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Predicting the Movie Box Office

The North American market for films totaled about US$11,000 million in 2013, with over 1300 million admissions. The film industry is a big business that not even Ishtar, nor Jaws: The Revenge, nor even the 1989 Australian film “Houseboat Horror” manages to derail. (Check out Houseboat Horror next time you’re low on self-esteem, and need to be reminded there are many people in the world much less talented than you.)

Given the importance of the film industry, we were interested in using Ranker data to make predictions about box office grosses for different movies. The ranker list dealing with the Most Anticipated 2013 Films gave us some opinions — both in the form of re-ranked lists, and up and down votes — on which to base predictions. We used the same cognitive modeling approach previously applied to make Football (Soccer) World Cup predictions, trying to combine the wisdom of the ranker crowd.

Our basic results are shown in the figure below. The movies people had ranked are listed from the heavily anticipated Iron Man 3, Star Trek: Into Darkness, and Thor: The Dark World down to less anticipated films like Simon Killing, The Conjuring, and Alan Partridge: Alpha Papa. The voting information is shown in the middle panel, with the light bar showing the number of up-votes and the dark bar showing the number of down-votes for each movie. The ranking information is shown in the right panel, with the size of the circles showing how often each movie was placed in each ranking position by a user.

This analysis gives us an overall crowd rank order of the movies, but that is still a step away from making direct predictions about the number of dollars a movie will gross. To bridge this gap, we consulted historical data. The Box Office Mojo site provides movie gross totals for the top 100 movies each year for about the last 20 years. There is a fairly clear relationship between the ranking of a movie in a year, and the money it grosses. As the figure below shows, a few highest grossing movies return a lot more than the rest, following a “U-shaped” pattern that is often found in real-world statistics. If a movie is the 5th top grossing in a given year, for example, it grosses between about 100 and 300 million dollars. if it is the 50th highest grossing, it makes between about 10 and 80 million.

We used this historical relationship between ranking and dollars to map our predictions about ranking to predictions about dollars. The resulting predictions about the 2013 movies are shown below. These predictions are naturally uncertain, and so cover a range of possible values, for two reasons. We do not know exactly where the crowd believed they would finish in the ranking list, and we only know a range of possible historical grossed dollars for each rank. Our predictions acknowledge both of those sources of uncertainty, and the blue bars in the figure below show the region in which we predicted it was 95% likely to final outcome would lie. To assess our predictions, we looked up the answers (again at Box Office Mojo), and overlayed them as red crosses.

Many of our predictions are good, for both high grossing (Iron Man 3, Star Trek) and more modest grossing (Percy Jackson, Hansel and Gretel) movies. Forecasting social behavior, though, is very difficult, and we missed a few high grossing movies (Gravity) and over-estimated some relative flops (47 Ronin, Kick Ass 2). One interesting finding came from contrasting an analysis based on ranking and voting data with similar analyses based on just ranking or just voting. Combining both sorts of data led to more accurate predictions than using either alone.

We’re repeating this analysis for 2014, waiting for user re-ranks and votes for the Most Anticipated Films of 2014. The X-men and Hunger Games franchises are currently favored, but we’d love to incorporate your opinion. Just don’t up-vote Houseboat Horror.