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LOS ANGELES — Hollywood’s friendship with Facebook is showing signs of strain.

The entertainment industry was among the first to embrace the Silicon Valley phenomenon. Studio executives thought the giant social network held great promise in reaching moviegoers for less money than traditional advertising such as trailers and TV ads. Facebook’s origins even became fodder for the 2010 Academy Award-winning movie “The Social Network.”

These days, major studios are taking a hard look at the cost of winning friends on Facebook. Some industry executives are increasingly skeptical that Facebook ads and promotional campaigns that ask users to “like” a movie can deliver big box-office returns.

“For people who are actually looking at the research and are looking for return on investment, for metrics that indicate specifically what Facebook’s role is in the movie-marketing equation, the jury’s still out,” said Jim Gallagher, a movie-marketing consultant who formerly oversaw marketing for Walt Disney Studios.

Fred Leach, Facebook’s head of entertainment measurement, said the Menlo Park, Calif., company is working more closely than ever with Hollywood studios to help them target the right audience for a film, including giving studios more data showing the connection between ads and movie-ticket sales and more tools to track the effectiveness of Facebook campaigns.

In Hollywood, few are openly critical of the world’s biggest social-networking company.

“Facebook continues to be an important advertising partner,” said Dwight Caines, president of worldwide digital marketing at Sony Pictures Entertainment. “They are on every campaign we do today.”

But other film executives confide privately they are considering cutting their spending on Facebook ads, just as carmaker General Motors did last year, when the nation’s third-largest advertiser dropped its annual $10 million Facebook campaign after deciding the ads didn’t help sell cars.

Sensitive time

The skirmish with Hollywood comes at a sensitive time for Facebook. The company, under pressure from Wall Street to grow revenue after its initial public stock offering in May, is competing with other social media for a share of the estimated $1.5 billion a year each major studio spends promoting movies globally.

Part of the problem is that studios are being asked to pay for the exposure they once got for free.

For years, studios have set up Facebook fan pages to connect with moviegoers, sending photos, video clips and other updates to the News Feed of users who “liked” a particular film, at no cost to the studios.

Then, in September, Facebook made a change to the algorithm that decides what users see in their News Feed. Facebook says it made the shift because users were tagging posts with negative feedback.

Decline in numbers

Major brands, including Hollywood studios, have seen a dramatic decline in the number of fans who see their messages.

For example, 72 percent of movies and network TV shows experienced a drop in the number of people who saw new Facebook posts after the new algorithm launched, according to BlitzMetrics, a Facebook marketing firm that analyzed 9 billion page posts generated over a 60-day period before and after the change.

That decline took a toll on two factors marketers watch closely: reach and engagement.

Twenty-three percent of the biggest studio pages saw a reduction in “engaged” users — people who click on a post, share it with friends or write a comment — because of decreased exposure in the News Feed, BlitzMetrics found. The drop in “reach” — the number of people who saw these updates from the most popular film and TV sites — was even sharper: 45 percent.

The change in the algorithm coincided with a push from Facebook to get studios to buy ads in the News Feed.

Different ways

Social-media experts say studios will have to find new ways to appeal to users and interact with them more. Pages that get a lot of likes and comments are favored by Facebook’s algorithm.

Some studios are responding by bringing in their own writers and production teams to help create more engaging campaigns. Studios will also have to place ads to recapture the attention of their audience on Facebook, the experts said.

“The days of free traffic are over,” said Dennis Yu, founder of BlitzMetrics. “Facebook has been trying to educate marketers on how to be social — to post the most engaging content — so as not to be penalized by their algorithms.”

Still on Facebook

To be sure, movie studios haven’t turned their backs on Facebook and its 1 billion-plus users around the globe. Every major holiday film — including “Twilight: Breaking Dawn — Part 2,” “Skyfall,” “Lincoln,” “The Hobbit: An Unexpected Journey” and “Les Miserables” — has a splashy presence on the site.

Facebook’s Leach said 99 percent of all films released this year advertised on the social network, although he declined to say how much the studios spent.

At the same time, studios have been turning to the next generation of social-media players, including Twitter, Tumblr and Pinterest, said Todd Steinman, chief executive of the social-media marketing agency M80.

“Nothing exists in a vacuum. You’ve got all these platforms that have emerged,” Steinman said. “Facebook is still the behemoth, but for immediacy and for intelligence and for market penetration, I think Twitter has probably surpassed it as far as a marketing vehicle for movies that are coming out.”