Athlete to Actor

Just a thought that popped up when watching The Dirty Dozen but it's interesting how many American sportsmen transition to acting. Jim Brown is actually an OK actor, not all are, but it seems to be American thing.
Off hand I can only think of two British sportsmen who did this, Vinnie Jones and Brian Glover - who was actually a pretty good character actor.
Is it because sport is so big in America that the top players become household names in a way that rarely happens in the UK? Is it because Hollywood provides the opportunity? Is it because so much American sport is much closer to being showbusiness by another name - it does seem to be televised in that way.