Center Forward Backdoor.

To anyone who played men’s basketball at Princeton during Pete Carril’s 29 years as coach, it is a play call that comes with reflexive recognition. So much so that even septuagenarian former Tigers could be summoned to a gym now and run — or at least walk — through it with rhythmic precision.

As for the rest of us? The name describes the play: the center flashes from underneath the basket to the free-throw line and receives a pass. He then looks to the wing for a forward, who cuts to the basket and receives a bounce pass through a gap in the defense — the backdoor — for a layup.

The set is a foundational element of what is often characterized as the Princeton offense — the balletic ball movement, crisp cuts and selfless play whose roots trace back to the old Boston Celtics dynasty of the 1950s and 1960s and live on in today’s Golden State Warriors.

It is at once simple, as the nomenclature suggests, and sophisticated, as the myriad permutations and required intuition demand. The same goes for Carril, who died Monday at age 92, the rumpled, beer-drinking, cigar-smoking son of an immigrant steelworker who carved out a home — and a Hall of Fame career — among the Ivy League’s privileged and academic elite.

Carril’s teams won 13 league titles and an N.I.T. championship in 1975 (when the tournament carried some cachet) and regularly became March characters by throwing a scare into basketball powerhouses in the N.C.A.A. tournament.

The last of his 514 victories came when Princeton finally took down one of the giants in 1996, upsetting the defending champion U.C.L.A., 43-41, on a last-second basket. Steve Goodrich, the sophomore center, delivered a clinical bounce pass to a slashing Gabe Lewullis, the freshman forward, who laid the ball in over a defender’s arms.

Center Forward Backdoor.

“It was the perfect play, the perfect setup,” said Chris Doyal, the only senior to play that night for Princeton.

The moment seemed poetic on many levels.

It had taken place at the cavernous old RCA Dome in Indianapolis, not far from Hinkle Fieldhouse, the basketball barn where the climactic scenes from “Hoosiers” were filmed. It had come against a school that the year before had won its record 11th championship. And it came less than a week after Carril shocked his players, writing on a locker room chalkboard, “I’m retiring. I’m very happy,” after Princeton had won the conference by defeating rival Penn in a playoff game in Bethlehem, Pa., where he had grown up.

That win may have meant more to Carril than any other.

Penn had dominated the Ivy League, with a winning streak that reached 48 games, including eight in a row over Princeton. The last of those was a thumping in the regular-season finale, which left the teams tied for the championship even though the Quakers had won both league games. (The Ivy League did not have a conference tournament until 2017.) The previous season, after another loss to Penn, Carril had an assistant distribute box scores from his best teams’ games to the players at practice. He told them they were embarrassing the program. “It was eating him up that Penn is killing him,” Goodrich said.

Carril’s charm, wit, coaching acumen and the figure he cut — 5-foot-6, balding and with a healthy paunch — made for an easy caricature: a basketball Yoda.

Playing for him, though, was an acquired taste — sometimes bitter.

Practices, before the N.C.A.A. imposed limits, typically went for four grueling hours. Carril frowned upon stretching, grudgingly allowed water breaks and was even more parsimonious with compliments, afraid that his players would become complacent. And his criticism could be withering. Once, he stopped practice, sat his players in a row on the court and went down the line detailing their shortcomings. The session lasted 90 minutes.

Sometimes, he’d get so angry that he would rip his shirt off, spending the remainder of practice topless while puffing on a cigar. “He was extremely hairy,” Doyal said. “He looked like a gorilla.”

Players, and his assistant coaches, would sometimes have to stifle laughter, like when Carril lit a photo of himself as a Little All-America selection at Lafayette on fire to make a show of how he didn’t want to be like his players, who might have been all-state this or all-America that. The photo was more flammable than Carril thought, prompting him to drop it and stomp out the fire on the court — but not before “All-America” had been burnished onto the court.

