Let me preface this discussion by drawing a clear distinction between a fan and a geek. The sports fan is an enthusiastic supporter of his favorite teams and an avid consumer of sports news. The sports geek wouldn't just just feel anguish or elation when a trade is announced, he could recite every trade in the team's history. It's geekery when you know all the stats, collect all the cards and/or know every piece of trivia, the same way I have friends who can't wait for the next episode of Doctor Who, but I'm probably the only one of the group who knows every story since 1963, who wrote them and which features Sigmund Freud's granddaughter playing an alien.
In the end, I guess it comes down to tribalism. As a youth, I was terrible at sports and loved reading. There were those who were good a sports and who hated reading, and because 90% of the school curriculum is academic rather than physical, that created an inequity that made me the perfect target for bullying. Gym class was when the nastier breed of these kids could get their revenge on the class "brain". It made me associate sports with cruel meat heads, and that may be the case for many traditional geeks who not only preferred non-sports geekery, but sought refuge in it. That said, I've known many people who were interested in both, even made peace with bullies when we discovered a mutual love of comics or role-playing games.
But it never did make me enjoy sports more. A live sporting event from time to time can be a fun experience, a day out, an occasion to lay your best heckling on the opposing team. On TV, I find it oppressively boring, and the commentators on games I get to catch too often fail to make the story come alive for me. But that's okay. I can respect another person's fandom and geekery without needing to absorb it into my own.