For most of the Flyers’ 55 years of existence, the link between them and the value of fighting in hockey has defined their identity. It’s rare to find a sports franchise so closely aligned in the public’s collective mind with a particular image or style of play, but the Flyers remain one. The Cubs were lovable losers for more than a century before winning the World Series in 2016. The Lakers are Showtime. The Yankees still retain the gleaming gravitas of their pinstripes. And the Flyers, now and forever, are the Broad Street Bullies.

It doesn’t matter that 46 years have passed since the Flyers won the second of their two Stanley Cups with their back-alley-brawl methods. It doesn’t matter that they’ve won one playoff series since 2012 and have settled into an era that could kindly be called “boring but mediocre.” It doesn’t matter that the amount of fighting in the NHL has decreased over time as the sport has evolved and more attention has been paid to head injuries. The Flyers still carry that rep, even if it isn’t as deserved or relevant as it once was, and their fans still embrace it.

So those fans, and maybe some members of the organization itself, might be surprised by the results of a recent study from OnlineGambling.Ca, a sports-betting firm based in Canada. The firm examined whether teams that fought a lot won a lot, and it found that the Flyers perhaps should have been fighting less frequently than they were.

Over the last five seasons, a Flyers player had a fight once every five games, a rate right in the middle of the pack among the league’s 32 teams. But the Flyers won just 37.7% of those games in which one or more of their players dropped the gloves. During that same half-decade, they won 51.2% of their games that didn’t feature a fight.

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“Less fighting could mean more winning for them,” the study’s authors write, “Philly is winning 35.8% more than when they do fight. A 37.7 winning percentage in games with a fight is nothing to be proud of. Maybe the Bullies should clean up their act and pick up more wins.”

Now, let’s deal with a couple of the obvious caveats to this study, starting with the difference between causation and correlation. The study’s authors make no attempt to explain why the Flyers’ record lately has been so much worse when they do fight, and neither the authors nor the study’s intended audience is likely interested in the reason. This is a gambling firm offering information to gamblers, who are looking for any piece of data that might give them an edge when they bet. They care about the trend, not its origins.

More, the study doesn’t take the context of fighting in hockey into consideration. Often, fights happen after a game’s outcome has pretty much been decided; a team is down by several goals and wants to send a message that it won’t be pushed around next time. In such a situation, a fight or fights would in no way be the cause of a team winning or losing.

But what’s interesting is this: The Flyers lost 13 times last season by three goals or more, yet they were guilty of just four fighting majors in those 13 games. If anything, that statistic might provide an insight into why general manager Chuck Fletcher, with input from coach Alain Vigneault, made the roster changes that he did this offseason — why, for instance, he acquired Ryan Ellis and Rasmus Ristolainen, defensemen who play with an edge.

Vigneault told reporters this week that he and Fletcher wanted to make the Flyers “tougher to play against,” and the fact that they didn’t fight much in those lost-cause situations last season, that at times they seemed to roll over and concede, might have been more revealing of their problems and shortcomings.

Maybe the Flyers don’t need to fight more per se. Maybe they just need to adopt a more rugged style. Remember: The physical nature of the sport is still vital, still matters, even if the NHL has largely moved on from gratuitous fighting, as former Flyers head coach — and enforcer — Craig Berube acknowledged during a 2014 interview.

“It’s just getting beyond it,” Berube said then. “I still think it is part of the game at the right time. I don’t like staged fighting. I never did. I didn’t even like it when I did it maybe back in the day. I liked the emotional part of the game, and when you play hockey and it’s physical and guys are fighting and battling and you get [ticked] off and you fight, I like that. I don’t mind that. I think it’s good for the game. Fights have been used to change the momentum of the game, and I still think it has its place a little bit for that.”

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If a few more of those situations arise for the Flyers this season, if this team looks even the slightest bit more like the clubs that created and came to define the franchise’s identity, it’s a safe bet that neither Fletcher nor Vigneault will mind much. The fans certainly won’t, either, especially the ones who, when the fists do start flying, can figure out how to make themselves a buck.