Yes, baseball is a team sport, but it's very easy to get consumed with our individual accomplishments and statistics. As a player, you must be very careful of this trap and adjust your priorities accordingly.
Wrapping ourselves up in ourselves like an orange peel is a miserable, selfish way to approach the game--not to mention ineffective. We've all been there. It's one of the main challenges of baseball and life.
Process Over Results
Here's why it doesn't work. Results are elusive and unpredictable. The only thing that happens when we focus on stats and base our worth on results is we get a front row seat on a never-ending roller coaster of ups and downs.
It's the nature of baseball and you can't control it. This ride saps all enjoyment from the game and has burned out many a player--especially over the course of a 162-game season.
What Players Can Do
My suggestion is to take control of what you can take control of. While you can't control whether you walk away from a game with four hits, you can control how well you pulled for the guys on your team. You can give up your at-bat and bunt a guy into scoring position. You can run the bases intelligently.
As a catcher (my particular specialty), you can control how much you helped your pitching staff by calling a good game or blocking the ball. In short, you can control how good a teammate you are.
Keeping Score
If you base how great a game you had on how good a teammate you were, I'll guarantee a couple things. One, you'll have a lot more fun. And two, the baseball gods will reward you with the best statistical season you ever had. Don't ask me how, the game was just designed that way. Remember, results are just a by-product of your approach to the game.
The simple fact is, when the team does well, everybody shines.
"Ask not what your teammates can do for you. Ask what you can do for your teammates."? ~? Magic Johnson