Washington has been one of the league’s more successful teams — 26 playoff appearances and nine division titles across the last 33 seasons — but also one of its most disappointing. Last season, leading the Rangers by three games to one, the Capitals were 101 seconds from advancing to the conference finals for the first time since 1998. They allowed a late goal that forced overtime, in which they lost, as they did in Games 6 and 7.

Watching the collapse from home, Williams detected many of the same traits that defined his Kings teams: great goaltending, top-end talent, a shutdown defenseman. All that was missing, perhaps, was someone like him.

“You want to come in with your confidence, you want to come in with a little swagger,” Williams said. “I think that’s very important, a sense of belonging like, ‘I’m going to beat you and I’m going to show you.’ ”

Oshie sensed that vibe from Williams as far back as 2012, when Los Angeles swept his division-winning Blues in the second round, and again the next season, when the Kings overcame a 2-0 deficit in the first round against St. Louis. But Oshie himself personified it during the 2014 Sochi Olympics, when he scored four shootout goals in the United States’ victory against Russia.

He joined the Capitals in a deal with St. Louis, the Western Conference version of Washington — a regular-season stalwart that flopped in the playoffs. But Oshie said he was unaware of the Capitals’ painful postseason history. He brought his own scars, his own regret and a doggedness, a consistency of effort, that, Trotz said, the team had been lacking.

Without a trace of fondness, forward Jay Beagle remembers battling Oshie in the corners, trying to jimmy the puck free.

“When you hate playing against certain players,” Beagle said, “you love to get them on your team.”

Alzner said he told friends how much the dynamic in the locker room had changed since the arrival of Williams, Oshie and another new player, defenseman Taylor Chorney.