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LOS ANGELES (AP) — Movies make more money when exactly half their casts are non-white, according to an annual analysis released Thursday that shows an increasing demand for diversity in film.

In previous years, movies did better at the box office if two or three of the top eight billed actors were non-white. In 2014, four of eight was the magic number, ticket sales show.

“These aren’t momentary glitches. It’s the handwriting on the wall,” and it points to how profoundly out of touch the motion picture academy is when giving Oscars only to white actors, said Darnell Hunt, who directs the Ralph J. Bunche Center for African American Studies at the University of California, Los Angeles.

The Bunche Center has taken a close look at each year’s top-grossing films since 2011, grouping each movie according to how many non-white actors hold the top eight roles, and calculating the median global haul of each level of diversity.

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The best performers, with a median ticket revenue of $122.2 million, turned out to be movies in which half the main cast was non-white. That’s more than double the $52.6 million median haul for films with no non-white actors in the top eight. Films where more than half the principal actors were non-white also did worse, with a median of $52.4 million.

Casts with non-whites in four of the eight top roles also provided the best return on investment, delivering ticket sales that were 3.4 times the films’ budgets, on average.

The study points to “Lucy,” a science-fiction film with Morgan Freeman, Min-sik Choi and Amr Waked in prominent roles alongside Scarlett Johansson, grossing $444 million worldwide according to IMDb.com; and “Annie,” with Jamie Foxx cast as Daddy Warbucks and Quvenzhane Wallis as the orphan, with Cameron Diaz in a supporting role. That multiethnic update of the classic musical made $119 million, according to IMDB.com.

And for franchises like the widely hailed “Fast and Furious” — which has swallowed $3.9 billion in global ticket sales — marketing campaigns and posters have purposefully played up the multiracial casts of the seven movies.

“The main payoff is always going to be the seven people on that poster,” said Kenny Gravillis, chief creative director and co-founder of movie marketing company Gravillis Inc. “The diversity of that ensemble, you feel like it adds to the box office. Absolutely.”

Not every box-office hit has a hugely diverse cast — you have to scan down to the eighth listed actor to find Chinese actress Bingbing Li in 2014’s top-selling movie, “Transformers: Age of Extinction,” which made $1.1 billion worldwide.

But that may be changing — especially with actors who can draw crowds outside the U.S. and Canada. Overseas audiences represented 72 percent of the total global box office of $36.4 billion in 2014, up from 66 percent just four years earlier.

China alone is on pace to overtake the U.S. as the world’s largest movie market in a few short years. The trend has given rise to direct appeals to Chinese audiences, with filmmakers inserting scenes with Chinese actors in a handful of recent films, including “Mission Impossible: Rogue Nation” and “Iron Man 3.”

It stands to reason why a modestly diverse cast pays off. In the U.S., Caucasians remained the largest moviegoing demographic in 2014 at 54 percent, according to the Motion Picture Association of America. But U.S. Hispanic and Asian audiences punch above their weight, making up a greater proportion of frequent moviegoers than their population.

Sometimes diverse audiences are core — 60 percent of the “Transformers” audience was non-white.

The motion picture academy has been responding to an uproar after nominating an all-white acting pool for the Oscars again this year. Academy president Cheryl Boone Isaacs has taken steps to diversify the membership of the overwhelmingly white and male institution.

Sony Pictures CEO Michael Lynton said recently at the Code Media conference that the move was a “positive step” toward aligning the awards with the reality that diversity can be good for business.

“You only need to look at a film franchise like ‘Fast and Furious’ to see what an enormous success that movie has been, and in large part I would argue it’s because of the diversity of the cast,” he said. “I think the Academy has reacted very, very quickly and positively to what I think was a very, extremely unfortunate situation this year.”

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See what regular people think of diversity at the Oscars: https://youtu.be/Fo3dvuZizB4

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Follow AP Business Writer Ryan Nakashima at https://twitter.com/rnakashi . His work can be found at http://bigstory.ap.org/content/ryan-nakashima