I debated whether or not to post this here, because in spite of its title, the song itself isn’t actually about baseball. Rather, if you pay attention to the lyrics, you realize the song is about infidelity.
However, the title still grabs your attention if you’re a baseball fan, so I did a little poking around to see what I could find in terms of an explanation. While there is some uncertainty about the general meaning, the consensus seems to be that the title is a reference to Pete Rose — in fact, some people indicate that Fall Out Boy originally included Rose’s name in the title, then changed their minds to avoid the potential for a lawsuit. So instead of using his name, the band referenced Rose’s tendency to utilize headfirst slides.
Beyond that, the connection gets a bit hazy, but here’s what I found that makes a modicum of sense: In the song, the narrator is having an affair with a married woman. He is the other man, if you will. More than anything, he wants the woman for himself. However, due to the fact that she is married (his bad bet), he can never have her. In the same way, Pete Rose has found that he cannot have what he truly wants — a place in Cooperstown — due to his own bad bet.