It could just be a self-selection effect due to playing a relatively expensive sport (since income and education are correlated), but given how popular sports of all types are (both watching and playing) among so many different types of people I am amazed that the denizens of ivory towers have been able to maintain the stereotype of sports as "low brow" for so long. Especially given that many ivy league universities have historically had popular and successful teams in sports like boxing and wrestling.
It's deeply, tragically ironic when you consider that the origins of those same intellecutal bubbles are rooted in Greek and Roman classical studies, both cultures that prized a well developed body and mind, and considered a man incomplete if he lacked either:
"No man has the right to be an amateur in the matter of physical training. It is a shame for a man to grow old without seeing the beauty and strength of which his body is capable." - Socrates