Craig Kimbrel throws during the ninth inning of Game 1 of the World Series in 2018. (Matt Slocum/Associated Press)

A few days ago, Washington closer Sean Doolittle noticed a social-media buzz that his Nationals might be one of three teams, including the Philadelphia Phillies and perhaps the Atlanta Braves, that were interested in Craig Kimbrel, the unsigned free agent reliever who has the lowest ERA in the majors in the past 100 years.

“I went into [Manager] Davey Martinez’s office and said, ‘I have an empty locker next to me, right between me and Trevor Rosenthal,’ ” Doolittle said, grinning. “If we get him, I would be the first guy at the door to welcome him.”

Because Kimbrel is a man without a team, that’s not tampering — unlike Phillies outfielder Bryce Harper saying he’d like Los Angeles Angels star Mike Trout to join him in 2021.

“I told Davey that I had some incentives in my contract [for saves], but a World Series check goes a long way,” Doolittle said. “I love closing. But I love winning more.

“We’ve had a great offseason. . . . We do feel like we have three closers now,” he added, referring to new additions Rosenthal and Kyle Barraclough. “But you can never have too many weapons at the back end of the game.”

Kimbrel already has an agent. But he should consider Doolittle, the man who would be affected most and perhaps lose the most money if his closer job were taken away. Of Kimbrel’s career ERA of 1.91, well ahead of immortal Mariano Rivera at 2.21, Doolittle simply said, “It’s insane.”

Kimbrel remains unsigned because he started the offseason asking for $100 million over six years — $14 million more than the record for a reliever — and he hasn’t adjusted his sense of reality to today’s free agent market, especially for relievers, which has crashed.

Also, Kimbrel has shown a flaw only once in his career — but he picked an expensive time for it. His 2.74 ERA and 42 saves last season for the Boston Red Sox look fine, especially after a brilliant 2017. But after the All-Star Game, including October, he had a 5.01 ERA with 6.4 walks per nine innings. His velocity was career normal (96.8 mph), and his vicious breaking ball snapped. But his bouts of wildness made you sweat.

“Kimbrel is 30. He’s got 330 saves. He’s as proven and battle-tested as you could want,” Doolittle said. “He’s durable, dependable and incredibly effective. He’s been superhuman. Okay, so the second half last year wasn’t as good. He wasn’t lights out in the playoffs. . . . But look at his whole body of work.”

What if Doolittle is now a bit more effective than Kimbrel?

“We can figure that out,” Doolittle said, shrugging away that and any other bullpen usage issues. “I’ve heard nothing but great things about him. Quiet guy, but really funny.”

Armed with these ideas, I tried to provoke a Nats veteran by saying: “This team looks good. But it may be one Craig Kimbrel away from a deep October run.”

“That’s exactly right,” he said, to my surprise.

Most players on all teams want to add stars so they can win more. Just like fans (and writers), they love to spend the owner’s money. But Kimbrel would be a decent payroll fit for the Nats. He’d probably cost about $5 million extra in luxury-tax penalties this season. But next season, the Nats have more than enough money dropping off their payroll to get under that ceiling, even if they extend Anthony Rendon, too.

What about the compensation pick, and the international draft money that the Nats would lose if they signed Kimbrel? MLB’s current mantra is that the Chicago Cubs, Houston Astros and Red Sox built their core through the draft. True. But it’s conveniently forgotten that those clubs added big contracts in years when they could smell a title, including Justin Verlander, Gerrit Cole, Jon Lester, John Lackey, Jason Heyward, Yu Darvish, David Price, Chris Sale and (the past three years in Boston) Kimbrel.

“The guy you get for that second-round compensation pick won’t be as good as you already know that Craig Kimbrel is,” the veteran player said.

Recent history among free agent superstar relievers has crunched Kimbrel’s market. Two years ago, Aroldis Chapman and Kenley Jansen shattered reliever records with five-year deals for a combined $166 million. Since then, both have been good, but Chapman’s ERA has risen by 0.75, and Jansen allowed 13 homers last year. Even four-year deals have been questioned since Mark Melancon, who got $62 million, was a bust.

As a result, no free agent reliever has gotten more than three years or more than $39 million (Zack Britton).

General managers, including the Nats’ Mike Rizzo, get a stern expression when Kimbrel is mentioned. Rizzo knows his veteran performance may have rolled over. He hates losing compensation picks and international money, especially when he sees the fruits of those dollars in Juan Soto, Victor Robles and Luis Garcia. And he knows his owners don’t want to go over the luxury tax for a third straight year, meaning every extra dollar is hit with a 50 percent tax.

“A lot of people involved with a team want to spend more money. It’s ‘free’ [to them],” Rizzo said. “But [over time], that approach catches up with you.”

For me, this comes down to the opportunistic use of precious baseball money. Kimbrel, even as a slight overpay, is an opportunity, especially when the Phillies, Braves or maybe Los Angeles Dodgers, all in the NL, are most likely to grab him.

When the stock of a great company plummets until you can’t believe it has gotten so cheap, that is either a great investment or a “value trap.”

The Nats need to decide which Kimbrel is — and fast. If he’s “value,” then he takes pressure off setup man Rosenthal, who is coming back from elbow surgery, and helps Doolittle, who is not fragile but hasn’t been a workhorse, either. Also, if you’re not going to spend money in 2019, 2020 and 2021, when your rotation includes Max Scherzer, Stephen Strasburg and Patrick Corbin, when will you?

The best comparison to Kimbrel for me is the career arc of Jonathan Papelbon. When young, he had a 1.74 ERA for four years. Then at 29 and 30, his ERA jumped to 3.41. That scared some teams away from him in free agency at Kimbrel’s age. But he tweaked his style and had a 2.38 ERA in the next four years.

Big-money mistakes come in drastically different sizes. When you’re wrong about a $250 million to $330 million contract, it’s a decade-long anchor. But for one-fifth of “Harper money,” the Nats can make a very good run at Kimbrel and seriously improve their chances of making noise in the next three Octobers.

And after staring at that empty locker between Doolittle and Rosenthal, I think the Nats should — gulp — Doo the Right Thing.