What I get from this thread is that Bradley should focus on its educational mission first and foremost, and not so much relying on athletics as the end-all be all. To me, a university is only as successful in the tools that it provides to its student to compliment their learning. Project Springboard comes into mind as something that applies all of the entrepreneurship principles they learned in class, and then apply them to a real-world scenario in a competition with fellow students.
Having said that, just as you cannot focus all of your attention on athletics, you cannot just sell "None of students have TAs, or the majority of class sizes are of a manageable student/teacher ratio." I mean, that can only get you so far if you want to attract kids from places farther from the Midwest. They can go to schools closer to home if those schools also sell that line as well. And I'm sure community colleges mention that in their admissions materials as well.
What differentiates the Bucknell's from the Bradley's?
On the flip side, I've also heard complaints about students not going to games because they are too busy studying, there are Greek events, or the like. Honestly, people cannot have their cake and eat it too. If you want to attract an intelligent kid who has no clue about the history of Bradley athletics, or follows sports but not the Braves, so be it. And these intelligent kids do not have to introverted either. Like I said, they could be part of numerous student organizations and not care about intercollegiate athletics at the school they attend.
Don't confuse this with not having pride for Bradley, though. They will enjoy the education they receive, enjoy the various outlets of student life, but I'm not sure if they will follow them any more closely than they would if they were still in school.