When the University of Connecticut was hit with a postseason ban before the 2012-2013 season, the men’s basketball team became a house divided.

“It was confusing because we didn’t know how guys felt,” the senior guard Shabazz Napier said Thursday after the Huskies narrowly defeated St. Joseph’s in their N.C.A.A. tournament opener. “Some guys were saying one thing and doing another thing.”

The UConn players faced a vexing decision, one that would have long-term consequences: Do they jump ship, or stay and steady the ship? When the smoke cleared, center Alex Oriakhi had transferred to Missouri, forward Roscoe Smith transferred to U.N.L.V. and Michael Bradley made a convoluted journey to a junior college and finally wound up at Samford.

A tight-knit core of sophomores chose to stay and weather the storm: Napier, from the Roxbury section of Boston; Tyler Olander, a forward from Mansfield, Conn.; and Niels Giffey, a forward from Germany.