I love to kick back and just watch a game because I love baseball. I also enjoy having statistics available to back up what I otherwise wouldn't know by just watching. I think people need to realize that you don't have to be 100% in the "Just watch the games!" or "Stat nerds" camp. It's a mix of both to determine how valuable a player is, and baseball front offices across the league have come to realize this within the last 10 years. There's a reason the A's had some great teams (with such a low payroll) during the early part of the 2000s with Billy Beane running the show. Not many MLB teams were using the more valuable stats to measure players. They were stuck in the old days, and Billy Beane was able to get extremely good players for cheap because most other teams thought they were worthless.
If anyone hasn't read Moneyball, pick up a copy at a bookstore sometime soon. It's really a great read.