By Brian Robb, CBS Boston

BOSTON – For the past two seasons, Jared Sullinger did not have to worry much about earning time on the floor. The former first-round pick showed plenty of promise in his rookie year, and that alone was enough to guarantee the 6-foot-9 forward a steady stream of minutes on a rebuilding squad in transition.

Unfortunately for Sullinger, that dynamic has changed quite abruptly heading into the 2015-16 season. Thanks to the additions of Amir Johnson and David Lee to the roster, and a surprise run to the postseason last year, the Celtics are no longer looking just to develop youth: They want to win games and are committed to doing it with the best bodies available.

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Sullinger is surrounded by four talented veteran bigs in the frontcourt in Kelly Olynyk, Tyler Zeller, Lee and Johnson. For the first two preseason games in Europe, he played behind all four, sharpening the possibility that the 23-year-old may be the odd man out in the rotation at the start of the regular season.

Brad Stevens spoke about what he has in mind for his frontcourt and the difficulty of juggling a collection of bigs that could all be playing.

“My thought right now is we wouldn’t play more than four on most nights,” Stevens said at practice Monday. “So whoever those four might be may depend on the night, it may depend on how they are playing, it may depend on who is healthy. All that other stuff.

“That’s the challenge with our team right now. All the guys that are in that mix have been great. Not only some of the time, but all the time. They’ve all been really good about it, they all understand it. It is what it is. I think we all realize that we have good players, up and down that group. I’ve said this before: Some of it is going to be determined on who fits well with other guys to make those other guys better and that’s a big part of this.”

It will be up to Sullinger to prove that he’s an ideal complement for Stevens to turn to as he finds fits for lineups. Despite being the fifth big off the bench overseas, he did that during his first two games in Europe. The former Ohio State star looked sharp offensively, producing 10.5 points and five rebounds in only 13 minutes per contest. He also scaled back his three-point shooting compared to last season, taking just one of his 16 field goal attempts from beyond the arc.

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The best chance Sullinger probably has for regular minutes is beating out Olynyk as a fourth big, but the power forward is taking a team-oriented approach when talking about the new dynamic.

“[I feel the minutes crunch] for sure,” Sullinger said. “At the same time, I’m not here to make it a rivalry between me, Amir, Tyler, Kelly, Jonas or D-Lee. My biggest thing is I just want us to win. If that’s me cutting back my minutes, that’s me cutting back my minutes, but the ultimate goal is to win basketball games. That’s the ultimate goal as a team, as a unit. Going forward, it’s a long season so you never know what’s going to happen. You just have to stay ready.”

Lee dealt with the dynamic firsthand last year in Golden State when he lost the majority of his playing time to teammate Draymond Green. He pointed to the value he saw in the competition there and how it could translate well in a similar situation for Boston’s bigs this year.

“We’re obviously competing every day and it makes everybody better when that happens. I was fortunate enough to be a part of that last year in Golden State and it made everybody better when we were competing and we had so much depth. There are guys that have good days every single day and it challenges the other guys to have a good day the next day. That’s how everybody gets better and that’s how you ultimately become a better team throughout the season,” Lee said.

Lee later added: “We’re legit 2-deep, sometimes 3-deep at every position. And if we can use that to our advantage by everybody playing at a feverish pace and challenging one another, and when you’re ready to slow down, putting your hand up and the next guy comes in and continues right where you left off. That can be our advantage against teams that are not going to play as many guys. Let’s use that as a strength. I think that that’s going to be a good thing for us this year.”

Despite the advantages of the situation, some player is going to draw the short straw at the start of the season. After a couple weeks of camp, it looks like it’s Sullinger. Now, it’s up to the big man to find his way up from the bottom of the depth chart.

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Brian Robb covers the Celtics for CBS Boston and contributes to NBA.com, among other media outlets. You can follow him on Twitter @CelticsHub.