An RPG game is a story driven experience. This is a sim sport game, you build your own story playing game after game. There's no need of narrative or script and i don't want to play a fictional character with an established background. Maybe that's a good idea for a tutorial mode, in which through the story of Joe Random you learn the basics of baseball. What RTTS mode desperately needs is more immersion and more relationship with your teammates. Those are key features to build a story in a sport game. It's not only about you, it's about you and who is around you. Who they like, who they dislike, what they think about you, about your performance, who is more friendly, who's not, etc... .
A sort of relationship system, something like the new morale one.