The secret is to bounce up your speed as far as you can, and track the target, that way it will be sharp as a tack. You do not need a large f stop if you are shooting a single object. Try F 3.2 at around 3200/sec. bump up your ASA to what ever it needs to make it happen. It will put a nice blur to the background too.
I and other shooters hand hold fixed 300mm 2.8 at NHL games all the time on the ice and it works fine. for NBA games we use a mono pod as there is more room.