Here came another low point in Brett Connolly’s career, the onetime top-10 NHL draft pick being informed that the Boston Bruins weren’t going to extend him a qualifying offer, essentially letting him walk for nothing.

But when Connolly unexpectedly became an unrestricted free agent, it created another opportunity. Here came an offer from the Washington Capitals — and a chance for Connolly to finally realize his offensive potential in a low-pressure situation.

“I mean, I thought I was [going to get a qualifying offer], but things change and then they go and sign [David] Backes and it’s like, ‘Well, what are you going to do?’ ” Connolly said. “I was fortunate that Washington called right away and I didn’t have to worry about it too much over the summer.

“It was a no-brainer. No matter what the money looks like, with that comes opportunity, and I can come in here as a cheap player and be a good player and turn some heads and help this team win. They’re a good team that’s on the cusp of winning, and I want to be a part of that.”

For the Capitals, a one-year, $850,000 deal for Connolly was a low-risk move. If he doesn’t produce, then at least he was inexpensive, and if he does, then he was a bargain. Washington is hopeful that Connolly can rediscover the traits that made him a top prospect and not only boost the team’s bottom-six scoring but also eventually move up in the lineup. He’ll be a restricted free agent next summer, so the Capitals will retain his negotiating rights.

“I think his skill set is there,” General Manager Brian MacLellan said. “You know, he’s got good size, he’s got good hands, he’s got the ability to score and make plays. I think he’s got the ability to play with good players.

“I don’t want to necessarily put pressure on him to, ‘You have to produce offensively.’ We’re just going to let him find his way and try to fulfill his potential. I think that’s what he wants, too. He’s going to have an opportunity to play with some good guys.”

Expectations were high for Connolly in Tampa Bay when he was the No. 6 overall pick in 2010 and made his NHL debut a season later. They were arguably even higher when Connolly was traded to the Bruins during the 2014-15 season for two second-round picks; Boston General Manager Peter Chiarelli proclaimed at the time that Connolly would be a top-six forward on the team.

But Connolly suffered a wrist injury upon arrival, playing in just five games after the trade. He saw time on Boston’s first line, with Patrice Bergeron and Brad Marchand, at times last season but didn’t score enough to get more. Averaging almost 13 minutes in a career-high 71 games, Connolly had nine goals and 16 assists. As his role changed, so did his game, taking on a grittier and more physical nature.

“Maybe it hasn’t happened yet, but I’m still very confident in my abilities,” Connolly said. “There have been some good times, there have been some not-so-good times, so it’s just a matter of putting it together. I’m 24 years old now. I’ve been in the league a little bit, so, you know, you want to come in and put up some numbers and play well defensively and be a good all-around player.”

Associate coach Todd Reirden said Connolly has the potential to be a “gem,” someone who could play anywhere in the lineup with a high-level shot. With three top-six players still competing at the World Cup and top-line right wing T.J. Oshie not playing in the Capitals’ first two preseason games, Connolly is expected to have an early opportunity with Washington to show what he can do in a feature role that includes power-play time.

“What happens sometimes when you get to your second or your third [team], I think as you get a little bit later in your career, you start to realize that you’ve lost some opportunities,” Reirden said. “Now he knows this one is ripe for the picking for him, and he’s able to do the things that he does.

“Every team has them, the players not able to fulfill the potential in your organization. Sometimes, you have to do different things with them because of salary cap reasons or whatever and you move past a player. Our scouting staff and management did a good job of targeting him as a guy that we thought could come in and help us right away.”