By Christopher L. Gasper, Boston.com Columnist

To listen to president of basketball operations Danny Ainge, the Celtics are like a precocious, procrastinating college kid who can't bring himself/herself to write a term paper until the day before its due. Then said student buckles down, pulls an all-nighter and gets an A.

That's the basketball equivalent of what the Celtics will try to accomplish in the playoffs, which start on Sunday against the New York Knicks. After more than a month of mediocre play, a sub-.500 record in their final 21 games (10-11) and a tumble down to third place in the Eastern Conference standings, the Celtics begin writing the final chapter of their season -- and possibly of the Big Three/Doc Rivers renaissance. They've finally reached the basketball that really matters to them, and the only games their season will be graded upon.

They want a big, fat B -- for Banner 18.

Of course there is always the possibility that like that dawdling college student, the Celtics oversleep and never get to hand in their best work. But on the brink of the playoffs, Ainge remains confident in the championship chances of his team.

"We faded a little bit at the end, but I think this team has what it takes," Ainge said.

The reality is that these Celtics aren't just playing for another championship, or to avenge last season's Game 7 loss in Los Angeles or to augment their legacy. They could be playing to stay together. This could be the last go-around for this incarnation of the Green. Ainge said that thought has crossed his mind and has been broached with the team.

"Oh, yeah. This may be it. This may be our chance. You just never know. We have talked about that," said Ainge. "I hope they have that mentality."

Based on his history as a hoops decision-maker and his comments about how he would have handled the decline of the original Big Three, Ainge won't hesitate to break this team up if it fails to reach the Finals. He's not going to let them simply age gracefully and cede Eastern Conference eminence to the young guns in Miami and Chicago.

Perhaps the Kendrick Perkins trade was just the beginning of the deconstruction of the Celtics. That's a sobering thought for the parishioners of the parquet. But no roster is safe with Danny the Dealer, and Ainge already gave these guys another shot.

This is a bonus season for the Core Four of Paul Pierce, Kevin Garnett, Ray Allen and Rajon Rondo.

After the final horn sounded last June at Staples Center and the confetti rained down from the rafters, it looked like the closing credits had rolled on this team. An emotional Rivers punctuated his postgame press conference that night with past tense references and received farewell applause as he left the podium. Then miraculously the band was back together, with Rivers, Pierce and Ray Allen returning in lockstep.

Win or lose, Rivers could be gone at the end of the Celtics' playoff run, especially with son Austin, a future NBA lottery pick, off to Duke. Allen and Garnett both enter the final years of their contracts, which means their expiring deals heading into the 2012 free-agent frenzy with Dwight Howard and Chris Paul, et al might be able to bring back retooling parts in return. Plus, there is the seeming inevitability of an NBA lockout that could make the NFL's labor dispute look like a pillow fight. That's a lot of uncertainty.

The Green going Al Green ("Let's Stay Together") might be just the added motivation they need to transition from energy conservation to self-preservation and make another spirited run to the NBA Finals without homecourt advantage.

The fate of the Core Four's future rests largely in the hands of its junior member, point guard Rajon Rondo. Rondo has had more success selling jerseys than sinking shots lately. Over his last 21 games Rondo is shooting 41 percent from the floor and averaging 9.1 assists, compared to an average of 12.1 per game before that stretch.

Theories abound as to why. They range from nagging injuries, including plantar fasciitis, to being burned out from his summer stint with USA Basketball, to having a hole in his heart after teammate/soulmate Perkins was shipped to Oklahoma City.

"I think that those are just all excuses," said Ainge. "I think that Rajon is a pretty tough kid. I don't think he's that sentimental. He's friends with Perk. I think he understands the game. I think he is way more professional than to let anything like that bother him.

"By the way, he was playing pretty well. We won five games in a row right after that [trade]. But I think he's been sort of banged up, but not really hurt. I just think it's a lot. The kid was playing at such an unbelievable level. That's hard to maintain. ...I think there is a lot put on him. I think nobody has really played at the same level they played before the All-Star game."

Ainge admitted the road in the East is tougher this time around -- "New York in the first round, it's scary. They got some great game finishers. It just gets tougher from there."

Indeed it does with the Heat and Bulls lurking, and homecourt advantage lacking for the Celtics.

But Ainge believes his team is up to the task. That the possible final run is a Finals run.

"I really know what's inside these players, especially those Four," said Ainge. "I know what's inside Delonte [West]. I know what's inside Big Baby. I've seen that resolve in them. I've seen how they know the moment. They thrive and live for the moment. So, we'll see. I believe in them, and I can't wait for the playoffs to start. It's exciting."

Sunday represents a fresh start for the Celtics. Hopefully, it's the beginning of a long playoff run and not the beginning of the end for a brilliant bunch.