We advanced to “Baby, Baby, All The Time,’’ when, after Kevin Garnett went down, he was a useful starter on a team that came within a game of going to the Eastern Conference finals.

And now, sadly, it’s “Bye Bye, Baby’’ for the foreseeable future, the result of a broken thumb sustained in a strange off-the-court confrontation with what was supposed to be a friendly visitor from the South.

If you’re Doc Rivers, you’re thinking, “Almost a clean getaway.’’ Doc thought he had every base covered. Hah. A coach’s life is never that easy.

Glen Davis is a big part of the Celtics picture, in more ways than one. He was an integral part of a bench unit Doc had hoped would be among the league’s best. His uncategorizable versatility made him a difficult matchup for opponents, because Baby has both a power game and a finesse game flowing out of that 6-foot-8-inch, God-knows-whatever-pound body. He has grasped the team defensive concepts in a way the lovable and rootable Leon Powe never did. He is also one of those guys around whom things just kind of happen. In the entire NBA, there is no one quite like him.

I suppose the timing is good, actually. Better to know right now that a person you thought was going to be important won’t be there than to lose him after you’d gotten used to what he would bring to the table, isn’t it? I think so. The Celtics know precisely where they stand, and what they must do. Anyway, it’s not a career-threatening incident; it’s a setback. Every player has a physical setback, sooner or later.

But it’s troubling to the Celtics, because in the back of their minds they’ve probably always worried that Baby would live up to the nickname and get involved in something stupid. Lord knows he’s good-natured and fun to have around. But he’s also out there, you know? On a 1-to-10 maturity scale, the brass has had him pegged at about a 5.

“I’m very disappointed,’’ said Danny Ainge before last night’s game. “He’s a big part of our team, and he made a bad decision. I feel bad for our players, I feel bad for our coaches, and I feel bad for Glen.’’

Anyway, this is where we find out what Shelden Williams can do.

This is why coaches preach to everyone the need to stay ready. Until 24 hours ago, there was no identifiable role for him on this team. Now he’s going to get some legitimate PT. He’s got a chance to make both himself and Ainge look good.

If you don’t follow the college game very closely, you probably don’t even know who Shelden Williams is.

He happens to have been the fifth pick of the 2006 draft. The fact that he is now on his fourth team in four seasons tells you that he has not exactly lived up to that promise. He has bounced from Atlanta to Sacramento to Minnesota to Boston, and the truth is the majority of headlines attached to his name have come from marrying WNBA superstar Candace Parker.

He had a golden college pedigree, playing four years for Mike Krzyzewski at Duke while twice being named the NABC Defensive Player of the Year. He left Duke as its career leader in rebounding and blocked shots. He was a smart player, and no one ever questioned his heart.

So, what happened?

In college, he did what he did as a pure post player. His offensive repertoire wasn’t overly sophisticated, his game consisting of power stuff and putbacks. There should have been some questions about him, simply because he’s often listed at 6-9 but always looked more like a cheating 6-7.

After three NBA seasons, he’s averaging 14 minutes a game while scoring at just under 5 (4.7). His 36-minute projections would make him an 11-point, 7-rebound player, but you could say that about a lot of guys. The truth is the basic numbers just haven’t been there.

But there are horses for courses, and the Celtics won’t be asking him to score. Baby was Baby. He had that increasingly reliable 15-footer. He’s a legit scorer. But on a unit with Rasheed Wallace, Eddie House, and Marquis Daniels, plus whichever one of the Big Three who’ll be on the floor, Shelden Williams won’t be needed to score. He’ll be needed to execute his defensive assignments, rebound aggressively, and make a layup every now and then. He has a winner’s DNA; we know that.

“He was a high draft pick for a reason, and he was a great college player for a reason,’’ Rivers declared. “It’s there. It’s our job to get it out of him.’’

Meanwhile, one can only imagine what the Celtics have in store for Glen Davis. He is suspended indefinitely, according to Ainge. And you can be sure the team will be thinking in terms of a “Baby’’ sitter, if only to keep him from raiding the refrigerator every five minutes.

The Celtics say they are satisfied they know what happened. But it will have to be a pretty clear case of self-defense for Glen Davis to come away from this with anyone’s sympathy. Break your thumb trying to block a shot. Do not break your thumb fighting someone in a moving vehicle.

Celtics owner Wyc Grousbeck said something about becoming tired of the “Baby’’ thing, and he may be onto something. Glen Davis will be 24 on New Year’s Day. It may be time for him to shed the nickname. Along with his explanation and apology, perhaps he should announce that, henceforth, he no longer wishes to be called “Big Baby,’’ or any derivative.

Glen Davis has a chance for a long and lucrative career. A chance. It really is time he grew up.