The jerseys that hang in Adrian Peterson’s locker could be in Canton, Ohio. They belong to Tom Brady, Eli Manning, Christian McCaffrey and who knows how many other stars. But it just means that players of that caliber — Super Bowl MVPs, Hall-of-Famers-to-be and the best at their position at the moment — have asked for, and likely received, a Washington Redskins No. 26 in return.

“It’s always an amazing feeling when you got guys coming up to you,” Peterson said. “They just kind of pay their respects, and maybe request a jersey. I done said yes to about 30 requests this season, and that’s not including the guys here in the locker room.”

It’s the end of the latest lost season in Washington, with the only intrigue about Sunday’s finale in Dallas involving whether the Cowboys can sneak into the playoffs and save the job of Coach Jason Garrett. Washington, again, is a national afterthought, playing for next year before next year begins.

But in the course of any miserable season, there are little elements to appreciate. Peterson is Washington’s, here and now. It’s a wonder he doesn’t walk around in a gold blazer all day long. In the past 50 seasons, here are the players who were at least 33, rushed for at least 800 yards and averaged at least four yards per carry: Marcus Allen once, and Adrian Peterson twice — each of the past two seasons, both in Washington.

“I compare his 34 to 26 or 27,” said fellow running back Chris Thompson, whose locker is next to Peterson’s.

It’s a reasonable assessment. Peterson came to Washington in the middle of the preseason of 2018 when he was out of work and when, frankly, it would have been reasonable to next hear from him at his induction to the Pro Football Hall of Fame. He was available because, in 13 games with three teams over the previous two seasons, he had averaged just 3.1 yards per attempt. Running backs age fast, and he was aging. He seemed on the edge of the cliff that claims back after back.

Peterson came to Washington only because Derrius Guice, then a rookie, blew out his knee in an exhibition game. Now, Guice is down again; at 22, he’s managed to be healthy for five games over two seasons. Peterson, at 34, is still standing.

“I feel like I have a lot left in the tank,” he said.

At some point, the tank has to empty. But when will that happen? I was a doubter when Peterson arrived, not just because of those iffy numbers in his final season with Minnesota and then a year split between New Orleans and Arizona, but because of what history tells us about old running backs. Over the previous half-century, the only backs to have gained 1,000 yards at age 33 or older were John Riggins (twice), Frank Gore and Franco Harris. And then Peterson did it for Washington in 2018.

Barring a 180-yard day in Dallas on Sunday, that won’t happen again. Still, think of the arc of Peterson’s season. When it opened in Philadelphia, he was healthy but in street clothes for the first time in his career. Jay Gruden, then the coach, preferred Guice, and it was reasonable to wonder whether he even wanted Peterson on the roster because after the game he offered a candidate for quote of the year:

“If we have a game where we think we can run the ball 55 times in a game in an I-formation,” Gruden said, “then sure, I’ll get him up.”

At the time, I thought it was both funny and reasonable. Guice represents the future. Peterson seemed part of the NFL’s past.

Yet I’m done doubting Peterson, finished putting parameters on what he might do. That’s in part because of what we see on Sundays, the running for impossible yards between the tackles, avoiding direct contact, and squeezing out more mileage after contact. But it’s also because of what you hear about how he prepares.

“His training is on a different level,” Thompson said. “He hasn’t even changed anything that he was doing in his 20s.”

In the offseason, Peterson invited Thompson to join him in Houston for preparation. In one workout, Peterson jumped in a workout pool. He turned up all the underwater jets to offer resistance. He cranked the underwater treadmill all the way up. And he ran for 20 minutes.

“I tried to do it,” Thompson said. “And I could not. I was like, ‘How is he able to do this?’ ”

Thompson has also watched how Peterson manages his body during the season. Typically, Peterson takes a day off practice during the week, reasonable maintenance.

“But other than that, it’s full-go at full-speed,” Thompson said. “Sometimes I think it’s difficult for the O-line and for him, because they’re going at a different speed in practice and he’s fast, fast, fast. His walk-through is at like 80 percent. For him, it’s a constant feel and telling them, ‘This is going to look like this. This is how I’m going to move. I want my line to know that I’m doing this. I want my receivers to know that I’m doing this.’ ”

The result, in a disastrous season for Washington, is another admirable season for Peterson.

“Just hungry, continue to get better,” Peterson said, “and continue to chase that championship.”

Uh, okay, here’s where Peterson loses me. Washington will finish the year either 3-13 or 4-12. It needs a new coach, and who knows who will be running the front office. Peterson is under contract for 2020, when he’ll be — gulp — 35. A championship? He’s running out of chances.

“You’re telling me I’m running out of chances, huh?” Peterson said.

Fair enough. Who’s to say? He has 14,138 yards rushing, and who knows how many more? The list of players who have gained more on the ground in NFL history: Emmitt Smith, Walter Payton, Gore and Barry Sanders. It’s why Case Keenum, the journeyman who will start the finale at quarterback, said this week, “I’m going to get to tell my kids I handed off to Adrian Peterson.”

And we’ll get to say we watched him. These aren’t his most productive years, and this isn’t the way any historic figure should head into the sunset. But neither is this Willie Mays with the Mets.

Adrian Peterson isn’t hanging on. He is moving forward. In a Washington season that has provided almost nothing to appreciate, we can watch No. 26 run the way he does and understand why, when Sunday’s game is over, several Cowboys will line up to shake his hand, to kiss the ring, and to maybe, just maybe, get a signed jersey.

For more by Barry Svrluga, visit washingtonpost.com/svrluga.

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