WALTHAM, Mass. — Much of Danny Ainge’s news conference Tuesday was spent discussing the Boston Celtics’ approach to the upcoming NBA draft.

But Ainge, the Celtics’ president of basketball operations, did take a moment to touch on his team’s current roster — and, in particular, its bevy of young players.

“I think they’re progressing a lot,” Ainge said of the team that made a surprise run to the NBA playoffs this season. “I think they’re all going to have their best years of their career up to this point.

“I think Marcus (Smart) is just beginning to grow. I think that he had a good year as a rookie, but I think he’s going to be much better this year and probably much better next year. I think Kelly (Olynyk) and (Jared Sullinger) and Tyler (Zeller) are all ready to step their games up. I think they made a lot of strides last year. Avery (Bradley)’s continuing to progress. I don’t think he’s even close to what he will be and can be. I think all of our young guys are just becoming better all the time.”

So youthful is the Celtics’ core, Ainge said, that the team actually had difficulty enticing draft prospects to visit its practice facility for workouts this spring.

“I think that we have a lot of good players,” Ainge said. “and that’s why sometimes it’s hard to get some of the draft players to come in. They say, ‘Oh, you have Isaiah (Thomas) and Marcus and Phil Pressey at point guard. Why am I coming in?’ Because they respect those guys. And we have Marcus or Avery and James Young — ‘Why would we come in to be drafted by Boston right now?’ A lot of the guys in the draft don’t really see an opportunity to play for our team, because we have a team that’s loaded with good, young players.”

The Celtics will add a few more young players Thursday night, as they currently own the 16th, 28th, 33rd and 45th picks in the 2015 NBA draft.

Carrying four rookies on a 15-man roster isn’t the most desirable option, however, meaning there is a strong chance Boston either will trade one or more picks or use one of their later selections on a lesser-developed prospect who can be stashed overseas.

“I’d prefer not to add four, no,” said Ainge, who also added the team hopes to trade up in the first round of the draft.

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