Sean Doolittle and catcher Matt Wieters celebrate a Nationals’ victory Monday night. (Rob Carr/Getty Images)

For months Washington waited desperately for the Nationals to acquire a pitcher who could bring sanity to their bullpen. Instead, they got three of them. When you call for the cavalry, you expect more than one guy on one horse.

Strength in numbers is the Nats’ new mantra. The hallmark of World Series bullpens in the past decade is not just one effective closer, although that’s essential, but four to six relievers, all on a roll together. Will General Manager Mike Rizzo pull it off?

“It starts with an anchor at the back, then everything falls in place after that,” said Ryan Madson, who has been a key to three bullpens that reached the World Series, including the 2015 champion Kansas City Royals. “As a bullpen, you start a wave and you ride it as far as you can. When it crashes, you catch the next wave. I think we’ve started a nice big wave here.”

“Bullpens’ success is contagious. That momentum builds as you all count down the outs. You can smell the win,” said Sean Doolittle, who arrived with Madson from Oakland in a trade that also subtracted anxious Blake Treinen, who was contagious in his own way. He already has blown three saves for the A’s.

Failure also can sweep through a bullpen, as the Nats learned this spring. By adding three arms, all of whom have had success as closers, including all-star Brandon Kintzler from the Minnesota Twins, the Nats dispersed the burden.

Ryan Madson believes he’s in the best shape of his life at age 36. (Mitchell Layton/Getty Images)

“Sometimes when one person comes to a new team, there are these expectations,” Doolittle said. “It takes a little bit of the pressure off. We can carry those expectations together.”

Added Madson, “It helped that it wasn’t just me or any one of us.”

Of the past 20 teams to make the World Series, 18 had at least three relievers with either ERAs under 3.20 or a WHIP under 1.00. Last year the Chicago Cubs had six such pitchers on their World Series roster, not just closer Aroldis Chapman. A majority of the 20 had at least four.

The Nats now have Madson and Doolittle with infinitesimal WHIPs of 0.77 and 0.82, respectively, plus Kintzler (2.55) and Matt Albers (2.23) with low ERAs.

Madson sees further similarities to his past World Series bullpens.

“Oliver Perez is J.C. Romero,” Madson said, referencing the lefty specialist on the 2008 Philadelphia Phillies. “Doolittle is like Brad Lidge. They depend on one wipeout pitch. They are simple machines.

Brandon Kintzler was a deadline acquisition from the Twins. (Katherine Frey/The Washington Post)

“If I taught mechanics, I’d use Doolittle’s as the model.”

Could Koda Glover (if healthy), Sammy Solis or Enny Romero be bullpen-lengtheners by October?

“The more guys, the better,” Madson said. “A common theme in good bullpens is that you take care of your own gardens. Don’t worry about [what] the manager, the defense or the hitters [do]. That’s not our lane. Just keep our garden nice and tight — no weeds.”

When the shaved-headed Madson, who recently touched 100 mph for the first time in his life, says he dislikes “weeds,” it’s unlikely anyone in the Nats’ bullpen would want to risk getting uprooted.

All three new Nats have overcome three-year periods in the wilderness. Few have had such long periods when only they still believed in themselves. To find them in the seventh, eighth and nine innings for one team may have some karma.

Kintzler, a 40th-round draft pick — that means he was taken just before you, sitting on your sofa at home — spent three years in independent leagues. He even sold tickets for the Winnipeg Goldeyes and was a limo chauffeur in Las Vegas.

But every year, Kintzler mastered the ancient arts of pinpoint command and extremely late movement on his sinker and slider.

“What we liked so much with Kintzler is his last five feet — that’s when all his pitches move,” Rizzo said.

Late movement is the grail. The ability to “read the bat” — sense what the hitter is thinking and planning — is a similarly rare gift, and Kintzler has it. The combo, Rizzo said, allows Kintzler to “throw 91 mph in the zone for strike one and still get outs. In the minors, you can get hitters to chase. Up here, your stuff has to be good enough to get outs in the white of the plate, not the black [edges].

“All three of these guys can do it.”

Doolittle had the worst break of the three: a snapped right wrist tendon ended his career as a hitter. At the University of Virginia, he hit twice as many homers as teammate Ryan Zimmerman (22-11). At 21, he had risen so fast that he torched the elite-prospect Arizona Fall League (.943 on-base-plus-slugging percentage).

“Oh, I was good,” Doolittle said.

After his injury, he was told never to touch a bat again for danger of reinjury.

“I don’t even know if I could swing,” Doolittle said.

It took nearly three years to recover and play another pro game. Yet, as a pitcher, where he also had starred at Virginia, his fastball finished with such hop, undiminished speed and swerve that, after essentially starting a new career at 25, he made the majors after 17 games in the minors. What? Yes, 17.

Madson once told an A’s pitching coach that Doolittle had the best fastball of any left-hander since Billy Wagner. Not just speed, but how hitters couldn’t pick it up.

“What you can’t analyze with a radar gun is how uncomfortable hitters look against certain pitchers. You have to see it,” Rizzo said. “That’s Doolittle.”

Can Doolittle stay healthy enough to Do More? His shoulder miseries cost him two months last season and five more weeks this season. One reason the Nats have him closing is so he won’t strain his arm by warming up multiple times. With closers, it’s “get him up and get him in.”

Also, though all three new Nats are basically equal in closer qualities, Doolittle would be the biggest payoff if he succeeded, because the Nats can control him through 2020 if they choose for just $17 million total.

Right now, Madson has the menacing look, the four-pitch arsenal and, this year, the 1.75 ERA that evoke the image of a dominant closer. His career disaster — three years out of the majors after Tommy John surgery — is the reason, he believes, that he is better at age 36 than ever before.

“I never trained at all till after the injury. It was just talent. Then my body said, ‘No more,’” Madson said. The rehab and conditioning methods used by the EVO UltraFit program transformed him, he believes, although some methods, such as higher-than-normal electric shock stimulation, have MLB doubters.

“When others said I couldn’t even come back, Jay said I would hit 100 mph someday for the first time. I just did,” Madson said. “I got nervous. ‘What now?’ So I set new goals. It’s like climbing Mount Everest: New base camps at every level as you go up.”

What are the new goals?

“Someday, throw 120 mph and pitch until I’m 50,” said the 6-foot-6, 225-pound Madson, earnestly.

You tell him he can’t.

Maybe these new Nats don’t have the reputations and accolades of some relievers whom the Nats probably will face in October. But all zeroes on a scoreboard are created equal, no matter how you do it. And each of these three may be better than ever before. As an interchangeable trio, they brace each other.

Or maybe fate wears a crooked smile. The Nats chose Teddy, Abe, George and Tom as the original racing presidents because they were the presidents carved on remote Mount Rushmore. What’s the closest city? Rapid City, S.D.

Where Sean Doolittle was born.