Adam's post below discussed the apparent "finders keepers" rule for baseball ownership -- both on the field for players and off the field for fans. For fans, this could be explained as a promotional effort of the team -- a sort of lottery that increases the attractiveness of attending the game.
For players, one would expect on the margin that this property regime would benefit the catching position. This is because the catcher has a greater chance to catching the final out, assuming that closers tend to be strike out pitchers. Therefore, this property rights regime is a subtle way of adding to the attractiveness of catching -- a position that needs all the help it can get.