Do laws of probability explain why athletes are like coins?

The first law, as usually stated, is a bit circular, as it asserts independence of individual events. It doesn't demonstrate that the independence exists. Dozier and Plouffe both improving at bat, for instance, might be because the two of them both benefit from Brunansky being with the parent club; or it could be from them sitting together on the bench between at-bats and discussing their approaches at the plate and having some kind of simultaneous epiphany about Uncle Charley.

Nothing really wrong with 7 heads out of 9 flips as a quick estimate of how much assumption is being built into one's season forecast. But it's not really a mathematical theorem either.