The number is nine. Or maybe eight. Celtics coach Doc Rivers knows the answer to the question – how many players will be in his playoff rotation – but he will need the final five weeks of the season to determine which players actually fits into the equation.

Honestly, Rivers acknowledged that he does know which nine he wants in that group, but he also knows that injuries will play a part and he likes that there will be vigorous competition for those spots.

“That’s great. That’s what you want. That makes all 12 really play hard,” Rivers said. “When we won it, we had Baby [Glen Davis] and Leon [Powe] and went back and forth. I thought that was terrific. I thought it pushed both of them.”

With the addition of Carlos Arroyo, the Celtics now have 15 players on their roster for the rest of the regular season. Considering that four are obvious – Rajon Rondo, Ray Allen, Paul Pierce and Kevin Garnett – and one (Avery Bradley) lack experience, that leaves 10 players competing for five spots. Getting those complementary pieces in order may be harder than you might think.

Five of those 10 players are currently injured: Shaquille O’Neal, Jermaine O’Neal, Glen Davis, Delonte West and Von Wafer. And five of them are brand new: Arroyo, Jeff Green, Nenad Krstic, Sasha Pavlovic and Troy Murphy. During practice on Tuesday, the Celtics had 10 healthy players available and half of them were with other teams two weeks ago.

Rivers said that practices right now are harder than games because there’s no one to sub out and the new players have to absorb so much information. He pegged the defensive learning curve as a higher priority at the moment. “It’s probably a tie, but I would say defense,” he said. “Not only learning the rotations, but learning the urgency.”

But one thing Rivers isn’t really concerned about is developing a true second unit. With only 21 games left in the regular season, and all of the injuries, there probably isn’t enough time to have one in place. Also, things change in the playoffs.

“There will be eight guys or nine guys [playing], and it’s never going to be five [reserves] on the floor at the same time,” Rivers said. “During the playoffs Paul, Ray, Kevin and Rondo, two of the four are usually on the floor all the time.”

Rivers will mix and match for the rest of the season depending on availability. West is likely to miss the next two games at least, so Arroyo steps into his spot. Wafer is out indefinitely with a leg injury and that opens the door for Pavlovic. With Davis and the O’Neals out, Murphy gets a chance to burn some minutes as he tries to work his way back into playing shape.

In a perverse way, the injuries allow Rivers to see what he has with all his new faces. It also affords him the luxury of experimentation, especially with players like Green who are versatile enough to make them big or small depending on the matchups.

“I like our team,” Rivers said. “I like it when everybody’s healthy. I’ll take us all day. I like that we’re versatile. We showed that the other night in Milwaukee when we went small down the stretch.”

The other big issue for the coach is making sure that he doesn’t blow out his big four. Rondo’s minutes have been a major concern and he would also like to get Allen and Pierce’s time down to a more manageable level, as well.

“Each night you have to choose between Ray and Paul, who’s going to play the 38-minute night and Rondo’s playing the 40-minute nights,” Rivers said. “Kevin’s minutes haven’t changed at all in this stretch. I will not change his minutes ever. But I do want to get Ray and Paul’s minutes down.”

As the playoffs approach, Rivers will be looking for two centers (one starter), a backup guard and two forwards. Here’s a look at how the pieces may fit with the big four:

THE OBVIOUS CHOICES: Krstic, Davis, Green

To say the Celtics have been thrilled with Krstic would be an understatement. He has seamlessly fit into their offensive structure and given the Celtics a perimeter shooting big man and post-up presence. To date, the Celtics have said that Shaq will be back in the starter’s role when he comes back, but that doesn’t seem like such a foregone conclusion anymore.

They are also beginning to tap into what Green can provide behind a quality backup for Pierce. His ability to run the floor with Rondo is a huge benefit and he has also seen crunch-time fourth quarter minutes with the starters. There may be games when Green plays 25-30 minutes and there may be others where he sees just 15-20, depending on the matchups. He’ll have to make the mental adjustment.

Davis has been the one constant bench presence this season and it will be interesting to see how Rivers uses him when he comes back from his strained knee. While his outside shot has come and gone, Davis has played strong defense and also learned how to finish better at the rim. He will have a role. The question is: What role will it be?

THE INJURED: West and the O’Neals

In a perfect world, West would backup Rondo and Allen and provide smart, heady playmaking with tough, aggressive defense. He also wouldn’t be hurt. If his body is able, West will be a major part of the playoff rotation.

One of the justifications the Celtics used for the Kendrick Perkins trade was their record when Shaquille O’Neal was the starter (27-9). But Shaq has been out for over a month with an Achilles injury and the Celtics have kept winning games. He’ll have a role and it makes sense to keep with the starters where he’s comfortable, but Krstic’s emergence has lessened the make-or-break aspect of the big man’s return.  

Imagine if you could acquire a defensive-minded, shot-blocking seven-footer with postseason experience for the playoffs. That’s Jermaine O’Neal. Don’t count him out becoming a P.J. Brown-like X-factor this spring.

Remember, Brown played only 18 regular seasons games and 209 minutes for the 2007-08 championship team and didn’t emerge until the second round of the playoffs. If O’Neal can give them anything – and the Celtics insist he can – he can still be a major part of a playoff run.

DELONTE WEST INSURANCE: Arroyo, Pavlovic, Wafer

Arroyo is here because West is hurt. Pavlovic and Wafer provide depth on the wing if West is unable to play. That the Celtics need three players to cover for him shows just how important West is for the postseason.

These three may not be part of the playoff rotation, but they will serve a valuable purpose during the rest of the regular season and will also be on hand in case of emergency.

THE WILD CARD: Murphy

The first three games in a Celtics uniform have not been kind to Troy Murphy. In 41 minutes he’s taken nine shots and missed them all. He’s appeared tentative and is obviously not in game shape yet.

All that said, 6-foot-11 guys who make 3’s and can rebound are still valuable and the frontcourt injuries allow Murphy the chance to make his case before the playoffs begin. If everyone is healthy, Murphy is a luxury item – the basketball equivalent of a lefthanded pinch-hitter with pop.

As with all the new additions, Murphy makes the Celtics deeper and more versatile. It’s up to Rivers to make it all work.