Brett Connolly’s shooting percentage of 28.6 is the highest on the Capitals. (David Zalubowski/Associated Press)

In the example in Brett Connolly’s head, he is coming down the left wing with the puck, there is an imaginary defenseman in the middle of the zone, an imaginary teammate streaking on the other side of that defenseman, and a puzzle.

He is at an odd angle and has two options. The first is the one on everyone’s imaginary mind: to shoot the puck, test the goaltender, give his team a perceived high chance at a goal. The second requires a bit more thought: to do something other than toss a save-able shot at the net, to pass or skate around the back of the goal or do anything to raise a low-percentage scoring opportunity into a higher one. Connolly, more often than not, goes with the latter.

“Generally, I’m not just going to throw a puck at the net just to get a shot on goal or because that’s what you’re ‘supposed to do,’ ” Connolly said before the Capitals’ 3-2 win at Columbus last week. “I like to look for really good scoring chances — one or two a game that have a good chance of producing a goal. That’s where my game is right now.”

That is working for Connolly this season, and it’s also a microcosm of sorts for this year’s Capitals. The Capitals are last in the league in shots on goal per game (28.6) and, while they’ve at times acknowledged a need for a few more “pucks at the net,” they are generally uncompromising in their search for the right scoring opportunities. Connolly has 14 goals on 49 shots (which also puts him one goal short of a career high he set last year). He has a team-high 28.6 shooting percentage, which would be a league-high if his low shots on goal total didn’t disqualify him in the category. He is making the most of limited chances, like when he scored once on one shot on goal in a 5-4 overtime loss to the Red Wings on Sunday, or when he scored six times on 12 shots on goal across 14 November games.

This approach for Connolly, who counts shooting as his best offensive asset, is not only born of calculation, but of a time early last season when he was trying to hang in a lineup and didn’t want to waste any opportunities. Now he’s a fixture on the Capitals’ third line and ranks third on the team in goals behind Alex Ovechkin (NHL-leading 33) and Evgeny Kuznetsov (15). The Capitals (32-17-6) have a four-point lead over the Pittsburgh Penguins in the Metropolitan Division heading into an 8 p.m. matchup with the Winnipeg Jets at Bell MTS Place on Tuesday night.

“When you’re trying to prove yourself and get on a line or stay in the lineup, I don’t think five or six shots on goal are going to help you too much unless they lead to goals,” Connolly said. “So that’s where those one to two chances come in. I always go back to that. Sometimes, if you go without a shot on goal for a few games, maybe you throw a puck on goal just to get yourself going and feel it a bit. But for the most part, you’re looking for the spots that you can score in, and that’s it. At least that’s what I do.”

And, at least for now, so do the Capitals.

The rate at which Connolly is scoring, in relation to his shots on goal total, is extremely rare. Since the 2005-06 season, nine players (including him) have scored 10 or more goals on 50 or fewer shots in a season. According to hockey analytics site Corsica, Connolly should have six goals based on when and where he took his shots, an indication that there may be some luck on his side.

But Connolly, who needed 81 shots on goal to score 15 times last season, doesn’t often factor luck into his calculations. The Capitals tend not to, either. Last Friday, they finished with 17 shots on goal in a 4-2 win over the Blue Jackets. Columbus, a team known for tossing puck after puck at the net, finished with 37 shots on goal. The Capitals then had just 10 shots on goal through two periods against the Red Wings on Sunday, and they trailed by three due to flat offense and scrambling defense.

So on one hand, the Capitals’ low shot volume was fine because it produced the chances they needed to score. On another, it was detrimental in producing hardly any scoring opportunities at all. Sometimes, Connolly’s own low shot volume produces the one chance he is looking for. Sometimes that second chance comes soon after, like when he scored twice on four shots on goal against the New Jersey Devils on Jan. 18. Then he went back-to-back games without a shot on goal last week — making it impossible for him to find the net — and he may start to question himself a bit before the next time he beats a goalie.

“It can all be really confusing,” Connolly said while scratching his head in the visitors’ locker room in Columbus.

He was talking about himself. He could have been talking about his team, too.

Here’s how the Capitals’ lineup is expected to look against the Winnipeg Jets:

Alex Ovechkin-Nicklas Backstrom-Tom Wilson
Brett Connolly-Evgeny Kuznetsov-T.J. Oshie
Andre Burakovsky-Lars Eller-Alex Chiasson
Chandler Stephenson-Jay Beagle-Devante Smith-Pelly
Scratched: Jakub Vrana

Dmitry Orlov-Matt Niskanen
Christian Djoos-John Carlson
Brooks Orpik-Madison Bowey
Scratched: Taylor Chorney

Braden Holtby (starter)
Philipp Grubauer

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