Just use a software solution. Put 6 or or so cameras pointing out radially and then stitch the views together for a full 4pi view. No need for a fancy gyroscope. There's an idea for a startup...
(I suspect you'd want the view of wherever the ball was projected to land.)
Perhaps another approach would be to have a bunch of cameras around the stadium, motion-track the ball in 3d, then stitch the ball's POV together using a process sort of like Google street view, or that dumb 3d revolving-subject thing that was in all the commercials five years ago. Then you could calculate a 'line of best fit' for the ball's trajectory and render video 'just-in-time' for a quick, smooth replay.
Also what about having flying robocams? How would they work?