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.

Ken Blaze/USA TODAY Sports

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 for the first time in 19 seasons they accomplished the feat without Duncan.

The Spurs belong to Leonard now, and he has 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, along with Michael Jordan and Hakeem Olajuwon, to win NBA Finals MVP and NBA Defensive Player of the Year. He joined more elite company on March 1, when he scored 31 points against Indiana to become the fourth player in franchise history with 20 or more games with 30-plus points in one season, joining George Gervin (7), David Robinson (4) and Tim Duncan (1). Leonard now has 23 such games after Monday night's heroics vs. Houston.

Against Indiana, Leonard backed down Paul George to hit 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.

"He is a really unique player. 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." Pelicans coach Alvin Gentry on Kawhi Leonard's impact on the NBA

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 at 28.68, behind Oklahoma City guard Russell Westbrook's 29.81, though Leonard's Spurs are winning games at a much higher rate than Westbrook's Thunder -- .790 for the Spurs compared with .556 for the Thunder.

Kawhi Leonard lets loose the winning shot over Indiana's Paul George, capping a 31-point effort in the Spurs' victory on March 1. Soobum Im/USA TODAY Sports

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, he 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."

Last year's runner-up in the MVP voting, Leonard said he 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."

Waiting to be 'the guy'

Waiting seems to be what Leonard has done most of his career in the shadow of Duncan, a future first-ballot Hall of Famer. But Leonard never became impatient.

"I was just coming in and doing my role, and that's basically it," Leonard told ESPN.com. "I was working, hoping that I could get an opportunity to be able to lead. That's all it was, just being focused, and just trying to be the best player I could be at the time."

Teammates certainly took notice.

"It's been good to watch, because he's taken the necessary steps to be able to get to where he is today. He didn't jump any steps," Patty Mills said. "He went through the route in terms of learning from Timmy, learning from Tony [Parker] and Manu [Ginobili] and understanding what it takes to be able to be who he is now. He really learned and evolved into the player he is by doing all the little things, understanding what this culture is all about, understanding who he is as well in trying to work all that in together.

"So it's been good to watch, because he's deserved it. He really has. He's understanding what his expectations are from the coaching staff and from the whole organization, and he's just been a professional about it. He's fallen into that category of no hurrah like Timmy, and has just gone about business day in and day out. I wasn't here at the beginning years of Timmy, but I've heard the stories about him just getting up every night for a game and producing. Well, that's what Kawhi has been doing this year. In that sense, it's really impressive to watch."

After San Antonio's loss to the Los Angeles Clippers in the first round of the Western Conference playoffs in 2014-15, Leonard discussed with Popovich the improvements he needed to make for 2015-16. Popovich, expecting opponents to start regularly fronting and double-teaming Leonard, asked him to become more comfortable in the post.

So Leonard learned to improve his decision-making in the post and spent that summer watching film of Charles Barkley to learn all the aspects of post play.

After last season's loss to Oklahoma City in the Western Conference semifinals, Leonard spent the summer improving his ball-handling and moves on catch-and-shoot situations.

All the work continues to manifest itself on the court.

"I've been here watching him throughout the years blossom and grow, which has been kind of fun for me and interesting," Green said. "Each year, he's always come back with something new, something better, and he's always gotten better. He's worked on his game. He has more poise and is better at decision making. You can tell he wants to be one of the greats in this game, and he works at it."

Popovich agreed, saying Leonard has handled all the new responsibilities "fantastically."

"He's really quiet as we all know, very respectful as we all know. But he has a hunger in him as far as wanting to be a great player," Popovich said. "Everything that I've given him, he's taken it seriously, and he handles criticism because he wants to learn. He just adds something to his game every season."

Having been involved in San Antonio's continuous passing of the torch since the age of 19, Parker, now 34, is fine with Leonard now carrying the load. Such is the circle of life in San Antonio.

"I love it," Parker said. "I think the evolution of anybody's career is as you get older, you have to adjust to who are the main guys on your team [and] try to be a factor just like Manu did, just like Timmy did. I just try and do the same thing."

Someday, Leonard will find himself in a similar situation. But until then, the plan for Leonard is to continue to ascend in his new leadership role, and hopefully -- like Robinson, Duncan, Ginobili and Parker before him -- take the Spurs on a few more championship runs.

After all, this is what Leonard has always wanted. Leonard let out a rare laugh when asked whether the enormity of this current undertaking ever scared him.

"There's nothing to be scared of," he said. "We're playing basketball. The only thing that could happen is you failing. But as long as you're going hard, there's nothing to be scared of for me. I don't know what there is to be scared of."