Atkinson, now the head coach of the Nets, imbued Williams with the importance of routine.

“Kenny is one of my all-time favorite people in the world,” Williams said. “I give him a lot of credit for getting me back on my feet when I was down and out.”

By 2015, Williams was the N.B.A.’s sixth man of the year with the Toronto Raptors. But he has never been better, more efficient or more dynamic than he has been in his last two seasons with the Clippers, all at an age — early 30s — when most players see their production begin to erode.

Instead, Williams, who has scored more points off the bench than any other player in league history, has only improved. This season, he averaged 20 points and 5.4 assists in just 26.6 minutes a game. Williams also had the ball in his hands more than ever, with the Clippers running 32.4 percent of their plays through him whenever he was on the court, according to usage-rate statistics compiled by Basketball Reference.

Coming off the bench was never something that he necessarily wanted to do, but Williams has no doubt that the role has helped preserve his career because it has kept his minutes down. He has averaged 24.6 minutes a game over his 14-year career. (LeBron James, by comparison, has averaged 38.6 minutes.)

“It’s given me an opportunity to stretch my career out, and I think I’m in my prime right now, man,” Williams said. “I’m just rolling.”

At the same time, Williams has his quirky customs, which help give him a sense of stability, starting with his game-day breakfast: hash browns, egg whites, French toast and chicken sausage along with a fruit smoothie that he sweetens with honey. He loads up because he knows he won’t eat again for a while.

“I guess my body’s gotten used to it,” Williams said, who will just do the smoothie if the Clippers have an early tipoff.