The University of Richmond, which was founded in 1830, is a lavish-looking campus with impressive brick buildings that surround a lake that, until a few years ago, divided male and female dormitories. It is private, has about 3,000 students and costs nearly $50,000 a year in tuition and room and board. It traditionally draws a significant number of students from the Northeast.

It also has a football team, although it plays in the Football Championship Subdivision, one step down from college football’s top tier. In 2008, it won the F.C.S. national championship.

V.C.U., in contrast, does not have a football team. Instead, there are satirical sweatshirts that proclaim V.C.U. football on the front and the fact that the team is still undefeated on the back.

V.C.U. is also a public university rather than a private one; has a student body seven times the size of Richmond’s; and costs about 60 percent less for students from Virginia and 20 percent less for those from out of state. Many students live on campus at the University of Richmond; many do not at V.C.U.

On the court, the teams play completely different styles. Richmond’s coach, Chris Mooney, has modeled his patient offense after the one he learned from Pete Carril during his four years as a starter at Princeton.

V.C.U.’s coach, Shaka Smart, has his team play an up-tempo running style with a pressing defense that is similar to the one called 40 Minutes of Hell that Nolan Richardson made famous at the University of Arkansas.