Capitals Coach Barry Trotz continues to chase an elusive goal. (Jonathan Newton/The Washington Post)

In an office decorated with mementos of his long and rewarding career, pictures and keepsakes chronicling the highlights, Barry Trotz allowed himself to dream about an absent image. In his hand, he held a stainless-steel travel mug, engraved to read “2ND FAVORITE CUP.”

This wasn’t the first time he’d leaned back in his chair and envisioned what he’d do with the Stanley Cup if he ever earned a day with it. “I think that’s what motivates you, too,” Trotz said last week.

Trotz recently moved into fifth place on the NHL’s all-time coaching wins list, 740 to his name in 19 years. His .685 points percentage in three-plus seasons with the Capitals is better than any coach in franchise history. For a third time in his career, he was tabbed as a bench boss for the All-Star Game. He is one of the most respected and accomplished coaches in the league.

But just like Washington star captain Alex Ovechkin, Trotz lacks a Stanley Cup on his decorated  résumé. He’s also never gotten past the second round of the playoffs. If the window to do so is steadily closing for this aging Capitals core, it’s especially so for Trotz, 55, coaching on the last year of his contract and potentially in his last opportunity to win with this team.

“I realized I want to have a Cup, but I may not get it as a coach,” Trotz said. “It may come as a scout or a GM; it may come in a different form. I don’t know. I still want to be a part of a Cup winner. I would like to be the coach, but I wish I could say, ‘Yeah, it’s going to happen’ — and I’m saying that every day to myself, ‘It’s going to happen, it’s going to happen’ — but I don’t know if it is. And I wouldn’t trade anything.”

There’s a case to be made that this season is Trotz’s most impressive coaching job with Washington. The Capitals were discounted after a difficult offseason that saw the departures of forwards Marcus Johansson, Justin Williams and Daniel Winnik and defensemen Nate Schmidt, Karl Alzner and Kevin Shattenkirk. Washington attempted to fill those lineup holes and work around its considerable salary-cap constraints with two rookie blue-liners, two forward prospects and two veteran forwards making the league minimum after their previous teams didn’t want them anymore.

The Capitals are somehow in first place in the competitive Metropolitan Division halfway through the season, weathering the roster turnover, early-season injuries and the lingering hurt from last year’s disappointing early playoff exit. Since Trotz became coach before the 2014-15 season, the Capitals are first in the NHL in cumulative wins, points, goals and power-play percentage, and they’ve allowed the fewest goals per game.

“I thought I prepared well, and I’m not even close to what Barry can do,” said Dallas Stars Coach Ken Hitchcock, third all-time in wins with 805. “I think the thing that is remarkable about Barry is that nothing is spontaneous. There’s a plan for everything. I was surprised how ultra-organized the plan was. … Barry plans every hour of every day in advance of what he’s going to do. There’s a reason that his teams are going to be consistent.”

Over the course of 15 years, Trotz helped build the Nashville Predators from a lowly expansion franchise to a regular playoff presence through that meticulous attention to detail. “You could beat Nashville, but you could never outwork them,” Hitchcock said. But that didn’t mean Trotz had no fun. On one occasion, recognizing his team needed to loosen up during a losing streak, Trotz had the Predators’ right-handed shooters use left-handed sticks and vice versa, making for a comical practice.

This season required Trotz to similarly relinquish some of the control and order he might prefer. For a second straight year, the Capitals had compiled the league’s best regular-season record, and for a second straight year, they lost to the Pittsburgh Penguins, eventual Stanley Cup champions. Washington was still in a collective hangover in October, and Trotz knew he needed to give his team some space.

“The teams that have won experienced adversity,” said Hall of Fame coach Scotty Bowman, who won 1,244 games and nine championships. “I mean, it’s not a good formula, but you usually get pretty close, then you slip down a bit, then you’ve got to retool or do something different. … You’ve just got to keep working at it, that’s what I would tell people. You can’t drink any kind of Kool-Aid to make it better. You just have to stick with it.”

The Capitals floundered through their first 20 games, appearing on the verge of collapse after November blowout losses at Nashville and Colorado. There was concern that after Trotz’s first three seasons all ended with the same result, a heartbreaking second-round loss in the playoffs, players were tuning him out in the fourth year. The time for giving the players space was over, and Trotz was harsh in the locker room after a 6-2 loss to the Avalanche in Denver. It wasn’t a guarantee he’d still be the coach at the end of the month, but the Capitals turned a corner the next week, and they’re 16-3-2 in the past 21 games.

“We’ve talked about why certain teams won and why certain teams didn’t that we’ve coached,” Hitchcock said. “What were the core ingredients? We spent a long time this summer talking about it. You know, it was a tough summer for him. … The teams that did have success, they have certain qualities, and we talked about what those qualities were, and how much we could influence those qualities. It was a pretty direct talk, to be honest you. The one thing we came up with, which was really interesting, is you can’t be afraid to coach people up.”

Working with Ovechkin the past four years has given Trotz a unique perspective on legacies. He doesn’t believe Ovechkin’s individual accomplishments as the greatest goal scorer of this generation should be tarnished because his teams haven’t won a Stanley Cup. Trotz asked if legendary defenseman Ray Bourque had stayed in Boston for his entire career and not won a championship with Colorado in his final game, would he be less of a player? Or what about San Jose center Joe Thornton, who could have more than 1,500 career points but no Cup by the time he retires?

He’s talking about others, but he’s also talking about himself and how his career will eventually be judged.

“I wouldn’t trade anything to have a Cup,” Trotz said. “I think all the experiences that I’ve had and what we’re doing are the right thing.

“But I want the Cup. There’s no question.”