Interesting topic. I'm a huge stat guy - I've got my degrees in statistics - and sometimes I actually miss the days before I knew anything about sabermetrics. The game just felt that much simpler. Today, I'll watch a game and I imagine the chance of every possible outcome and then how each outcome affects the probability of winning the game.
I remember getting the 1992 Strat-O-Matic set for my birthday, and thinking that Mike Moore was a great pitcher because he led the 1992 A's with 17 wins. Now I look at the 90 ERA+, 1.489 WHIP, 1.14 K:BB ratio and just above average WAR and think "Ok... nevermind"
It definitely has a place, a large place, but like a lot of things in life it needs to be balanced with something else. Sometimes I wish I could just watch a game with my stats mind off.