The formula for getting to the top of the NBA is having big-time players, and right now, the Celtics are lacking in that area.

BOSTON – The agreement that was reached on July 2, 2016 served as a long-awaited breakthrough for the Celtics.

Finally, after a number of failed attempts, the franchise had won over a big-name free agent when they successfully recruited Al Horford to wear a Celtics’ uniform.

After nine seasons with the Atlanta Hawks, Horford made the move north with a four-year, $113 million contract, giving the Celtics a very huge piece to their puzzle.

This was not Dominique Wilkins or Shaquille O’Neal, who joined the Celtics in 1994 and 2010, respectively, well past their primes and lasted only one season each, or Jermaine O’Neal, who played only 49 games over two seasons at the start of this decade.

Unlike those former All-Stars, Horford had a lot left to offer, and the Celtics showed that they could making something significant happen on the free-agent market.

The door was open now and the Celtics had another avenue in which to build their team.

They went back into free agency a year after getting Horford, signing Gordon Hayward to a four-year, $128 million contract after he had spent his entire career with the Utah Jazz.

And after making a trade in the summer of 2017 to land one of the top players in the NBA, Kyrie Irving, the Celtics had reason to believe he would re-sign with them at the end of his contract.

Winning big in the NBA requires star players, and the best path to finding star players is usually free agency. The Celtics had been rebuffed in the past, but now the door had been opened.

They had built a team that looked capable of winning a championship with Horford, Irving and Hayward plus rising stars in Jayson Tatum and Jaylen Brown and the capable Marcus Smart as the nucleus.

But now, after a disappointing 2018-19 season in which everything fell apart, the Celtics are once again on the lookout for stars in order to get back on their feet.

Irving, who has played in the NBA All-Star Game six times, and Horford, who has been selected five times, are expected to exit the Celtics when free agency arrives next Sunday night.

Hayward, who appeared in the All-Star Game in 2017, is struggling to return to form after a gruesome injury suffered in his first game with the Celtics.

So the Celtics are left without a big-time player capable of leading them away from mediocrity.

For proof of how important such a big-time player is, look no further than the Toronto Raptors, the reigning champions who are in possession of their first title thanks in large part of Kawhi Leonard.

In one season north of the border, Leonard delivered, leading the Raptors by the shorthanded Golden State Warriors.

Year after year, the Raptors would be stopped well short of the NBA Finals, then they decided to gamble by trading for Leonard, who had one year remaining on his contract and is probably headed to the West Coast in free agency.

But the Raptors got a championship out of it because they had a superstar player in Leonard capable of getting them over the hump.

It is very rare in the NBA that a team wins a title without that kind of player, and nowadays, it takes two or three of them to get it done.

The Celtics thought they had that formula covered when Horford and Hayward signed and Irving came via the trade that sent Isaiah Thomas to the Cleveland Cavaliers two summers ago.

But it never worked out, starting with the Hayward injury and the growing unhappiness of Irving throughout the 2018-19 season.

The Celtics are going to have money to spend now, but the players being mentioned don’t exactly conjure up a ride to the Finals next June. Center Nikola Vucevic of the Orlando Magic or point guard D’Angelo Russell of the Brooklyn Nets are not going to be difference makers, though the Celtics are confident in their ability to attract the right players.

“Maybe the players and the names on the jersey change, but the approach is the same,’’ said president of basketball operations Danny Ainge following last week’s NBA Draft. “We have a very attractive franchise to play for. There’s a lot of people that will be dying to come play here.’’

The Celtics, who seemed so close to getting back on top of the NBA at this time last year, are going to be waiting for their next run at a championship.

They are going to have to hope that the 21-year-old Tatum can develop into something special and that the 22-year-old Brown can keep elevating his game to give them a one-two punch for the future.

Tatum did not take the next step forward in his sophomore season after having such a promising rookie year, but with Irving out of the picture, his opportunities are going to be on the rise and perhaps his game takes off.

The search for stars is going to take some time after the Celtics thought they were all set in that area.

Jim Fenton may be reached at jfenton@enterprisenews.com. Follow him on Twitter at @JFenton_ent.