Interesting that you mention higher powers, and I take the context that you're speaking in a more general way than specifically about organized religion. The things you hear religious players say perfectly embody the main principles of good sports psychology...no matter what the faith of the athlete. Religion gives the Christian athlete a unique tool to use to bend his mind in the right direction, ("Only God can decide if I get a hit. All I can do is swing the bat the way I've been taught"). It's a little more difficult to teach the secular athlete to have that sort of faith in his ability - but it can be done.
That higher power isn't necessarily an old man in the sky with a long white beard and His sandal-wearing long haired Son, after all...