Some interesting numbers on 4.0 BLM

[RyeMinx]

Second. 4.0 Rotation vs 3.0 Rotation
When it comes to a dummy parse, 4.0 is better, but not by game breaking amounts. The problem with only showing the PPS of 20-35s, is it doesn't show how everything stacks up over time, especially Foul timing and Dots. Foul always needing to be used during UI, and not wanting to overwrite dots without T3P. Now on the flip side, 3.0 is better on a dummy parse, if you get a T3P at least every 2 our of 3 Astral Fire phases... which is RNG, but very plausible with having to cast T3 over T1. Also 3.0 has the advantage of movement friendlier phases during actual fights... for now.
I do believe once we get back to 1600+ SpS, 4.0 will be safe enough to just always do. During end of HW, it was safe to cast 4 spells before refreshing with F1... albeit unnecessary, but doable.

My opinion: Use 4.0 when you know the fight wont require movement (like all of Lakshmi...) and 3.0 when you have to move (like all of Susano...)

[Galvuu]

snip

Lots of things here.
The base 600MP is so I don't (sometimes) need to stay put for 0.5 seconds doing nothing to wait for the mana tick.
In the 4.0 rotation, if your Fire III finishes before you get a refund on your UI cycle, you won't have enough mana to F4x3>F>F4x3>B3 (you'll be left at 0 MP) and will need to Transpose. This is a dps loss most of the time.

You should always use the 8xFire IV opener to buy time on the Foul clock. This opener is quite long (like 40ish seconds), so you buy enough time to ensure the next three 3.X rotations always have Foul up. By then, you have Triple/LL up again, and should do one/two 4.0 rotations to, again, buy Foul clock time. I never even considered the old Sharpcast opener (you won't even have Foul for your first UI cycle if you do it).
I didn't math this, but I'm very confident the Sharpcast opener loses in pps when you consider the full UI cycle (Foul is no joke).

The reason why you only need a rotation is because pps is inherently normalised for time. The 4.0 rotation lasts, on average, 33.5 seconds. The 3.X lasts 26.5 (if memory serves me correctly). If the 3.x yields more expected pps than the 4.0, any arbitrary least common multiple of the two lengths of time will reflect this. Think of it as speed- if 3.0 has higher velocity than 4.0, then it'll outrace it for any length of time (travel farther = doing more damage). The only thing that can offset this is if the time it takes to clear a fight/get to a transition, for instance, would align one just as you cast Foul (maximum pps) VS as you cast the first Fire IV (worst case scenario, Thunder has barely ticked and your last spell was an unboosted Fire III, least pps). But you cannot realistically predict when the fight will end this accurately with any degree of confidence.
Or, if you want to keep that analogy from before, pps isn't a monotonically increasing function over time (it has some bumps as you enter the low pps end of the UI cycle), so you could end up on one of these valleys for one and not the other.
That said, preliminary data, if top parsing BLMs are anything to go by, shows that 3.0 wins.

Just explaining the reasoning behind stuff.