Trying to capture breaking clays with the 300/2.8 AFS-II and D810 has been one of my photographic challenges, I still haven't perfected it and it is a numbers game (shoot 100+ to 1). These are shot with luck and anticipation, I prefocus and check where most average clays are breaking (about 30-35 yards from me standing 10 yards behind the line for 16 yard trap shooting)(Auto focus just can not follow a clay pigeon). Most of these are cropped 50% but I don't think a longer lens would help me. A D5 might help me but I'm not sure, I have the timing so speed isn't as important and a burst of out of focus action is just more files to trash. Choice of background helps (dark trees, low angles, side lighting later or early in day) and stopping down to f/8, 1/4000th or faster. Someday I will shoot enough to get the perfect break in perfect focus....
It's situations like this where Canon or Nikon optical VF DSLRs still reign supreme.