Credit Brad Stevens with Gordon Hayward signing with Celtics

Brad Stevens (left) and Gordon Hayward have unfinished business.2010 FILE/JEFF HAYNES/REUTERS

Gordon Hayward was asked last February at the All-Star media session in New Orleans how often the thought about that half-court shot that could have beaten Duke and led Butler to an improbable national championship in 2010.

Back then, Hayward was a gangly, baby-faced kid, and he had a look of disbelief when that shot bounced off the backboard and then the rim. Last February, Hayward pondered that question, smiled, and said, “I think about it every time someone asks about it.”

He had moved on, sort of. Hayward, with his college coach in the same city, coaching the Eastern Conference in the All-Star Game, had downplayed their relationship over the years, and Brad Stevens’s impact on his career, because years had passed.

But Stevens turned Hayward into a pro, so much so that that half-court shot was his last college play. A player from mid-major Butler University was good enough to enter the NBA Draft and become a lottery pick.

Hayward spent seven years in Utah after being drafted No. 9 overall, became a Jazz franchise cornerstone, but strangely, that one play, that missed shot, that chance to beat Duke, had always stuck with Hayward, more than he revealed.

Hayward finally let his feelings known late Tuesday when he announced he was rejoining Stevens with the Celtics, becoming the latest free agent to spurn other clubs, other more popular cities, to play for Stevens.

That missed opportunity has obviously been in the back of Hayward’s mind his entire professional career. Stevens has never overplayed his relationship with Hayward or contribution to his success. He pointed out that he nabbed a skinny tennis player from suburban Indianapolis and offered him a scholarship.

That bond never wavered. And after the Celtics’ brass hosted Hayward and his wife, Robyn, at Fenway Park on Sunday, Stevens sat down with Hayward and talked to him about his options. He spoke of continuing Hayward’s progress as a sparkling small forward, his role with Isaiah Thomas, his ability to spread the floor, and certainly the unfinished business.

“Coach Stevens was so great about it, all of it. He helped me lay out my options, and talked it through from both sides . . . but in the end, when I needed it, he also gave me my space. And he also let me know that it was my choice to make — and that he would be there for me, on the other side of it, either way,” Hayward wrote Tuesday on The Players’ Tribune. “And of course I ended up deciding to leave: I declared for the draft, and got drafted, and started my new NBA life in Utah. But it always meant a lot to me, to know how, in that moment, even with our lives at this strange crossroads together, Coach Stevens was someone I could count on.”

So that relationship closed the deal. Credit one of the Celtics’ biggest saves in recent years to Stevens. And it’s another major step for an organization seeking respectability. The Celtics gained a semblance of that this past season by being the No. 1 seed in the Eastern Conference and winning 53 regular-season games. But their loss to Cleveland in the conference finals showed that this team needed more help, needed more star power.

The Celtics had been eyeing Hayward for three years. He was a restricted free agent in 2014, and the Celtics, with Stevens leading, hosted him for a meeting. And Hayward even signed an offer sheet with the Hornets before the Jazz matched.

Utah could have signed Hayward to a more lucrative deal and avoided restricted free agency three years ago, but it didn’t. Perhaps that wasn’t a sign of disloyalty, but it definitely encouraged Hayward to consider other locales when free agency began.

He opted out of his four-year contract after the third year, and this time Stevens met Hayward at Logan Airport, sort of like a big brother picking up his little brother from college and saving him the Uber fare.

There is something very natural and organic about the relationship between Stevens and Hayward, as it is with Stevens and several of his former players. There is something magnetic about Stevens’s honesty and sincerity, and as much as Hayward has tried to downplay those characteristics, especially when he was playing for another organization and another coach, it was critical in the end.

The Celtics got their man Tuesday. And while it came with some drama after the news was reported in the early afternoon and then refuted by his agent, it was worth the experience for the Celtics. After years of feeling like a second-class organization, as free agents wouldn’t even accept interviews or never even considered Boston as a destination city or the Celtics as a destination team, a big free agent signing has occurred in each of the last two years with Al Horford and now Hayward.

It’s a beautiful fit. But the Celtics have to make some uncomfortable roster moves to make it happen. Change and adjustment, however, are part of the process of greatness. Hayward is just 27 years ago. He is bearded now, with a wife and two daughters. But that 20-year-old kid who watched that ball clang off the backboard and then the rim is still very much alive, and he’s coming to create some better memories with his old coach.