I see a lot of questions about when to apply DoTs and I wanted to weigh in with my 2c. I'm not claiming that my choices are optimal, but I find them to be a 1) workable, and 2) decent dps.
This post will be by necessity non-mathematical. Not because I think math is a bad idea for this, but because I haven't been able to figure out how to model the benefit of a DoT when compared to casting another spell during Eclipse.
(An interesting thought I just had on that is that maybe my basic premise is wrong. I've been trying to work out a formula of the form of f(A,B) = X, where A is the benefit of the DoT, B is the opportunity cost, and X would be the number of seconds left in Eclipse where it is still a good idea to reapply DoTs. But if the number of seconds left doesn't matter, then a formula like this is impossible - I'll have to think on that more).
The basic problem I have with modeling the benefit of DoTs is that there are two negative factors. When you apply a DoT during Eclipse:
1) You lost the benefit of Eclipse to one Wrath or roughly 1/2 of a Starfire.
2) You have to reapply that same DoT slightly earlier then you would otherwise.
The first is very easy to model, and my math based on it led to a "6-second rule" - if Eclipse has >6 seconds, it's better to reapply DoTs.
The second seems to be almost impossible - how to determine the negative effects of having to refresh Insect Swarm, for example, in 15 seconds instead of 21. This makes it extremely hard to compare to the damage of a DoT and determine when to refresh.
The end result of trying to come up with this is I've changed my philosophy on reapplying DoTs. I previously used the 6-second rule on most fights. After thinking about it though, it seems like this was optimistic - it ignores the effects of using slightly more GCDs on DoT damage... I think. Therefore:
Single Target Stand-And-Nuke/Light Movement
1) Reapply Moonfire if it drops off to ensure maximum idol uptime.
2) Reapply Insect Swarm at the end of every Eclipse if it's off. This has an additional benefit of allowing smoother Lunar->Solar transitions with WiseEclipse.
3) Reapply Insect Swarm during Solar Eclipse only if it falls off, no matter when it falls off.
The main benefit of these changes is that they require slightly less thought (as I never take into account the amount of time Eclipse has), and they lead to a slightly more predictable rotation, both of which are beneficial if I'm distracted, tired, or anything goes wrong during a fight.
Single Target with Medium to Heavy Movement
1) Reapply DoTs if they drop off and I know I won't have to move for 5+ seconds. Otherwise save them and use them for when I have to move.
2) Ignore the above for Insect Swarm if I know there's predictable movement in the duration of the DoT (for example: Ignis, and there's going to be a flame Jet within 14 seconds).
This is pretty simple - basically if I know I have to move a lot (H Twins as a goalie is a good example of this) then my DoT strategy changes significantly. It becomes much more important to optimize dps by using DoTs as instant cast spells that I can hit while moving, instead of worrying about more optimal uptimes. In general I try to keep Moonfire up just for the Idol effect, but other then that it's more important to save DoTs for when you can't cast anything else.
Two/Three Target Fights
1) Apply DoTs on any target that A) provides useful dps, and B) will last long enough for the DoTs to fully tick on.
The important note here is that it must be useful dps. I don't advocate DoTing up all the adds on Iron Council because it's not useful - they heal to full. I don't advocate DoTing up both worms in Heroic NrB because killing Acidmaw fast is key - lowering your dps to make the overall fight shorter just isn't that important. Faction Champions is about focused dps, so again - no DoTing up targets (at least until the end, or on pets to draw off heals).
Good fights for this are stuff like Flame Leviathan (if you go up top and kill sentries), Freya triplets (as long as you don't kill anything too early), Mimiron p4 (same as Freya triplets), and Yogg-Saron p2.
AOE Fights (4+)
1) Keep up Moonfire for the idol effect.
It isn't worth it to spam DoTs on 4+ targets, Hurricane is better dps.
Hope some people find this useful. I'd also be interested if anyone else has good math on when to reapply DoTs in Eclipse, I haven't seen anything concrete on it.
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