@Miniman chart coming that may interest you. First, a bit of description:
Concept is sharpshooter, looking for good DPR on longbow attack. I plot career average DPR vs. character level for a handful of different progressions.
(Career average DPR on the theory that sessions per level is roughly constant, so this is like a time-weighted average. I don't want to consider a DPR progression like (1 2 3 4 20) the same as one like (1 17 18 19 20); the second is clearly preferable.)
DPR is not assuming "always hit" like many others seem to do and which I don't understand. I'm using an AC=12+floor(character level/2) as the target, totally off the top of my head. (Spurring what may be a later project: running a CR-AC regression on the MM and modeling the ~15 encounters per level to come up with a better "foe AC curve")
I do, however, over-simplistically assume that Sneak Attack will always trigger. That's obviously weighting things in favor of rogue levels, but I think you'll see that doesn't seem to skew, qualitatively, the final recommendation.
Legend interpretation: Fa/Rb/Fc/Rd means "progress fighter to level a, then rogue to rogue level b, then fighter to its level c, the rogue to its level d." &c.
Short takeaway: there's a really nice synergy between SA dice and extra attacks. Neither, alone, drives up DPR as quickly as some mix.
(Again, my "target zone" was character levels 10-12, assuming that's about where a full AL campaign will get to. However, I just got a note from my DM that there's a lot of milestoning in the first chapter of SKT, so he expects tier 2 to come pretty quickly. That's why I extended the analysis to character level 16, which doesn't really seem to change much.)
@BESW can you delete that ^^ chart? I want to re-post with a slight improvement.
Re-post: this time the legend is in the same order as the right-endpoint of each curve...
Notes on the builds: F1/R1/F5/R3/F9 (or, possibly, swapping the first two) was my first thought from the get-go--you may recall from our earlier conversations. Idea being: "establish Archery fighting style and get longbow, grab expertise, get to that first extra attack, take as many Sneak Attack dice as possible while still, eventually, getting to third attack."
F5/R3/F9: "is it worth it to try and get to that first extra attack a little earlier, putting off SA dice? (Also, putting of the expertise I like so much?)" Nope.
R1/F1/R3/F9: "let's start R1 to get the good saves, immediately grab longbow and archery, then grab another SA, before finishing fighter?" The R1/F1 swap might be worth it, but delaying the onset of the first extra attack is a big long-term hit.
F1/R11: "maybe just a rogue who's got the longbow and archery?" Starts out pretty nicely--rogue's got pretty consistent damage growth, while ftr has to wait 5 levels to get that hockey-stick bend at extra attack. But, oh... those extra attacks!
F12: just for comparison. (And look at that comparison! F12 vs F5/R3/F9. This is what, for me, makes the synergy with SA so obvious.)