WALTHAM, Mass. (AP) – It didn’t take long for Ray Allen to show his new coach what adding a veteran can do for the Boston Celtics.

Holding up his No. 20 uniform on Monday for the traditional news conference photo shoot, Allen displayed it front-facing, so the jersey read “Celtics.” Minutes earlier, when newly minted draft choices Glen “Big Baby” Davis and Gabe Pruitt posed for a similar picture, they held it so their names were shown.

“OK, now turn it around,” Boston coach Doc Rivers chided them. “That’s the only name that matters.”

The Celtics acquired Allen on draft night last week for the fifth overall pick, which turned out to be Georgetown forward Jeff Green, along with Delonte West and Wally Szczerbiak. The move signaled Boston’s intention to build a playoff contender around Paul Pierce and Al Jefferson, rather than adding more young pieces to an already young team.

“When you’re playing with veterans, they know what to do. It’s going to make it a lot better,” Rivers said at the team’s practice facility. “They’re professional. It helps everyone. It helps Ray having Paul. It helps Paul having Ray. It helps Al.”

Rivers said another draft choice might have helped out the starting lineup. But by adding Allen, a seven-time all-star, instead of another highly touted youngster, he also gets a veteran presence that can carry the team when Pierce needs a rest.

“When Paul comes out, you have Ray on the floor,” Rivers said. “Hopefully, we won’t have the times any more when Paul sits for 30 seconds and we’ve got to bring him back into the game.”

The Celtics picked Pruitt, from Southern Cal, with the 32nd overall pick, and then grabbed Davis with the 35th selection that they got back from Seattle with Allen. They’re both expected to leave on Tuesday for the Las Vegas Summer League.

“It’s an honor for me to play with Ray Allen and Paul Pierce, two guys who are really supreme at their positions,” Pruitt said.

Davis was a star of LSU’s Final Four run in 2006 and nearly declared for the draft after last season. But he returned for his junior year, and his stock dropped when his numbers dipped and missed several late games with a strained quadriceps.

Davis, who led the Southeastern Conference in rebounding last season while averaging almost 18 points, admitted being disappointed that he wasn’t drafted in the first round, but vowed to make the most of it.

“Everybody wants to go in the first round. … In spite of what happened, I have the chance and I’m in the NBA now,” he said.

“It just means so much, being in basketball, to hear the ‘Boston Celtics.’ You think about immortality, all the championships, being a part of this organization is a blessing. I”m happy they gave me the chance, happy they believed in me.”

Allen, who turns 32 next month, averaged a career-high 26.4 points last season, his 11th. He had surgery on April 7 to remove bone spurs in both ankles, but said Tuesday his feet were “perfect … like having two new pairs of feet.”

“Ray’s a fantastic player coming off one of the best years of his career,” Celtics basketball boss Danny Ainge said. “He’s a player we as an organization has tried to acquire many times in the past. We think he’s a great fit.”

Allen played at Connecticut in college and was drafted by the Minnesota Timberwolves with the fifth overall pick in 1996, then traded to Milwaukee. One pick later, the Celtics took Antoine Walker.

Allen was traded from Milwaukee to Seattle in 2003 and said the past 4 years was like “being in the doldrums.” But now he’s so excited to be back in the Northeast.

“This was a long time coming,” Allen said before holding up his jersey to show off his new team.

“I love that,” Rivers beamed. “Did you see that?”