Well, I favour the buttering toast analogy - it's about as relevant.
Buttering toast... press too lightly and the butter won't stick. Playing piano... press too lightly and the note won't sound. You'd be surprised how relevant random things are.
As for the sports, we are talking about efficiency of movement in both, so please explain how the analogy is not relevant.
Anyway, for a more direct way to answer this thread,
After the note is depressed there is very little you can do to change the sound besides the way you release it. After I press the note, I can wiggle my finger all I want and it's not going to change anything. There may be certain subtleties with the releasing of the key, and yes any joe can press a button, but artistry in piano is the way we depress that key. What we do afterwards is either a psychological approach to depressing the key, or preparation for the next note.