Last July 1, the Celtics sent a deep and determined delegation to Atlanta to try to woo free agent big man Al Horford. They talked to him about their bond, and the Celtics’ rich history and rabid fan base. But they also talked to him about their vision.

Coach Brad Stevens laid out a thorough plan that showed all the ways the Celtics would utilize Horford’s unique skill set. Sure, they wanted him to score and get rebounds, but they also saw him as a gifted playmaker. They wanted him to be the rare 6-foot-10-inch basketball player who can help run an offense.

“Brad was very specific in how he wanted to use Al and play him,’’ president of basketball operations Danny Ainge said. “And that was one of the reasons why Al really appealed to us, was his ability to handle the ball and make plays and be involved in the offense, whether he was getting shots or not. He could be a threat in so many ways.’’

“I was excited about the chance to make decisions and make plays,’’ Horford said, “just make the game easier for everyone.’’

This season Horford has helped direct the Celtics’ high-powered offense, and he has been even more efficient and precise than most expected. While on the court, he has assisted on 23.8 percent of the Celtics’ baskets, blowing away the 14.1 percent assist rate he compiled over nine seasons with the Hawks.

Horford is averaging 4.9 assists per game, which is third in the NBA among players 6-10 or taller, trailing only Clippers forward Blake Griffin and Bucks guard Giannis Antetokounmpo. Horford also is one of just three players averaging at least 4.9 assists and fewer than 1.8 turnovers per game. The others — Ish Smith and Jameer Nelson — are true point guards.

“I just think his presence makes unselfish basketball contagious, because he always makes the right play,’’ Stevens said. “He probably looks to over-pass at times out of the post. But being able to play through him in the post has been huge for our team, and we need to continue to do that.’’

Guards are usually the primary playmakers, most often creating assists by knifing into the lane, drawing an extra defender, and finding an open teammate. Horford’s passes tend to come from a more stationary position.

He receives the ball in the post or beyond the 3-point line, and often makes the next play without even dribbling. In the post, he squares up to the basket and swings the ball like a pendulum, looking for a fresh angle as he waits for a play to develop.

Much of the Celtics’ offense is predicated on sharp, purposeful cuts. In the second quarter against the Nuggets on Friday, for example, Horford caught a pass beyond the left block, turned and waited for Marcus Smart to streak toward the hoop, before he zipped a pass to him for a layup.

“When we cut, we create confusion,’’ Horford said. “So if they’re trying to trap, if our guy is cutting all of a sudden and they’re not talking, we’re getting layups. And our guys do as good of a job as I’ve seen of cutting off the post and getting layups.’’

Horford can sense when these plays begin to give defenders pause. When they are leery of being beat for a backdoor layup, they might not play their man as closely, and that could create opportunities elsewhere.

Some Celtics fans have become frustrated with Horford’s lack of scoring punch, particularly in the interior. He is averaging 14 points per game, and 32.9 percent of his field goal attempts have been 3-pointers, up considerably from his previous career high of 24.4 percent set last year. Horford said he is not looking to shoot more 3-pointers; it is just that his role in the offense often sets him up in that area.

“I keep studying the film, and there’s definitely some opportunities where I can be more aggressive and score the ball more, but it’s really reads,’’ he said. “Sometimes I feel like I have a good shot, and then I see somebody that has a better shot. And honestly, I just want to win and I want the guys to feel good and for us to play at a high level.

“So sometimes I understand that I may not get as many shots as I want or have the opportunity to, because I know I’m going to get somebody else something. There’s a fine balance. There are some games where I will look to be more aggressive and score more, and then there are games that I want to be more of a playmaker.’’

Even though Horford has not been a dominant scorer, he is quietly in the midst of one of the most complete seasons in NBA history. He is averaging 14 points, 6.6 rebounds, 4.9 assists, and 1.4 blocks per game. If those numbers hold over the final 16 games, Horford would become just the ninth player in NBA history to finish a season at those levels.

“I think his unselfishness at his age and stage and accomplishment level and everything else demands that everybody else plays [unselfishly] and moves it to the next guy,’’ Stevens said, “and I think that’s a great leadership quality of his.’’

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