Three years ago, Jim Larranaga turned down his dream job at his alma mater, Providence, because he decided he had already found that job at George Mason. On Friday, he walked away from that job to a school that has been a basketball desert for most of the last 45 years.

“I think in the end, even though there were other factors, it came down to the money,” George Mason Athletic Director Tom O’Connor said Friday morning, not long after Larranaga called him to say he had accepted the coaching job at Miami. “We would have been able to pay Jim about $1 million — if all his incentives kicked in — next year. Miami was able to offer more than that in guaranteed money. I understand why he would make the move, but I think it is too bad. As far as I’m concerned, the court at the Patriot Center should have his name on it.”

Now, Larranaga won’t be coaching at Patriot Center any more, three years after it was presumed he would finish his career at the school he took from nowhere to the Final Four. The move is a surprise to many — including Larranaga, who believed the time when he would be considered for a job in the ACC had come and gone.

“At my age, you don’t expect these opportunities to crop up,” Larranaga said in a telephone interview Friday afternoon. “You expect people to go after the hot young guys like [VCU Coach] Shaka Smart or [Richmond Coach] Chris Mooney. When my name came up, I thought I had to at least consider it.”

Larranaga’s willingness to consider leaving a school where he is an iconic figure may have had as much to do with the “other factors” O’Connor mentioned as with the money Miami offered, believed to be in the range of $1.3 million guaranteed per year for five years (Larranaga made about $700,000 in salary this past season, and only after reaching a number of incentives). It was no secret that Larranaga felt his assistant coaches needed to be paid more and was frustrated with the fact that improvements to the school’s athletic facilities were moving more slowly than he had hoped. But the biggest “other factor” may have been President Alan G. Merten’s decision to retire at the end of the 2012 school year.

Merten arrived at George Mason in July 1996, about nine months before Larranaga was hired by O’Connor to take over a basketball program that was reeling after seven straight losing seasons. Merten and Larranaga became close friends; Merten and his wife, Sally, were a constant presence at George Mason’s games.

“I was in Florida right after we lost to Ohio State [in the second round of this year’s NCAA tournament] when Dr. Merten called and said, ‘I wanted you to hear this before it shows up in the papers,’ ” Larranaga said. “That’s when he told me he was retiring next year. My first reaction was, ‘Whoa, this is a stunner.’ ”

Timing is everything in life. Twelve days after Merten announced his retirement, Frank Haith left Miami to become the coach at Missouri. Miami President Donna Shalala is extremely involved in the athletic department (reportedly, she personally fired football coach Randy Shannon last December) and was looking for a coach who had a good reputation academically as well as a good won-lost record. That’s why Harvard Coach Tommy Amaker was in the mix early. After Amaker withdrew, the choices came down to Larranaga and Wisconsin-Milwaukee Coach Rob Jeter — the sort of hot young coach (41) who Larranaga thought would be more attractive to an ACC school.

Friday, Larranaga flew to Miami to meet with Shalala and accepted the job, bringing to an end one of the more unlikely success stories in recent college basketball history. When Larranaga first came to George Mason to succeed Paul Westhead in the spring of 1997, he had been successful at Bowling Green but had not yet reached the NCAA tournament as a head coach. That changed two years later, when the Patriots won the Colonial Athletic Association title. After going 9-18 in his first season, Larranaga never had a losing season again, and GMU went to five NCAA tournaments and reached the postseason a total of nine times.

But it was 2006 that changed Larranaga’s life, and life at George Mason, forever. Over the protests of many (led most vocally by CBS’s Billy Packer), the Patriots received an at-large bid to the NCAA tournament. As a No. 11 seed, they upset Michigan State, North Carolina and Wichita State before stunning top-seeded Connecticut in the region final to reach the Final Four. Even after losing to Florida in the national semifinals, Larranaga and George Mason became the rallying cry for underdog teams in every sport.

“Who will be this year’s George Mason?” became an annual question asked by basketball fans and the alleged basketball experts. The answer, more often than not, was no one.

Larranaga just completed his best season since 2006. The Patriots were 27-7, won the CAA regular season title and were a No. 8 seed in the NCAA tournament. They came from behind to beat Villanova in their first game before being blown out by top-seeded Ohio State in the second round.

“I sat with Jim on the plane coming home that day and he felt very good about our season,” O’Connor said. “He knew we had played what might be the best team in the country in a place [Cleveland] where the building was full of their fans. I think he also knew that we should be very good again next year.”

It was during that plane flight that Larranaga and O’Connor discussed changes Larranaga wanted: to his contract, to the contracts of his assistants and to some of George Mason’s facilities. Larranaga’s two most experienced assistants, Chris Caputo and Eric Konkol, were both candidates for better-paying jobs at other schools, and Larranaga was afraid he might lose both of them.

O’Connor said Friday that he felt he and the school were making progress in a lot of the areas that he and Larranaga had discussed, although he conceded that the raises he could offer the assistant coaches weren’t as much as they might otherwise have been because of Title IX considerations. That might have added to Larranaga’s frustrations. After all, Larranaga began looking to leave Bowling Green in 1997 — coming off his best season there — because he was told his budget would have to be cut because of Title IX, the law that mandates gender equality in educational programs that receive federal funding.

All that said, it may well have been Merten’s impending retirement that pushed Larranaga from the comfort of a job he loved — and where he was loved — into the dangerous waters of the ACC. Miami could be very good next year, especially if center Reggie Johnson withdraws his name from the NBA draft by the May 8 deadline. Most ACC coaches believe that with Johnson on the team, the Hurricanes could be picked as high as third in next season’s preseason poll.

Even so, Miami has not exactly been a hoops hotbed in the almost 50 years since Rick Barry played there. In fact, the school shut down the basketball program completely from 1971 to 1985, and since the sport was reinstated, the Hurricanes have been to five NCAA tournaments in 26 years and have never advanced beyond the Sweet 16 — which they reached once, in 2000.

Larranaga, with his Final Four pedigree and his reputation as a clean program builder, clearly is what Shalala was looking for, regardless of age (he’s 61). Whether Larranaga can thrive in the recruiting cesspool that is often the ACC — and can persuade players who arrive on campus with NBA aspirations to buy into his all-for-one, one-for-all philosophy — is unclear.

Only one thing is clear: Regardless of why Larranaga left George Mason, it is a shame that he did. And O’Connor is absolutely right about at least one thing: The court at Patriot Center should be named for him. If you are uncertain of that, just look overhead the next time you are there. The first thing you will notice is a banner that says “Final Four 2006.”

Enough said.