This is a story about a pen, a police officer and the playoffs.

It began in July on a turbulent night at Audi Field when, after an exasperating defeat to the New York Red Bulls, D.C. United Coach Ben Olsen fired his pen into the squishy grass.

Greg Alemian, a sergeant in the Metropolitan Police Department, was stationed near the team bench and witnessed Olsen’s antics. He picked up the pen and put it in his pocket.

By the next home game, Alemian had been reassigned to a spot behind the south goal, where steps link the field to the lower-level locker rooms and where fans gather for autographs.

“Hey, Ben,” Alemian said. “You threw this pen after last match.”

Alemian felt comfortable saying something to Olsen because they had been recently introduced by a mutual friend — Chris Stiles, the pregame DJ. Olsen and Stiles had lived near each other; their daughters remain good friends. Alemian is a former marketing director in the music industry who for years ran in the same circles as Stiles.

Olsen did not remember flinging the pen. Alemian pulled out the Marriott-branded silver instrument with red features.

“I’m not giving it back until you make the playoffs,” Alemian said.

“Yeah, yeah, yeah,” Olsen said. “I probably blew him off. It was pretty dire.”

Having spent most of the season on the road while Audi Field was being completed, United was mired in last place in the Eastern Conference. With the arrival of the new stadium and Wayne Rooney, the team’s fortunes had begun to turn, but the margin of error in pursuit of a postseason berth was paper-thin.

Over the next three months, with United playing at home almost exclusively and climbing the standings, Alemian would flash the pen at Olsen before every match.

During the exchanges, the men — one conducting performances on the field, the other protecting an area around it — forged a pregame bond that was built, in part, around that pen. They will cross paths again Tuesday when United (3-1-1) hosts the Montreal Impact (2-2-1).

Olsen remembered: “It got to the point where I was thinking, ‘There might be something to this pen thing.’ He never really said much about it. It became more of an acknowledgment after we started getting some wins that this playoff thing could go down.”

There was nothing valuable about the pen, but it became a symbol.

“I’ve gone through hundreds of hotel pens,” Olsen said. “This one, it’s a beautiful, bedside, run-of-the-mill Marriott pen. With a clicker. I like clickers. I have arthritis in my thumb from clicking pens. It’s a nervous habit during games.”

Team administrator Francisco Tobar supplied Olsen with new pens. The winning ways continued.

“He would come upstairs and I’d say, ‘Not yet’ and pull out the pen,” Alemian said. “At the end of the game, he would point at me, and I’d say, ‘Not yet, Ben; not yet.’ ”

Finally, in the, er, penultimate match of the regular season, United secured passage to the playoffs with a 3-1 victory over visiting New York City FC.

When the on-field celebration faded, Olsen made his way toward the stairs. “He hugged me from behind,” Alemian said, “and said, ‘Give it to me!’ ”

The pen, marked with “2018,” sits on a shelf in Olsen’s basement office at RFK Stadium, where United continues to practice. Other treasures include his boots from the 2006 World Cup in Germany and mini flags from international matches.

“It stays away from all the other pens,” he said.

Reflecting on the scramble last year, Olsen said “it was hard to enjoy even the wins you were amassing because everything was a must-win. For me, what moment stood out last year was when we made the playoffs. You could actually enjoy and breathe for a second. The pen was the backdrop.”

It also facilitated a game-day friendship with Alemian, a 16-year veteran of the force who is also a field-level presence at Nationals Park.

Alemian, 45, played soccer at Annandale High and remembers attending University of Virginia matches when Olsen, 42 next month, was playing in the mid-1990s.

Alemian has connected with United players as well — particularly goalkeeper Bill Hamid, an Annandale graduate.

He also has forged a rapport with the group of fans who plead for autographs near the staircase. They usually make their player requests by writing messages on posters and sheets.

During one game, Alemian asked, “Where’s mine?”

The next game, the fans obliged with a message saying, “Thanks to All the People That Keep Us Safe, Specially Our Officer Greg Alemian.”

Said Olsen: “In my life, I don’t know too many cops. I didn’t grow up with cops in my family. In a lot of ways, cops weren’t my favorite growing up [in small-town central Pennsylvania]. Then I grew up, got married, had kids, and you realize what an amazing profession it is. He is an awesome guy.”

D.C. United vs. Montreal Impact

Where: Audi Field.

When: 8 p.m. Tuesday.

Live streams: FloSports and ESPN+. Both are pay services. ESPN+ coverage is blacked out in the D.C. area.

Records: United 3-1-1, 10 points; Impact 2-2-1, seven points.

D.C. probable starters: GK Bill Hamid; Ds Leonardo Jara, Frederic Brillant, Steve Birnbaum, Chris McCann; MFs Paul Arriola, Russell Canouse, Junior Moreno, Luciano Acosta, Lucas Rodriguez; F Quincy Amarikwa.

Montreal probable starters: GK Evan Bush; Ds Bacary Sagna, Zakaria Diallo, Jukka Raitala, Daniel Lovitz; MFs Micheal Azira, Samuel Piette, Saphir Taider; Fs Orji Okwonkwo, Anthony Jackson-Hamel, Harry Novillo.

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