“The thing I took away from that was how authentic each leader was,” Banghart said. “When I got the job at Princeton, I didn’t try to be the next Pat Summitt or the next Geno Auriemma or the next Anson Dorrance. I realized that what made them great is they were who they were. I was going to be the best version of me.”

Princeton was 7-23 in Banghart’s first season, but the Tigers went undefeated in the Ivy League and finished 26-3 by her third season. It was the start of four consecutive conference titles from 2010 to 2013, a streak that ended last March when Princeton lost at home to Pennsylvania in the regular-season finale, which determined the league champion. Princeton hosts Penn on Saturday in the conference opener for both teams.

Since Banghart arrived, the Tigers have played as many major-conference teams as possible to prepare for the Ivy League schedule. This season, they have victories over teams from the Atlantic Coast Conference (Pittsburgh and Wake Forest), the Big East (Georgetown) and the Big Ten (Michigan). Princeton seems to have a good shot at joining the 1998 Harvard team as the only Ivy League squad to win an N.C.A.A. tournament game.

Of the Tigers’ 16 victories, 12 have come on the road and all have been decided by at least 12 points, except for a 63-56 win at American University on Nov. 23 in Washington. During that trip, Princeton had a private White House tour and played on the White House basketball court. The next day, at halftime of the American game, the first lady, Michelle Obama, addressed the players in the Tigers’ locker room. Obama is a 1985 Princeton graduate, and her niece, Leslie Robinson, is a freshman forward on the team.

“It was very clear that she was in tune and she had actually been watching,” said the senior point guard Blake Dietrick, who leads Princeton in scoring (15.2 points) and assists (5.7) and averages 5.0 rebounds per game. “She wasn’t just there to make an appearance. She was like, ‘Great job — keep pressuring them on defense,’ which was a focus of ours that we had talked about before the game.”