Being a sports fan used to mean plopping down on the couch—or, if you were lucky, in the stands—and watching a game. That’s not really how it works anymore. More people than ever care about sports, but they’re watching less TV and fewer games. Who has time for all the commercial breaks, blowouts and between-play nonsense? Instead, we’re checking reactions on Twitter, hunting for highlights on Instagram and sending OMG-that-shot faces on Snapchat.

Sports fans aren’t yet living the digital dream, though. For one thing, it’s...