To me, a professional hitter is someone who you trust at the plate to have a high probabibility of doing whatever is needed in that situation. I would say someone who works the count, has a high on-base percentage, can be trusted to make contact when contact is really needed, capable of drawing a walk, someone you don't mind leading off an inning, and someone who you can trust during a hit-and-run. It's a combination of the players' stats, their approach, and whether or not people have confidence in him when he steps up. Maybe someone that opposing pitchers also dread facing when it matters.