The quality of play wasn’t inspiring confidence, either, with looming questions about player safety and concussions. By January, ad dollars were declining, and as this season kicked off there were jitters on Wall Street. One research firm, MoffettNathanson, reported, “Any sign of continued ratings weakness could pose a long-term risk for broadcasters …”

For the moment, league and TV executives can exhale. Five weeks into the season — a large enough sample size to offer something of a progress report — the returns are plenty encouraging.

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CBS’s NFL audience is up 7 percent; FOX’s is down 2 percent; NBC’s Sunday Night viewership is basically flat; and ESPN’s Monday Night broadcast is down 4 percent, but with several marquee matchups still to come. All told, the league’s ratings are up a few percentage points.

Now consider that relative stability in a larger context: In September, the top 15 TV shows were all NFL games. Cable entertainment programming — not including news and sports — is down 11 percent this fall. And on Monday Night, the New Orleans Saints and Redskins more than doubled the audience of a playoff matchup between two of baseball’s most iconic teams, the New York Yankees and Boston Red Sox.

“The question was where is the floor going to be,” said Michael Mulvihill, executive vice president of research for Fox Sports. “Were we going to have more sharp declines or were we going to stabilize? Our hope was to stabilize.”

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Added Sean McManus, the chairman of CBS Sports: “The arrows are pointing up. The important thing is that we’re still dominant.”

The leading reason for the good news, several media and league executives said, has a shockingly simple explanation: better football. Through five weeks, the league has set a record for scoring (it’s up 11 percent from last year, the largest single jump since 1975), while the average margin of victory (counting ties) is just 9.96 points, which would be the lowest since 1932. Teams in big markets, meanwhile, have had renewed success, driving up ratings in Los Angeles, where the Rams are undefeated, and in Chicago, where ratings have jumped around 50 percent, thanks to the first place Bears.

The easiest explanation for the offensive outburst has been better quarterback play, boosted both by changing enforcement of roughing the passer rules and a wave of young talent, (just a few years after some in the league worried about the health of the position). Patrick Mahomes in Kansas City and Jared Goff in Los Angeles look like burgeoning stars, while rookies Sam Darnold and Baker Mayfield have made doormats like the New York Jets and Cleveland Browns watchable.

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Injuries, too, are down after crossover stars like receiver Odell Beckham Jr. and quarterbacks Aaron Rodgers and Deshaun Watson missed significant time last year.

“When the games are good, scoring is up, the best players are on the field and big markets are playing well more people watch,” said Brian Rolapp, the NFL’s executive vice president of media. “This is what we tried to tell people last year.” (Even last year, the league likes to note, 37 of the 50 most-watched TV shows were NFL games; that number was just 11 a decade ago.)

More compelling football has resulted in viewers watching games for an average of three more minutes this season (83 versus 80), according to Mulvihill, which may not sound like much but adds up when you consider the millions of fans watching.

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The good news has steadied nerves from New York to Los Angeles. In the lobby of the Fox Television offices in Southern California hangs a very big mural. It is 20 feet long, with larger-than-life depictions of the NFL’s brightest stars, Rodgers and J.J. Watt, among them. The mural’s caption reads, “Fox is Football.”

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Whenever Mulvihill saw that mural over the last two season, it was a reminder of the stakes. What did the sagging numbers mean for the league, and for his network?

“It’s my job to understand consumer behavior in TV and sports media,” he said. “We’re so connected to the NFL and I felt personal pressure to explain it.”

Inside the league offices, Rolapp has clippings on his desk that he revisits every so often, including a 1964 issue of Sport magazine that questioned the future of the league. “People have been writing about the death of football for a long time,” he said.

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That doesn’t mean it’s always easy to take the long view. Joe Lockhart, a former NFL spokesman, spent the last two seasons in league meetings, combing through research about the TV numbers, which suggested the NFL was not actually facing an existential crisis. Until this fall, that was just a theory in the face of troubling data.

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“I don’t care if you’re Bill Gates at Microsoft in 1976 who knows he has the best business idea, success is never a straight line,” Lockhart said. “We’d meet every week and go over the numbers. It was hard to see them and hard to see the president taking credit for them, but the belief was that if the games were great people would be watching.”

He added, “If you think of the NFL as a movie studio, this year they’ve got a blockbuster.”

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While there is plenty of optimism, there remains some disagreement over the Trump effect. In 2016, a historic presidential election dominated all facets of media (and life), sucking viewers away from the league. Last year might have been more complicated. Mulvihill said he saw some attrition in older, less affluent and rural viewers, which could be attributed to Trump’s attacks on the league, and that those losses are baked into this year’s data.

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“We underestimated the intensity of the news cycle of the Trump Administration,” Mulvihill said. “The president’s comments elevated the player protests last year. We couldn’t have foreseen that and it made an impact during the season.”

Others remain less willing to cede any ground to Trump.

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“I never saw a single piece of research that showed Trump made much of an impact,” said Lockhart, a former aide to Bill Clinton. “The threat to the league wasn’t Trump, it was Netflix.”

Five weeks does not, of course, solve the NFL’s serious safety problems, nor does it promise a long-term solution to ever-evolving media habits. The NFL’s TV audience, for instance, continues to get older. But the season’s strong start has, at the very least, been enough to stave off Trump’s tweets and also calm some of the hysteria.

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After Week 4, MoffettNathanson, the research firm that worried about the league’s viewers before the season, put out another memo. This one touted the good ratings numbers. It began, “We didn’t see this coming!”