GLENDALE, Ariz. — Roy Williams, another national championship in hand, his players and assistant coaches for a brief moment circling him in celebration, stood alone. Solitary. His body rigid with the sheer magnitude of it, with the greatness of a career now with few peers.

There will be time later to talk scandals or an oppressively ugly game or a trio of officials who choked on everything but their whistles.

Right now, in the aftermath of North Carolina’s 71-65 win against Gonzaga in the NCAA championship game, there should only be this: In an era and in a field brimming with coaching brilliance, Roy Williams has become one of the greatest men’s basketball coaches of all time.

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There is, with Williams, a tendency to glom to the less-than-favorable headlines that have come out of Chapel Hill. Or to disbelieve the goofy aw-shucks vibe. Or to just look past the sheer level of his accomplishments and coaching prowess. Feel free on the first two, I’m not likely to dissuade you if that’s your focus.

But time to let No. 3 go. The man is a savant, and the history he carved for himself with this title is now beyond dispute.

On Monday, in besting a Gonzaga team that was as formidable as any other in the country, Williams and his Tar Heels carved that history despite the ugliness on both sides of the court. UNC shot a painfully abysmal 14.8 percent on 27 three-point shots. That means they made just four.

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They were out-rebounded, 49-46, and they were called for 22 personal fouls, just as many as the Zags totaled. Yet Roy’s skill in marshaling his team and in responding against great coaches like Mark Few won the day. They won the points-in-the-paint battle, 40-18, and closed out the game with the steely grit you need in ugly games experienced under the severest of pressure.

And now there is this: Roy Williams is just one of six Division 1 men’s basketball coaches with three or more titles. That list includes John Wooden (10), Mike Krzyzewski (5), Adolph Rupp (4), and Jim Calhoun and Bobby Knight (3 each).

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Consider this, too: Williams now has, personally, more titles than all but six schools in the history of the NCAA Tournament — UCLA, Kentucky, Duke, Indiana, UConn and, of course, UNC, where he’s led the Tar Heels to half of their sixth titles.

He also has — and this is a stunner — as many titles to his name as Kansas has had in its rightfully revered history.

There’s a depth of feeling to Williams that, in the imperfect lens that television provides, can seem corny, off, even downright phony. But real life plays out differently, and the people in it do the same — with all their nuances, complications and the things that shape their lives and the people in them.

For Williams, those things have shaped a program that, though a blue blood, has extracted time and again excellence from players who are lionized if they reach the mountain top but misremembered if they come up short.

You can make a Final Four if you’re South Carolina, or my alma mater Mizzou, or some other good or not-so-good basketball school, and be heralded. But not at UNC. No way.

Case in point: Last year’s Tar Heels team, which literally came within one shot of a title but, in the land of blue bloods and the ACC, was less a story to be celebrated than a team that came up short.

Think about that. Williams was one Kris Jenkins shot away from back-to-back titles, and from having notched a fourth championship. That would have put him arguably in Coach K territory.

This is a scoreboard business, and so missed shots — or close calls — do not shape legacies the way they should. So let’s go to the scoreboard. Roy Williams’ reads six title appearances, three titles, and a winning percentage that is second among active coaches to only, hmm, Mark Few.

He’s ninth all time.

It should also be noted, even though it won’t be in enough circles, that Williams’ mark on the game includes picking up the legacy of his mentor, Dean Smith, giving it new life, building on it, and surpassing it.

“They try to say that’s more than Coach Smith. I’m not Dean Smith. Never have been, never will be. He was so much better,” Williams said. “...But we got three, because I got these guys with me and that’s all I care about right now is my guys.”

Such modesty makes people squirm, or disbelieve, or roll their eyes. So be it. But after you’re done rolling your eyes, look one last time at the scoreboard. It reads clearly: Roy Williams, All-Time Great.