22 * dotrem - 0.34 Lava Bursts before the next Shock comes off cooldown.
You gain:
Lava Burst: 3508 * dotrem - 5422 [(0.22 * dotrem - 0.34) * 13017 * (1 + 0.75 * overload)]
These Lava Bursts took 0.22 * dotrem - 0.34 * 1.1 = 0.24 * dotrem - 0.37 seconds, so we are left with 4.9 - (0.24 * dotrem - 0.37) = 5.27 - 0.24 * dotrem seconds until the next Shock comes off cooldown. In this time we will cast on average 5.27 - (0.24 * dotrem) / 1.46 = 3.61 - 0.16 * dotrem Lightning Bolts and gain 2.166 - 0.1 * dotrem Lightning Shield charges.
You gain:
Lightning Bolt: 28247 - 1251 * dotrem [(3.61 - 0.16 * dotrem) * 4316 * (1 + 0.75 * overload) * (1 + 1.09 * crit)]
You have also gained an average of 2.166 - 0.1 * dotrem Lightning Shield charges, worth 4789 - 221 * dotrem [(2.166 - 0.1 * dotrem) * 1494 * (1 + 1.09 * crit)] of damage on the next Earth Shock
After all that, Shocks come off cooldown and we can cast Flame Shock.
You gain:
Flame Shock direct damage: 2221 [1501 * (1 + 1.09 * crit)]
Assuming you have 6 seconds left on your Flame Shock, you would finish with 4.57 Lightning Shield charges and deal
3475 + 2211 * max(0,(LScharges - 3)) + 547 * 6 + 3508 * 6 - 5422 + 28247 - 1251 * 6 + 4789 - 221 * 6 + 2221 = 48808 + 2211 * max(0,(LScharges - 3)) damage
| LScharges to start | Damage |
| 3 | 48808 |
| 4 | 51019 |
| 5 | 53230 |
| 6 | 55441 |
| 7 | 57652 |
| 8 | 59863 |
| 9 | 62074 |
(2) cast Flame Shock, clipping the dot:
You lose:
Flame Shock dot for dotrem seconds: 547 * dotrem (0.46 * dotrem * 803 * (1 + 1.09 * crit))
Number of ticks: dotrem / time_between_ticks = dotrem / (3 / (1 + haste)) = dotrem * (1 + haste) / 3 = 0.46 * dotrem
You gain:
Flame Shock direct damage: 2221 (1501 * (1 + 1.09 * crit))
Flame Shock dot for 6 seconds: 3256 (2.74 * 803 * (1 + 1.09 * crit))
Number of ticks: 6 / time_between_ticks = 6 / (3 / (1 + haste)) = 2 * (1 + haste) = 2.74
After that, we have 6 sec - gcd = 4.90sec left of the Shock cooldown in which we can cast other spells.
If you are somewhere in your rotation, there's a chance of 4.90 / 8 = 61.25% that Lava Burst will come off cooldown naturally before the next Shock is available. There's also a 20% chance for every Flame Shock tick to reset the Lava Burst cooldown, so we get another 0.2 * 2.74 = 54.80% chance that we can cast Lava Burst. So on average, we will cast 0.6125 + 0.5480 = 1.16 Lava Bursts before the next Shock comes off cooldown.
You gain:
Lava Burst: 18497 (1.16 * 13017 * (1 + 0.75 * overload))
These Lava Bursts took 1.27 sec (1.16 * gcd) to cast, so we are left with 3.63 (4.90 - 1.27) seconds until the next Shock comes off cooldown. In this time we will cast on average 2.48 (3.63 / 1.46) Lightning Bolts and gain 1.49 Lightning Shield charges.
You gain:
Lightning Bolt: 19405 (2.48 * 4316 * (1 + 0.75 * overload) * (1 + 1.09 * crit))
After all that, Shocks come off cooldown and we can cast Earth Shock if (LScharges + 1.49) >= 9 (we only cast ES with 9 charges for max dps, unless Flame Shock might fall off)
You gain:
Earth Shock if LS_charges + 1.49 >= 9: 3475 (2348 * (1 + 1.09 * crit))
Fulmination: 2211 * (LScharges - 3) + 3294 (max(0,(LScharges - 3 + 1.49)) * 1494 * (1 + 1.09 * crit)
Assuming you have 6 seconds left on your Flame Shock, you would deal
2221 + 3256 - 6 * 547 + 18497 + 19405 + (3475) + 2211 * max(0,(LScharges - 3)) + 3294 = 46866 + 2211 * max(0,(LScharges - 3)) damage
| LScharges to start | LS charges when casting ES becomes available | Damage |
| 3 | 4.49 | 46685 |
| 4 | 5.49 | 48896 |
| 5 | 6.49 | 51107 |
| 6 | 7.49 | 53318 |
| 7 | 8.49 | 55529 |
| 8 | 9 | 60132 |
| 9 | 9 | 60132 |
Putting both choices into one table:
| LScharges to start | clipping Flame Shock | not clipping Flame Shock |
| 3 | 46685 | 48808 |
| 4 | 48896 | 51019 |
| 5 | 51107 | 53230 |
| 6 | 53318 | 55441 |
| 7 | 55529 | 57652 |
| 8 | 60132 | 59863 |
| 9 | 60132 | 62074 |
As you can see, only if you start with 8 Lightning Shield charges, clipping Flame Shock becomes worth it. These values are of course based on my current gear and I'm not perfect, so there might be errors in my calculations.
Using the math above, you could create a graph that shows you the better choice, based on available LS charges and remaining FS dot time, but you wouldn't consult a 3D-graph while raiding, would you?
[edit] I hope I don't get another infraction for posting a wall of text in the Simple Questions/Simple Answers Thread, after receiving one for posting the same without math to back it
