The Flyers took the ice on Tuesday night facing a situation that is appropriate for a season in which they have alternated greatness with disappointing play and ended up on the average side of things in the NHL’s Eastern Conference.

With a win over the Columbus Blue Jackets — which they got by a 5-1 score that was more impressive than the game itself — the Flyers moved into third place in the Metropolitan Division and, if the season ended today, a guaranteed playoff spot. Had they lost, however, they would have fallen into ninth place in the conference, and been outside looking in.

The season is far from over, of course, with 60 games down and 22 left, and all that ciphering is meaningless. But the swing that took place based on just one easily-forgotten game in mid-February is telling.

The Flyers are still finding their identity, even as the number of games remaining dwindles. On most nights, they are a better defensive team than an offensive one. On Tuesday, against the shorthanded Blue Jackets, they essentially shut down the opponent for the first two periods and took advantage of what center Kevin Hayes called “puck luck.”

Hayes, whose rights were obtained from Winnipeg ahead of the free-agent market last summer, was the first beneficiary of some good fortune that staked the Flyers to a 2-0 lead just five minutes into the game.

“I was trying to find T.K. [Travis Konecny] backdoor and it hit their skate and went off the goalie’s head and went in,” Hayes said.

That’s not the way you draw it up, but there is a value to just throwing the puck toward the net sometimes. Hayes was at the doorstep with no angle at all as Konecny dived at the far post and, just like the man said, the puck hit something, went almost straight up and clanged off the helmet of goalie Elvis Merzlikins and settled into the net. It wasn’t pretty, but it was the first point for Hayes after a six-game drought.

“I’m not complaining,” he said.

Hayes, centering the second line, was a presence throughout. He lost an assist when a goal was disallowed on interference, and he was a big part of the penalty-killing unit. On the season, he has 18 goals now, tying him for second on the team with Sean Couturier and James van Riemsdyk, behind only Konecny’s 20 goals.

“He’s been really big. He makes our team that much deeper and he’s such a threat when he’s handling the puck,” Konecny said of Hayes. “He loves holding onto it, and that makes the other team commit to stepping up on him and opens up something else.”

Hayes was originally signed to complement Nolan Patrick at the center position, perhaps allowing Patrick to take over the third line and get more favorable matchups. When Patrick was sidelined before the start of the season with a migraine condition, Hayes went from being a nice addition to a vital one.

“We didn’t know exactly what would be available as far as free agents, and I think Chuck [Fletcher, the general manager] did the right thing to sign him before free agency opened,” coach Alain Vigneault said. “He gave us more depth up front and has become a big part of this team.”

Hayes played for the Rangers under Vigneault and spent his first four seasons in New York before being dealt at the trade deadline last season to Winnipeg. With Hayes on the verge of becoming a free agent, the Flyers moved quickly and signed him to a seven-year, $50 million contract that seemed a touch extravagant at the time — and might still be — but no one is questioning it right now.

“I’m super comfortable here. These guys are awesome, and I’m comfortable with the coach,” Hayes said. “I’m happy with my decision and have no regrets. I’m just happy it turned out this way.”

The season still has a lot of turning out to do. Tuesday’s win began a stretch of games in which the Flyers are home 10 out of 14 times. It’s possible they can find some sustainable momentum to carry them toward the playoffs during that span.

That would be a departure, but it’s also the nature of a team that, without a scoring superstar, has to cobble together its wins carefully every night. The Flyers don’t have a player among the league’s top 30 for points. Couturier is their offensive leader with 53 points, and that puts him in a tie for 31st.

“We know we have to play a team game to win,” said captain Claude Giroux. “We don’t have a couple players that do everything. Everybody has a role and everybody knows their role.”

There is also a role for “puck luck,” and Kevin Hayes and all the Flyers will accept that, too. The standings swing wildly, the puck bounces in funny ways, and a team that brought in what it thought was an extra center finds that he might be just the extra they all need.