With No. 1 pick, everything is in play for Danny Ainge

Celtics president of basketball operations Danny Ainge is in an enviable position.Aram Boghosian for the Boston Globe/File 2016/Globe Freelance

This is the first year that Celtics president of basketball operations Danny Ainge’s draft preparations do not involve guesswork about how teams picking before Boston might proceed. Nor do they involve research about what it could take for the Celtics to move up to a more alluring spot.

Thanks to the fortunate bounces of Ping-Pong balls at the lottery, the Celtics secured the No. 1 overall pick in the June 22 draft. That has put Ainge and his staff in a position that is both unfamiliar and unbeatable.

But that is not to say that Boston’s coterie of decision-makers is simply sitting back and fawning over highlights of the presumptive No. 1 overall pick, Washington point guard Markelle Fultz.

Ainge said he has yet to identify the prospect he would select. And, most importantly, he is prepared to sift through all options that come from being in such a prized position. He said “a handful of teams” has already expressed interest in acquiring the No. 1 choice from the Celtics, and those suitors are probably just getting started.

“The only thing we know for certain is we have the No. 1 pick,” Ainge said in a telephone interview from Las Vegas. “What we don’t know for certain is who that person is yet and what sort of value the pick can get us if we choose to go another direction other than just drafting that pick.”

Over the next few weeks, the market price of the top pick will develop more clarity, although the final cost would ultimately be determined by Boston.

If the Celtics do consider trading the pick — and Ainge emphasized that he would be happy to keep the selection — there is a good chance they would get another first-round pick as part of the package they receive in return. And that is why they are hard at work grading the entire draft, not just the top of it.

“There’s two things that are happening,” Ainge said. “I think the value of [the pick] increases the closer you get to the draft is one, and two is we really need to know the value of the whole draft, because some of the conversations that you have are trading down in the draft and trading picks for players, moving backward and so forth.

“So we’re in the process of evaluating the whole draft, and we’re fielding phone calls.”

The Celtics began hosting draft workouts at their Waltham training facility in early May, though Ainge said most of those involved players the team would likely consider taking with its three second-round choices. Most of the top prospects are completing workouts that are organized and run by their agents.

This week, for example, Ainge and his staff are attending workouts in Las Vegas and Los Angeles.

But Fultz, the top prospect, does not have an agent yet. He mostly has been training in Washington, D.C.

The Celtics had a private meeting with Fultz at the NBA Combine in Chicago in mid May, and Ainge said he will soon try to arrange a visit to Boston for the 19-year-old point guard.

UCLA point guard Lonzo Ball, who is widely rated as the second-best prospect in this class, declined the Celtics’ invitation to come to Boston. Ball’s camp — led by his father, LaVar — has made it clear that it wants him to be drafted by his hometown team, the Lakers, who hold the No. 2 choice.

Also, there are concerns from Ball’s camp that his playing time could be limited in Boston because the deep team that just reached the Eastern Conference finals already has a talented backcourt. Ainge said that Ball’s decision did not frustrate him, however.

“It’s just part of the game,” he said. “You know the rules. You know that the possibility exists.

“Certainly with all the guards we have, we understand how a point guard would prefer to play somewhere else, especially a kid that grows up in LA.

“I’m not offended by any of it. I’m not affected by any of it.

“We’ve followed him in the summer in the past and we’re prepared on who he is, and it wouldn’t affect us in any way. I certainly don’t hold it against him or take it personal.”

Most of all, Ainge said, Ball’s stance is just a sign of the times.

“It’s strategic,” he said. “Whether it’s right or wrong, it’s what his team of people are suggesting to do.

“I think if Paul Pierce were coming out of college and he had a chance — growing up in Inglewood, Calif., and being a Laker fan and with his family in LA — I think if he had a choice of going to Boston or LA, he probably would have chosen LA. But he got drafted by Boston, and now he’s a Boston guy.”