NEW YORK — The past three times the Washington Capitals made the Stanley Cup playoffs, Peter Laviolette was behind the bench. But this time, it’s the opposing bench, as the New York Rangers coach tries to eliminate the Capitals from the postseason.

According to ESPN Stats & Information research, this is only the eighth time in Stanley Cup playoff history that a head coach has faced the team that dismissed him in the previous season. The Rangers have a 1-0 lead in their first-round series against Washington, with Game 2 Tuesday night at Madison Square Garden.

“On the positive side, it was great to be part of a great organization, great city and a fan base that loves their team and is passionate about their year,” Laviolette said of his time in Washington. “From a disappointment standpoint, it was not being able to make any noise in the playoffs despite having the opportunities.”

There would be a certain irony to the Rangers beating the Capitals in the first round, as that’s when Laviolette’s two postseasons in Washington ended in 2021 and 2022.

The Capitals missed the playoffs last season — only the second time in 16 years that Alex Ovechkin didn’t see the postseason — which led to what GM Brian MacLellan described as a mutual parting of ways between the team and Laviolette after three unremarkable seasons.

Washington’s loss was the Rangers’ gain. When New York fired coach Gerard Gallant after two seasons, it turned to Laviolette with a three-year commitment. The results have been historically good for the Blueshirts, who won the Presidents’ Trophy for having the league’s best record and had the third-best points percentage (.695) in franchise history.

That record earned the Rangers a first-round series against Washington, the second wild-card team in the Eastern Conference. And it earned Laviolette a reunion with some familiar faces one year after the Capitals let him go.

COACHES HAVE FACED their employer from the prior season in consecutive playoffs. Dallas Stars coach Pete DeBoer went against his former team, the Vegas Golden Knights, in the Western Conference finals last season. DeBoer actually had experienced this previously, meeting the Florida Panthers in the 2012 playoffs during his first year as coach of the New Jersey Devils.

Other coaches facing their former teams one year later are:

The combined record of these coaches in “revenge” series: 6-1, with DeBoer’s loss to the Golden Knights last season the only blemish.

Laviolette took over the Capitals in 2020. Washington followed its Stanley Cup win in 2018 under Barry Trotz with two first-round exits under his replacement, Todd Reirden. Laviolette was brought in to maximize the remaining contention window for Ovechkin and his veteran teammates.

“I thought the first couple of years, we were in a good position to try to get into the playoffs, make some noise and make a push,” Laviolette said. “Last year was a little bit tougher. We were dealing with a lot of things all year, but especially at the end.”

The Capitals ended up 12 points out of a playoff spot. MacLellan claims the door was open to have Laviolette return for a fourth season.

“I think he’s a good coach. I think he’s a good person. I think we were open [to it],” he said.

But after feedback from players and a conversation with Laviolette, it was decided they would part ways.

At the time, Capitals winger T.J. Oshie said “it’s the ugly part of the business” when Laviolette was let go, but he put his faith in management that it was the right call.

“I think he had some tough circumstances with injuries during his tenure here,” Oshie said. “But I’ve said since day one that I trust Mac in his ability to put a winning team on the ice, and the coaches are involved with that.”

In the end, things appear to have worked out for the best for both the coach and his former team.

LAVIOLETTE TOOK OVER a Rangers team that needed his defensive structure and encouragement to play with more pace, which turned it into a serious Stanley Cup contender. The Capitals hired Spencer Carbery, 42, who was an assistant coach with Toronto after three seasons as the Capitals’ AHL coach in Hershey. His own defensive system helped Washington emerge from a wild-card bubble pileup to return to the playoffs, while his age positions him well for the team’s ongoing youth movement.

“Very poised,” Oshie said of Carbery. “He’s very good at the message that he sends to the team. He’s very good at timing with what the message is and what it needs to be. He definitely came in not looking like a first-year head coach.”

Carbery isn’t the only new face for the Capitals. Laviolette, 59, coached just over a dozen players who are on the Washington roster for this series.

“It might be a bit more strange for guys that have been here for a while that had him for three years here. But I only had him for one year and we got along really well,” center Dylan Strome said. “I had my best year at the time when he was my coach. Very open and very honest with me as my coach, and I’ll always appreciate him for that.”

Still there are veterans who remain on the roster that Laviolette knows well.

“I think it goes both ways. I think they also have an insight into me and my systems,” the coach said. “But that was the case going into the four games we played in the regular season.”

The Capitals’ power play is filled with veterans Laviolette had all three seasons in Washington: Ovechkin, Oshie, Tom Wilson and John Carlson, for example.

The Rangers’ penalty kill, ranked third in the regular season, shut down the Caps’ power play in Game 1, as it went 0-for-4. In four regular-season games, Washington was 0-for-10 against New York.

Did coaching the Capitals give Laviolette insight on how to stifle their power play, including Ovechkin?

“I guess a little bit because you know the personnel. But that’s not how we went about our business,” the coach said after Game 1. “We do it more based on video and teaching and showing. I imagine that’s how most teams operate. You take a look at what you’re going to be up against, you get some video clips, you bring it into a meeting, you try to talk about a game plan on what you want to do and go from there.

“I know where Ovi’s going to stand. I know he might move around a little bit, but I think everybody else does too. It’s more about what they’re trying to do out there.”

BOTH THE CAPITALS and their former coach have downplayed the insights they carry into the series against each other — or really any semblance of extra motivation for one to eliminate the other.

“No matter who we play, we’re going to have a pre-scout on them. Not really strange at all. We’ll just prepare like we would anybody else,” Oshie said.

“It’s a business. We’re all here for a business,” Ovechkin said.

“The Rangers have had a very, very good season, and he’s a great coach,” Strome said. “With the way they play, we played that way last year. I think a little familiarity never hurts. But he has that with us as well. We’ll see how it plays out, but I know we’re all excited.”

Before the series, Laviolette said he “didn’t think about it much, to be honest with you” when asked about facing Washington in the playoffs after having coached them last season.

“I’ve got a lot of respect for the Capitals and the organization, their players,” he said. “They’ve obviously done some good things to make the playoffs. Our group’s done some good things to make the playoffs. The game gets decided out on the ice.”

Then again, facing a former employer is old hat for Laviolette at this point in his career.

“I’ve coached a lot of teams,” he said with a laugh, as the Rangers are his sixth NHL head-coaching stop.

“If this is the story, I’ll have a story every round, I hope.”