When you want a GM/CEO/Head/Main Director, etc. You look at high management profiles; the names come later.
I mean, I've seen GMs go from one industry to another completely different over and over and over again just like that due their SOLID MANAGEMENT SKILLS. I believe that a baseball organization or any other company beyond the industry it belongs, looks for a GM who can deploy with success those skills; it is not necessary the knowledge of the core business, it comes later. Sure, If this candidate has experience in that industry (ex. Baseball), even better, but it is not a most, you want the profile.