The Celtics will almost certainly not add four rookies to next season’s roster. But having four picks would give them myriad options. They could package them and move up in this draft, they could ship some out for future picks, and, of course, they could use these valuable pieces to acquire one of the game’s transcendent talents, Anthony Davis, who is likely to be traded at year’s end.

Based on various pick protections, the Celtics could have as many as four first-round choices in June. So Boston’s executives have kept one eye on their team, and one on the fortunes of the Kings, Grizzlies, and Clippers.

During this uneven Celtics season, some of the angst has been allayed by the fact that the future remains rife with possibility. Danny Ainge has stockpiled future assets, and this summer Boston could be in position to cash in some chips.


Now, as the end of the regular season nears, there is some clarity about what picks might actually be coming Boston’s way, and how valuable they might be.

The Grizzlies pick

The Celtics will receive the Memphis pick this season as long as it falls outside of the top 8. If it does not, it will roll over to next year, when it would be top-6 protected before becoming fully unprotected in 2021. While the possibility of getting a mid-to-late lottery pick this year might sound enticing, league sources have said that the clear preference within Boston’s front office is for the choice to roll over. The Grizzlies have some good young pieces, but they traded away Marc Gasol last month and their best player, point guard Mike Conley, is aging and injury-prone. The belief and hope in Boston is that by 2020, this pick could have tremendous value.

When Memphis surged toward the top of the West at the start of the season, there was some concern that a worst-case scenario might be unfolding: Not only would the pick convey this year, but it would end up as a late first-round choice. But that unease was short-lived, as the Grizzlies promptly tumbled.


It had then appeared quite likely that the pick would not convey this year, but Memphis is on a three-game winning streak that has coincided with freefalls all around it. The Grizzlies entered Tuesday with the NBA’s seventh-worst record, just a half-game behind the Wizards and 1½ games behind the Pelicans.

It is no secret that lottery teams often try to improve their draft positioning by losing, but it’s unclear how the Grizzlies view their unusual predicament. They may prefer to get out of the bottom eight so they can fulfill their obligation to the Celtics and move forward, or they may want to just try to reload now, even if the choice is not as high as it will be in the future.

The lottery system was reformed this year, so the top four selections will now be decided by Ping-Pong balls rather than just the top three. And the odds were smoothed so they are not as good for the worst teams, a half-hearted attempt to discourage tanking. So it’s worth remembering that even if the Grizzlies finish with a record among the 5th-8th worst, they could fall out of the bottom 8 — where their pick would go to the Celtics — if teams behind them jump into the top four.


By the same token, the Grizzlies could finish above the bottom 8 but still hold onto their pick by vaulting into the top 4 picks via the lottery. As of Tuesday night, Memphis had a 14.2 percent chance of getting a pick outside the top 8. But if it moves by just one spot, from seventh to eighth, that number would mushroom to 39.3 percent.

If the Grizzlies finish in the No. 9 spot, they would have a 20.2 percent chance of getting some lottery luck and sliding into the top four.

The Kings pick

This was once Boston’s crown jewel. The Celtics sent the No. 1 overall pick in 2017 to the 76ers in exchange for the No. 3 overall pick and a future first-round choice. The deal has already been a boon for Boston, which took Jayson Tatum while Philadelphia chose Markelle Fultz. But it will get even better.

The Celtics were to receive the 2018 Lakers’ pick — which Philadelphia had previously acquired — last June if it fell in the 2-5 range. But the pick did not convey, putting Boston in position to get the top-1 protected 2019 Kings pick that the 76ers owned.

But Sacramento has been one of the league’s most surprising teams this year. It now looks like the Kings will fall just short of a playoff berth, but at 33-33, the selection is unlikely to be as high as the Celtics once hoped. Sacramento is in the No. 14 draft spot, and the 32-35 Timberwolves could be the only team still in position to pass them. If the Kings maintain the 14th-worst record, Boston could still hope for some lottery luck, as it would have a 1.9 percent chance of landing in the 2-4 range.


The disaster scenario for the Celtics would come if the choice turned into the No. 1 overall pick, in which case the rival 76ers would get it, and Boston would receive Philadelphia’s late first-round choice instead. But there is just a 0.5 percent chance of that happening.

The Celtics used the No. 3 pick in the 2017 draft — acquired from the 76ers for the top pick — to land Jayson Tatum. File/Matthew J. Lee/Globe Staff/Globe Staff

The Clippers pick

The Celtics will receive the Clippers’ pick this season as long as it does not fall into the lottery. When Los Angeles was active at the trade deadline, including shipping its best player, Tobias Harris, to the 76ers, it appeared to increase the odds of slipping out of the playoffs. But the Clippers received substantial returns in their deals, with Landry Shamet, Ivica Zubac, Garrett Temple and JaMychal Green all playing at least 18 minutes per game since arriving in LA.

After Monday’s demolition of the Celtics, the Clippers are now all but a lock to reach the playoffs, meaning that their first-round pick will go to Boston this year. If it does not, the Celtics would get another chance at the first-round choice next year before it becomes a 2022 second-round pick, which would not be ideal. Once Los Angeles clinches a playoff berth, though, the Celtics would like to see it start losing ground so the choice improves a bit. If the season ended Tuesday night, Los Angeles would fall in the No. 20 overall slot.


Ex-Celtics can Doc Rivers still impact Boston’s future, depending on where his Clippers land in the draft order. File/Rick Bowmer/AP/Associated Press

The Celtics pick

The Celtics also have their own first-round pick. Even though just 14 games remain, Boston is in a congested draft range near the end of the first round, with the pick potentially falling anywhere from 18-26. The Celtics entered Tuesday night in the No. 21 slot, just one and a half games behind the 76ers, Pacers and Rockets at the top end of the range, and three games ahead of the Jazz at the bottom.

Interestingly, Boston’s playoff seeding is all but locked into the 3-5 positions in the Eastern Conference. Boston currently sits in fifth place and can fall no further, and if it reaches the point where this becomes the most likely landing spot, the Celtics would actually be well-served to begin a mini tank job of their own and allow some Western Conference teams whose records don’t affect their seeding to pass them in the draft pecking order.

Other relevant picks to watch

The only bad news for the Celtics is that due to the various protections, there is no way they can get the No. 1 overall pick. The same cannot be said of the Lakers and Knicks, the two teams most likely to challenge them in the Davis sweepstakes.

The 13-54 Knicks have the NBA’s worst record by 2½ games. But that is not as important to the lottery odds as it once was. Under the reformed system, the teams with the three worst records will all have a 14 percent chance of securing the first pick. If the Knicks had the worst record last year, they would have had a 25 percent chance of getting it. If New York finishes last, it will have a 52.1 percent chance of getting a top-four pick.

One month ago, the Lakers seemed primed to push for a playoff spot. But their season has unraveled since then and they are bound for the lottery. Los Angeles entered Tuesday on a five-game losing streak and could fall as far as the sixth-worst record by season’s end. That would give it a 37.2 percent chance of getting a top-4 pick, and a 9 percent chance of winning the top choice.

Adam Himmelsbach can be reached at adam.himmelsbach@globe.com. Follow him on Twitter @adamhimmelsbach