Published online 14 June 2005 | Nature | doi:10.1038/news050613-1

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# Modellers measure 'word of mouth' for films

Mathematics calculates quality of sleeper hits and movie bombs.

Audience response is everything when it comes to film quality.© Punchstock

It's official, says one group of researchers: Blade II is a bad film. Their study turns patterns of attendance into a single number that claims to grade a film's quality1.

The number attempts to gauge of how good the 'word of mouth' was around a given film, based on the behaviour of the harshest critics of all, the paying public.

César Hidalgo, now a graduate student in physics at the University of Notre Dame, Indiana, and his colleagues, decided to study the 'word of mouth' effect in the film world simply because reviews often have a huge impact on audience numbers and there are copious data on ticket sales.

Hidalgo, along with Carlos Rodriguez-Sickert, an economist at the Pontifical Catholic University of Chile, Santiago, and Alejandra Castro of the University of Michigan, Ann Arbor, constructed a mathematical equation that approximates box-office takings in the weeks after release. They assume that revenue relies on three major factors: the size of the possible audience, the initial desire of audience members to see the film (which is often dictated by the amount spent on marketing and publicity), and audience response to the film.

The team then plugged arbitrary numbers into their simple equation to create dozens of graphs describing weekly box-office results for a film during its cinema lifetime. If the marketing weighed in heavily, for example, but audience reviews were poor, the resulting graph would peak in the first week and then plummet. If the reviews were good, however, the graph would keep climbing.

When they compared their graphs with actual box-office data (available on the Internet Movie Database) for 44 recent films, they found good matches for films ranging from huge blockbusters to budget flicks. "It was a surprise that the model behaved nicely for all different behaviours, and was not just a coincidence for some of them," says Hidalgo.

## Staying power

The team says that the review coefficient (the word-of-mouth component of their equation) is a rough indicator of the film's quality.

The comedy Kissing Jessica Stein, for example, can be modelled using a large, positive review coefficient. It started with initially poor attendance, but increased its box-office take over the following five weeks owing to good reports from the audience. In contrast, Blade II looks like a classic bomb: a large negative review coefficient matches its quick dive in takings.

"It's a fun paper," says Gerben Bakker, an economic historian who studies Hollywood marketing at the University of Essex, UK. "But it's quite a basic model. They don't consider a lot of the complications."

Bakker says that the model could be improved by factoring in the effect of a film's availability on its box-office take, for example. Many people who would like to see a particular low-budget film are unable to because it is not playing in a local cinema, he says.

## Show me the money

Good quality films don't always win financially, even if they do have more staying power. A bigger initial interest in Blade II meant that its overall box-office take was more than ten times greater than that of Kissing Jessica Stein, which took just US\$7 million in the United States.

Big blockbusters are often simultaneously distributed to more than 3,000 cinemas in the United States, explains John Sedgwick, a media economist at London Metropolitan University, UK. So a film generally does enough business in its first two weeks to recoup its costs, which is the first priority of the studio.

However, about 70% of film revenue now comes from outside the box office, he adds. The rise in home video and DVD sales, along with toys and other products, means that pleasing the audience is ever more important for a film's overall financial success.

Hidalgo adds that thinking of films this way should help studios to decide whether to commission a sequel. Even high-grossing films can be deeply unpopular with the audience, which dooms their cinematic offspring, he says.

If only they'd thought of that before commissioning the third in the Blade series.

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