Rangers head coach Peter Laviolette looks on against the Islanders at...

Rangers head coach Peter Laviolette looks on against the Islanders at UBS Arena on April 9. Credit: Jim McIsaac

 GREENBURGH

Peter Laviolette was relaxed but all business when he spoke to reporters on Monday during a very optional off-day practice for the Rangers.

But he could not help but smile when the subject turned to his first playoff series as an NHL head coach, when his Islanders faced the Maple Leafs in 2002.

“It was awesome,” he said. “[Rangers assistant] Michael Peca was on that team. It was one of the best series I’ve ever been in. Islanders versus Toronto. Boy, was it a war. It was a great series.”

The Islanders won all three games at Nassau Coliseum and lost all four in Toronto. It was an invaluable experience for a young coach.

“Other than the fact that we lost in seven games,” he said, “I left there, never having experienced playoff hockey before, and I was like, short of the result, that series, the way it went back and forth and the energy .  .  . Managing the ups and the downs inside that series was incredible.”

Laviolette was 37 then. He’s 59 now, with a Stanley Cup on his resume from 2006 with the Hurricanes, two other appearances in the Final — with the Flyers and Predators — 14 overall playoff appearances and 155 playoff games.

His counterpart with the Capitals, Spencer Carbery, is 42 and has coached one NHL playoff game, the Rangers’ 4-1 victory in Game 1 on Sunday. Game 2 is Tuesday.

Logically, given all the above, Laviolette’s experience behind the bench in these kinds of situations should be a huge edge for the Rangers, especially given that Laviolette was the Capitals’ coach just last season.

Asked about that, he said, “I haven’t thought about it, to be honest with you.” But his players said they appreciate his been-there-done-that guidance.

“I don’t know how many games he’s coached and how many wins he has, but obviously it’s for a reason,” said Erik Gustafsson, who played for Laviolette in Washington last season.

“We know what he can do. We feel comfortable when he talks.”

After a scoreless first period in Game 1, during which the Capitals succeeded in their goal of slowing down and muddying up the game, the Rangers adjusted, figured things out, leaned on an energy boost from the fourth line and scored three quick goals in the second period.

“Obviously, playoff hockey is a little different,” Alex Wennberg said. “For him to have that coaching ability to read the games and feel the momentum, I feel like that is something that helps us a lot.”

The Capitals, who won the 2018 Stanley Cup, have plenty of playoff experience, too, led by Alex Ovechkin.

But in addition to a seasoned coach, the Rangers have players like that up and down the lineup, all the way to backup goalie Jonathan Quick, who has merely won three Cups, most recently 10 ½ months ago.

Laviolette said that kind of experience can help but that it is not an end-all.

Still, he said, “I think you rely on those guys in the room and on the ice for the way they play the game.”

Chris Kreider, who scored the final goal Saturday, has been with the Rangers since 2012. Barclay Goodrow won two Cups with the Lightning.

You get the idea. So in theory, this is the sort of team that will not shy away from the moment and certainly will not take anything for granted after one game.

Many are predicting the Rangers will make quick work of Washington. My pick was Rangers in four.

But most of the Rangers recall winning the first two games against the Devils by a combined score of 10-2 in the first round last year, then losing four of five.

Stuff happens. So it’s good to have people around who have seen it all before.

The year after that epic 2002 series against Toronto, the Islanders lost in five games to Ottawa, and Laviolette soon was off to Carolina.

Two seasons later, he won the Cup. Now he is 15 victories away from another, and he knows exactly what that road looks like and how treacherous it will be.