Nigel Hayes releases a shot over Villanova’s Josh Hart. (Maddie Meyer/Getty Images)

Wisconsin forward Nigel Hayes could wallpaper his apartment back in Madison with all the March Madness memorabilia he has collected over the years. He has spent more than 40 days of his 22 years on Earth pursuing NCAA tournament wins and has come away with 13 of them for the Badgers, the most of any team in the country over the past four seasons. All that time has taught Hayes to do one thing above all else in NCAA tournament games: Don’t panic.

Hayes, therefore, looked perfectly serene Saturday in front of a not-so-serene crowd at KeyBank Center as No. 8 seed Wisconsin picked off Villanova, the defending national champion and the tournament’s No. 1 overall seed. The Badgers’ 65-62 victory advanced them to the tournament’s Sweet 16 for the fourth consecutive season.

The final sequence of events would have given any player heart palpitations: After scraping back from a seven-point deficit with less than six minutes remaining, Wisconsin finally had the chance to seal a win. And yet Hayes barely showed any effort as he tossed up a reverse layup with 12 seconds left to put the Badgers up 64-62. On Villanova’s ensuing possession, another preternaturally calm senior, Vitto Brown, snatched the ball out of Josh Hart’s hands on the other end of the court. He was fouled in the process.

Brown made one free throw with four seconds remaining, Villanova was unable to get off a final shot, and Wisconsin moved on to the East Region semifinals Friday in New York, where it will play No. 4 seed Florida.

“You have all types of your ranking systems, statistic, analytic guys,” Hayes explained after. “The thing is with all those algorithms, they can’t calculate heart, will to win, toughness, desire. They can’t put that into a formula to come out with a percentage chance to win, and that’s the things that we have. The things that we’ve grown with.”

It may seem unfair, then, that in addition to those qualities, the Badgers possess calculable talents such as guard Bronson Koenig, forward Ethan Happ and Hayes, who led the team with 19 points and eight rebounds while the other two sat on the bench in foul trouble for long stretches and tried to, yes, stay calm.

The game was tied at 37 with 13:41 remaining when Koenig picked up his fourth foul. Coach Greg Gard had no choice but to sit his point guard, even though Koenig had made a program-record eight three-pointers in the Badgers’ first-round victory over Virginia Tech and was desperately needed against a Villanova team that was similarly seasoned and more decorated than the Badgers.

But Koenig sat for more than eight minutes, by which time the Wildcats pried open a seven-point lead and Gard had no choice but to put his star guard back in.

“I felt terrible, to say the least, when I got my fourth foul and I was just sitting on the bench. . . . I knew that’s not how my career was going to end,” Koenig said. “I knew that when Coach gave me the opportunity to get back in there, I was going to make something happen.”

Koenig scored eight points after returning with 5:14 remaining, including two of his three three-pointers. He finished the game with 17 points.

“That’s what close games come down to,” Villanova Coach Jay Wright said. “We’ve been on the other end of that a lot. And when another team steps up and makes those plays and two great players like Koenig and Hayes make those plays, you got to give them credit.”

Josh Hart (Sidwell Friends) led the Wildcats with 19 points in his final game in a Villanova uniform. Redshirt freshman guard Donte DiVincenzo added 15 points including three three-pointers.

“Josh and Kris [Jenkins] and Darryl [Reynolds] are three of the greatest Villanova basketball players of all time,” Wright said of his senior leaders. “Their class is going to go down as the most successful class in Villanova history. . . . To be that successful on the court and really represent the university like they do is something special. We told our younger guys that that’s what you want to be. That’s what you want to be as a Villanova basketball player. You want to be like Kris and Josh and Darryl.”

All three of those seniors know what it’s like to be on the winning side of a tight game like Saturday’s. Even more recently than last year’s dizzying national title game, the Wildcats had needed a herculean second-half effort to advance past No. 16 seed Mount St. Mary’s after a slow start on Thursday. So in a game in which both sides had experience, poise and comfort with last-second situations, Hayes had to pause for a moment in the locker room before deciding why one calm team advanced past the other. He looked down at the latest March Madness memorabilia for his collection.

“Sometimes,” he said, looking up, “it’s just two great teams and you run out of time.”