The way I handle it is I place anything that is similar in a super class that is added to all targets, and then I create a new class (for your example "Player") that is different for each target.
So in the source directory I would have subdirectories and files:
basketball/Player.m baseball/Player.m ...
And then I would select the "Target Membership" for basketball/Player.m to be the "Basketball" target.
This way I only have to instantiate a Player class once and depending on what my target is, it will automatically create the proper class. Hope this helps.