One person keenly aware of this challenge is Adam Cohen, a social media manager for Thomson Reuters, who has season tickets for the 2-8 Jets, who ended an eight-game losing streak Sunday. Cohen does not follow the Jets on social media, but, speaking generally, he said it can be difficult for big corporations to acknowledge when something goes wrong.

“You can’t be oblivious to the fact that you’re struggling,” said Cohen, who added that teams that treat social media like a “fantasy world” run the risk of losing trust among their fans. “If you’re losing all the time, but your activities are really positive and talking about how great such-and-such is, people are going to get angry.”

With nearly 1.85 million likes on Facebook, almost 700,000 followers on Twitter and about 183,000 followers on Instagram, the Jets rank among the N.F.L. leaders in social media engagement. On those platforms, they have absorbed criticism for what could be perceived as a lack of awareness, for Twitter posts like one from Oct. 30, four days after they committed six turnovers and benched their quarterback in a 43-23 loss to the Buffalo Bills. They teased an interview with the former quarterback Chad Pennington by asking, “Has the #Jets offense found a potential spark?”

It was all the more surprising, then, when their Twitter account last week referred to a plane that had flown over team headquarters trailing a banner calling for the dismissal of General Manager John Idzik. The post linked to video clips of selected players’ reactions to the “practice flyover & more.” The Jets, through a team spokesman, declined to comment for this article.

“It’s not to judge the Jets, but I know we wouldn’t have done that,” Griffin said. “In our case, for our brand, that’s not a unifier. That’s value-destructive for us.”

Marc Honan, the chief marketing officer of the 5-5 Buffalo Bills, said the organization holds daily meetings to determine the approach that day on social media, and its plan reflects the team’s performance. On Mondays and Tuesdays after losses, the Bills’ engagement is more modest.

When the Browns were flailing last season, Griffin said, they changed their tactics, but not their strategy. They scaled back on their activity, he said, at times their metrics showed that fans were most outraged: after losses, and into the next morning. When defeats piled up, they scrutinized every word of their content.