MINNEAPOLIS — If it can defeat third-seeded Texas Tech on Monday night, Virginia would not become the first national champion that had lost in the first round of the N.C.A.A. tournament the previous year. Duke did it in 2015, and Indiana in 1987. Connecticut won the 2014 title a year after it had been barred from postseason play for poor academic performance.

But nonetheless, a win by top-seeded Virginia (34-3) would be different. Of course it would be different. Not all losses are created equal, and Virginia’s tournament experience last year was quite a moment to overcome.

So many factors compounded last March to make the result of Virginia’s game versus the University of Maryland, Baltimore County, so awful for the Cavaliers. There was the sheer history of being the first No. 1 seed ever to lose to a No. 16 seed in the men’s tournament. There was the fact that the game itself was not close: The Cavaliers lost by 20 points. There was the size of the fall, as Virginia was not only a top seed last year but the overall top seed, deemed the very best team in the country only days before its stunning exit. And U.M.B.C., with its inspiring academic story and clever Twitter feed, was an underdog — a Cheseapake retriever, to be precise — straight from central casting, so magnetic that there was barely time to feel bad for a Virginia team that had just had the equivalent of a 20-ton weight dropped on it.