That final season, Carril stopped practice once to spit on the court, depositing a loogie near the feet of Lewullis. Carril asked if he knew what phlegm was. A pre-med student, Lewullis nodded. Carril said the way Lewullis moved reminded him of phlegm — it jiggles and shakes but doesn’t go anywhere.

“At the time it’s happening, you’re scared out of your mind,” said Lewullis, now an orthopedic surgeon near where he grew up in Allentown, Pa. “But he was right, and you don’t forget about it. I needed to cut harder, do things harder on the court.”

Since Ivy League schools do not award athletic scholarships, some players found the experience so dispiriting they quit and focused on academics. On Carril’s final team, there were only two seniors on the roster. The year before, there were three. Doyal, who works in finance in London, said he was so miserable he nearly quit early in his senior season. But he and others said they came to appreciate much of what they learned.

“So much of what comes out of my mouth is a Rolodex of what I’ve heard him say,” said Mitch Henderson, a sophomore guard on Carril’s final team who last season coached Princeton to the Ivy League regular-season championship. He is one of three players on that team who have become head coaches, joining Brian Earl, who is at Cornell, and Sydney Johnson, who has coached Princeton and Fairfield.

“He was the best teacher most of us had ever had,” Henderson continued. “The brilliance of the man was teaching people how to see and how to think, and he was relentlessly focused on that. The worst sin was the one where you’re not seeking excellence.”

That meant every moment.

Carril told his players there was always something to learn if they were paying attention. Practice was where all the work was done. Players didn’t watch film; they got brief verbal scouting reports from the coaches. Dribbling, passing and shooting drills ran for 45 minutes at the start of practice, followed simply by guys playing with their minds and their eyes open.

Think. See. Do. Repeat.

“He wasn’t an aesthetic, but he had a belief that you had to be clever,” said Goodrich, who would become the Ivy League player of the year as a senior and played briefly in the N.B.A. “We’d practice forever, mostly just playing. ‘What did you see? Why didn’t you cut? Why didn’t you get out of there?’ He had such a clear idea of how to play, and it was all about whether you could understand it in real time.”

Carril wasn’t much for substitutions, tactics or timeouts, so when Henderson brought the ball up court with the score tied, the shot clock turned off and the crowd on its feet, he was stunned to see Carril with his arms over his head signaling for a timeout.

As Carril huddled with his three assistants — Bill Carmody, John Thompson III and Joe Scott, each of whom would eventually become the school’s head coach — they quickly came to the same conclusion as everyone else in the building for what would come next: Center Forward Backdoor.

Scott, though, suggested a wrinkle. Princeton had scored on the play just before halftime so U.C.L.A. would surely be prepared for Lewullis to cut to the basket. Instead, he would revert to the 3-point line and make a second cut to the basket.

“As crazy as it was, the environment and the moment, it was really clear what we were being told to do,” said Johnson, the junior point guard. “A lot of things went well for us to be in that moment, but in that moment we were very well prepared to win the game.”

And so they did. After a handful of passes, Goodrich flashed to the right elbow and took a pass from Johnson with less than 10 seconds left. As he did, Lewullis cut from the wing and, as the coaches expected, was blanketed by U.C.L.A. forward Charles O’Bannon.

So Lewullis pivoted and took three hard steps toward the corner, just enough to pull O’Bannon with him. With the backdoor ajar, Lewullis zipped to the basket just as Goodrich took one dribble toward him and delivered an on-the-money bounce pass. Lewullis kissed the ball off the glass, just over the outstretched arms of forward Kris Johnson.

“I was just a naïve freshman,” said Lewullis, who was caught on camera mouthing “Oh, my God,” as he ran down court. Goodrich, who earned a master’s degree in business from U.C.L.A. and lives near campus, works with plenty of Bruins fans who are forgiving if not quite forgetful.

If it is the most visible memory sparked by Carril’s death, it is also an enduring one.

It’s hard to say if the appreciation of the art of a fine pass, delivered on time, is more acute among the Princeton basketball family, but Henderson figures he is not the only one who sees the game through that prism.

“What a gift to give to somebody else,” Henderson said of his old coach’s final assist.