Boston Celtics’ Malcolm Brogdon (13) passes the ball against Utah Jazz’s Walker Kessler (24) during an NBA game last month in Boston. AP file photo

BOSTON — When the Celtics traded for Malcolm Brogdon last July, president of basketball operations Brad Stevens had to be up front with the veteran guard.

Brogdon had been a starter for most of his first six seasons in the NBA. But the Celtics had a specific idea with him. They didn’t need a starter, or for Brogdon to be a top option. Their NBA Finals run exposed a need for a playmaker off the bench, and they viewed Brogdon as the perfect fit.

“They told me straight up, you’re going to come off the bench,” Brogdon recalled on TNT Thursday night. “We have a formula here, we have something that works. We think you can be a key piece and really help us, but your role is going to be coming off the bench, and I chose to embrace it.”

Brogdon, after a few underwhelming, injury-riddled seasons with the Pacers, saw it as an opportunity to join a championship team, and still be a major contributor. He not only embraced the sacrificial role, but excelled in it. On Thursday, Brogdon was recognized as the NBA’s sixth man of the year, edging New York’s Immanuel Quickley for the award.

Brogdon received 60 first-place votes (out of 100), finishing with 408 points to Quickley’s 326. He became the first Celtic since Bill Walton in 1985-86 to win the award, which is named after Celtics great John Havlicek.

“This is such an honor,” Brogdon said as he accepted the award on TNT’s pregame show.

“From day one, Malcolm has eagerly embraced his role as a game-changer off the bench,” Stevens said in a statement. “His emphasis on winning has been reflected daily in his work, his play, and his selflessness. Malcolm winning the award named after John Havlicek, an all-time Celtic, could not be more appropriate.”

Brogdon may have had a reduced role alongside stars Jayson Tatum and Jaylen Brown and fellow guards Marcus Smart and Derrick White, but his impact proved to be as significant as promised when the Celtics made the trade last summer. He was the only player in the NBA to finish top three in scoring (14.9 points), rebounding (4.2) and assists (3.7) among players who didn’t start a game. He finished the regular season fourth in the league in 3-point shooting percentage at 44.4%, a career high.

But more importantly, he embraced the responsibility of leading the Celtics’ second unit, which made the difference in victories all season long.

“I thought Malcolm taking on the identity of the second unit, getting with the patience of sometimes finishing halves, sometimes not,” Celtics coach Joe Mazzulla said. “Sometimes finishing games, not finishing games. I thought just, he handled it with an open mind, he handled it with a humility and kind of regardless of what his sub pattern or what he was doing, he just played. And we’re grateful for that.”

Brogdon said that his willingness to accept this role with the Celtics was rooted in humbling experiences to begin his NBA career, first with the Bucks and then with the Pacers.

“I had the pleasure of playing with Giannis (Antetekounmpo), one of the best players in the world,” Brogdon said on TNT. “Which was, for me, coming out of college I was All-American, I had good accolades. But you have to check your ego at the door, especially when I got to Milwaukee. And then I go to Indiana and me and (Domantas Sabonis) are really running the show there. And my last two seasons there weren’t super successful.

“So for me, that was another gut check for me in understanding, maybe I’m not a No. 1 guy. But I can be a great No. 2, 3 or 4. And then coming to Boston, and playing behind J.T. and J.B., these guys that are proven All-Stars and soon-to-be All-NBA guys. It’s definitely a good fit for me.”