SAN ANTONIO — Overtime victories on back-to-back nights in different cities left the San Antonio Spurs spent.

Fidgeting with a game book, Danny Green widened his gaze upon noticing he hadn’t played 38 minutes “in a long time.” To Green’s right, LaMarcus Aldridge slouched in his locker wrapped in towels and jokingly wondered whether he’d “be able to walk” the next day.

Across the room, Kawhi Leonard stood up and pulled on a hoodie.

“It is what it is,” he said. “Everybody plays back-to-backs.”

It’s tough to complain when this is what Leonard craved all along.

From David Robinson to Tim Duncan, Duncan to Manu Ginobili and Tony Parker, and now on to Leonard, the Spurs continue to transition from one superstar to the next, all the while never missing a beat. San Antonio clinched its 20th consecutive postseason berth Saturday by defeating the Minnesota Timberwolves 97-90 in overtime, and they accomplished this latest milestone for the first time in 19 seasons without Duncan.

The Spurs belong to Leonard now, and he’s snatched the proverbial torch from The Big Fundamental on the way to setting the league on fire.

“They’ve been very smooth,” Spurs coach Gregg Popovich told ESPN.com in explaining the team’s various transitions over the years. “The fact they’ve been so smooth is just a testament to the character of the people involved. Their awareness of the situation they’re in, their ability to have gotten over themselves and know where they are at that point in their career, and to look around and be knowledgeable enough to know what the newcomer can give — well, that’s what we’ve had all the way down the line. Those guys understanding that and wanting that to happen.

“They’d rather play for 10 more years, but realize that’s not going to happen. When they see the obvious abilities of the younger guys coming along, they’ve actually helped them and created an environment where they can be successful. So, it’s really a tribute to their character and their understanding of what’s going on.”

Not prone to hyperbole, Popovich apparently knew all along what the Spurs had in Leonard. In responding to a question from a fan in a Spurs mailbag going into Leonard’s second NBA season in 2012, Popovich wrote: “I think he’s going to be a star. And as time goes on, he’ll be the face of the Spurs I think.”

That time is now.

MVP candidate

Leonard is one of just three players in league history — Michael Jordan and Hakeem Olajuwon are the two others — to win NBA Finals MVP and NBA Defensive Player of the Year (twice). And he joined more elite company on March 1 with a 31-point night against Indiana, making the forward the fourth player in franchise history with 20 outings or more scoring 30-plus points in a single season (he now has 23 after Monday night’s heroics vs. Houston), joining George Gervin (7), David Robinson (4) and Tim Duncan (1). In the process, Leonard backed down Paul George to knock down the winning basket of a 100-99 thriller. The shot improved Leonard to 3-for-5 over the past two seasons on potential go-ahead attempts in the final 5 seconds of a game, which registers as the best percentage in the NBA on such shots (minimum five attempts) in that span.

Leonard relishes those opportunities.

“I work all summer and throughout the whole season to be prepared for the challenges that I have to face,” he said. “You just have to keep going. If you play bad or go 0-for-10 in the fourth, whatever, you’ve just got to keep pounding and going and going, and not give up if you want to become that guy.”

That’s one attribute Popovich loves about Leonard. The coach said very few athletes possess that mentality.

“He handles the responsibility well. Most importantly, he knows that things are not always going to be positive in the sense of win, lose, or make or miss a shot,” Popovich said. “And that’s what’s been very good about him because some people don’t understand that, and they’re afraid to have that responsibility night after night after night. You think of Kobe [Bryant], you think of LeBron [James], you think of Michael [Jordan], and you think of all these guys that had to do that. They got to the point where they realized the shot wasn’t going to go down all the time, or they might even turn it over. But they come right back. They don’t shy away the next time. They want it again. Kawhi has that knack. He has that ability, and that’s important because very, very few people have that.”

Leonard ranks No. 2 in the NBA in Player Efficiency Rating (28.68). Oklahoma City’s Russell Westbrook owns the best PER (29.81), though Leonard’s Spurs are winning games at a much higher rate than Westbrook’s Thunder (.790 for the Spurs compared to .556 for the Thunder).

Leonard also ranks third in win shares (11.3), just behind Harden and Kevin Durant. Leonard and Durant are the only players in the league to rank in the top three in both win shares and PER, and they are the only two players to rank in the top 10 of both offensive and defensive win shares.

Leonard is averaging a career-high 26.1 points per game, and according to Elias Sports Bureau, is one of just three players to increase his scoring average in each of the past five seasons, joining Gordon Hayward (six straight) and Jimmy Butler. Leonard has also produced five games this season in which he poured in 30 points to go with four steals or more. No other player has produced more than two such outings.

“He is a really unique player,” New Orleans Pelicans coach Alvin Gentry said. “You don’t want to say Michael Jordan, but it’s that type of situation, where you’ve got a really, really good offensive player and a tremendous defensive player. He impacts the game. There’s very few guys in this league that can impact the game on both ends of the floor like he can. For the last 15 years, they’ve been flying under the radar. So, it’s nothing new. They’re just a very good team, and they got a very great player. And, yeah, where they are record-wise and everything, he definitely has to be heavily in the conversation for MVP.”

Leonard, meanwhile, isn’t concerned about where he’ll fare in a race that also includes James Harden, James, Durant and Westbrook. In fact, Leonard said “it’s pretty easy” for him to block out the outside noise.

“I don’t watch ESPN, don’t listen to the radio,” Leonard said. “I just go home and deal with my family.”

But even they have to be discussing what’s expected to be a heated MVP race, right?

“It depends on who I’m with, but we don’t really talk about it,” Leonard said. “I’ll just be chillin’. We could talk about it, but we’ve got to wait and see really.”