Islanders Coach Barry Trotz watches from the bench during an April win over the Capitals. (Nick Wass/AP)

NEW YORK — Barry Trotz’s final visit to the Washington Capitals’ dressing room came five months after he was no longer their coach. He was invited inside anyway Nov. 26, just before the Capitals and Trotz’s New York Islanders played each other for the first time this season. The team presented Trotz his Stanley Cup championship ring, and in what he considered a final bit of closure, he left the Capitals with this line: “You’ll have to go through the f------ Island, but you guys can do it again.”

The speech felt like a motivational parting for the Capitals in their quest to repeat, but Trotz had his new team in mind, too. He figured if Washington and New York met in the postseason, it would represent a considerable step for an Islanders club that had missed the playoffs two years in a row and was widely expected to have one of the NHL’s worst records this season.

“That would mean we’d made some growth, to have the opportunity to knock them off,” Trotz said Saturday. “Or if they beat us, we’d make it f------ hard on them.”

He looked prophetic after New York swept the Pittsburgh Penguins in the first round. Had the Capitals won their series against the Carolina Hurricanes, their title defense would indeed have gone through the Island. But Washington was ousted in a Game 7 that went to double overtime, an upset that meant the Capitals’ former coach, the one team brass let get away, had outlasted them in the playoffs. The Hurricanes have a 2-0 series lead against the Islanders after a 2-1 win in Game 2 on Sunday in Brooklyn.

“Can you imagine winning a Cup with a head coach behind the bench and having him not return to your team the next year?” analyst Keith Jones said on the NBC Sports Network broadcast after that Washington loss in Game 7. “I mean, you’re trying to repeat, and you don’t have the guy that pushed all of the right buttons standing behind the bench, so to me, it’s not a remarkable thing that they were beaten out.”

Trotz and the Capitals parted over financial differences; his contract included an automatic two-year extension for winning the Stanley Cup, and while it carried a small raise, it still would have left him considerably underpaid compared with coaches with similar résumés. Trotz wanted market value, and Washington wanted him to honor the contract that he had agreed to four years earlier. After Trotz resigned, the Capitals promoted associate coach Todd Reirden to the head post, but especially after Washington’s early playoff exit, a segment of the fan base will always wonder what would have happened if the team had kept Trotz around on a more lucrative deal.

“I think that’s unfair,” Trotz said. “They have a good coaching staff — Todd and all those guys are good coaches. You don’t know, because you change one or two pieces and the circumstances and the expectations are different. … I couldn’t tell you if we would’ve even made the playoffs.”

Asked whether the change behind the bench played a part in Washington’s first-round loss, Capitals General Manager Brian MacLellan said: “Are we saying that we underperformed because we had a rookie coach? I don’t think so."

“You look at the performance of the players,” MacLellan continued. “Tom Wilson got better, Jakub Vrana got better, [captain Alex Ovechkin] had one of his better years at 33, [Nicklas] Backstrom played well, [T.J.] Oshie played well. We had a lot of guys play really well. The system is the same. Specialty teams, the power play is the same, the [penalty kill] changed a little bit — I think the personnel changes improved it at the end of the year. So we just changed coaches, and I think that [Reirden] did a good job. I think as with any first-year coach, there’s growth and there are ways he can get better as a coach, and I think he’ll pursue it.”

After his split with Washington, Trotz didn’t think he would coach at all this season; he was planning to take a year off and spend it in a British Columbia cabin. Islanders General Manager Lou Lamoriello reached out, as did other teams, and while Trotz had never worked with Lamoriello, his reputation and success over more than three decades in the NHL gave Trotz faith that it would be a good marriage. The duo suffered their first loss July 1, when superstar center and captain John Tavares chose not to re-sign with the Islanders, instead opting for Toronto. A roster that had struggled the year before looked decidedly worse.

“I think this team believed that they could win games, but I don’t know if this team expected to win games,” Trotz said. “We weren’t a sexy group.”

The Islanders and their fans lamented losing Tavares, but that might have made them embrace Trotz even more. His stout structure transformed the Islanders from the team that allowed the most goals in the league last season to its stingiest this year, a difference of more than a goal per game. Perhaps buy-in from the players came easier because Trotz had the credibility of having just won the Stanley Cup.

Trotz ranks fourth on the NHL’s all-time wins list, and he is a finalist for the Jack Adams Award, which goes to the league’s best coach. When New York briefly skipped ahead of Washington for first place in the Metropolitan Division in January, Islanders fans chanted his name.

“He did the same thing here that he’s doing there,” MacLellan said. “Our first year with Barry here was really good. He changed the culture, and we improved on it every year he was here. … I’m happy for Barry. He’s doing a good job, and he’s repeating what he did with our organization.”

Washington was often on Trotz’s mind this season as he drew from his experiences with the team, even though he avoided directly mentioning the Capitals around the Islanders. And sometimes Washington was on his mind because he can’t help but care about the organization and its players after their four years together culminated in the franchise’s first Stanley Cup title. Trotz said he reached out to a few people in Washington after the team’s first-round loss, but then he had his own series for which to prepare.

The Capitals’ bid to repeat may be over, but his isn’t.

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