I'd like to see certain personalities that impact how your player behaves and how everyone else views them. Maybe some different animations a cocky player might do more bat flips, the laid back player might laugh or smile after a play.
The Captain
The clubhouse leader of the team, As hard as they try the media can't say anything bad about you, and the fans like him.
The Diva
He's arrogant, cocky, talented but puts himself above everyone else, and may find himself clashing with the management and the fans.
If he goes to far he might find himself wearing a different uniform playing for another team.
Laid back "The Dude"
Fans love him, his teammates love him, he's always approachable and has a great attitude.