I've always thought that comment from people a little silly. You mean, if he wasn't playing for a contract, he wouldn't be trying? I would think, in fact, the opposite occurs. A player starts pressing, his pitches start coming up, and he gets whalloped. This isn't football. A man can rarely will a ball past a hitter.
Some people rise to the occasion, and some don't. Playing for a contract has no effect at this time.