That's another one of the great things about baseball...stat conversations. My son is only 13. I've kept stats for him since he was 8. However, I use them mostly for entertainment purposes. I like to see how he does against other players, I like to see how he performs in games we win vs. games we lose, etc.
I also use them as a gauge for how he is improving over the years.
But you have to be brutally honest when keeping the book. If my son is batting and a shortstop boots the ball, I HAVE to give the SS an error. What good does it do to tell your son he's hitting .750 when it's more like .250?
We once played on dry field with no fence. A player hit a hard ground ball that when right through the second baseman's legs and rolled about a mile. His dad ran over to make sure I scored it a home run.
Not only was it not a home run...it wasn't even a hit!