Pareto and the UK Box Office
Studies on the box office gross of movies have indicated that, for the top grossing Hollywood movies, a power law provides a good fit of the data for the total gross of a movie with an exponent of β ~ -0.5, where β = 1/α and α is the exponent of a Pareto distribution (and is, therefore, ~ 2) (Sinha and Pan 2005, 2006).Similar results are also cited for the opening weekend gross for movies. I have not been able to find an equivalent study of British films, so in this post I fit a power curve to the total box office gross for the top 20 films in the UK and the Republic of Ireland from 2002 to 2008, inclusive. The data used is from the the statistical yearbooks produced by the UK Film Council.
Table 1 lists the results, showing the number one ranked film in each year and its total gross, β and a 95% confidence interval, and the coefficient of determination as a measure of the goodness-of-fit of the power curve to the data. The curves for each year are presented in Figures 1 through 7.
Table 1 Power regression data for the top 20 films at the UK box office in the UK and Republic of Ireland, 2002 to 2008
From Table 1 we can see that the value for β tends to be approximately -0.6, giving an exponent for a Pareto distribution of ~ 1.66. The difference from the figure of -0.5 noted above may be attributed in part to the use of only the top 20 films in this data, where other studies have used larger sample sizes. It may also reflect a difference between the performance of films at the US box office and in the UK and Ireland, with a larger share of the box office gained by a smaller group of films. For 2008, β = -0.74, and this suggests that the top four films (Mamma Mia! [£69.17m], Quantum of Solace [£51.07m], The Dark Knight [£48.82m], and Indiana Jones and the Kingdom of the Crystal Skull [£40.27m]) gained a larger market share than is typical in the UK. Combined, these four films 45.1% of the total box office for the top 20 films in this year, with the fifth-ranked film (Sex and the City [£26.43m]) grossing nearly £15 million less than the fourth-ranked film.There is also another steep drop off that occurs with the shift from the eleventh-ranked film (Iron Man [£17.42m]) and the twelfth-ranked film (Chronicles of Narnia: Prince Caspian [£11.79m]). These breaks can be clearly seen in Figure 7. While other years have a single film or a group of films that dominate, the other top 20 films have a much more even distribution.for example, the proportion of the box office gross secured by the top four films for the other six years included here ranges from a minimum 35.1% in 2007 to 41.3% in 2006, but the values of β all indicate much more even distributions and there are no sudden drops in the distributions of the sort we see in Figure 7.
It will be interesting to see what value β will take when the next edition of the UK Film Council Statistical Yearbook is published in July 2010. Will it return to ~ -0.6, indicating that 2008 was an unusual year for the UK box office, or if there is a new trend emerging reflecting the changing choices for audiences? One possibility for the change in audience behaviour is the impact of the recession, with audiences rationing the number of times they go to the cinema thereby creating tiers within the top 20 of films they really wanted to see (the top four), and films they were less willing to pay to watch (5-11 and 12-20). If this is a reasonable explanation of how audiences behave when times are hard then we should see a similar distribution for 2009.
Figure 1 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2002 (β = -0.62)
Figure 2 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2003 (β = -0.55)
Figure 3 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2004 (β = -0.62)
Figure 4 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2005 (β = -0.61)
Figure 5 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2006 (β = -0.61)
Figure 6 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2007 (β = -0.52)
Figure 7 Power regression for the top 20 films at the UK box office in the UK and Republic of Ireland, 2008 (β = -0.74)
Sinha S and Pan RK 2005 Blockbusters, bombs and sleepers: the income distribution of movies, in A Chatterjee, BK Chakrabarti, and S Yarlagadda (eds.) Econophysics of Wealth Distributions. Milan: Springer: 43-47. (here)
Sinha S and Pan RK 2006 How a “hit” is born: the emergence of popularity from the dynamics of collective choice, in BK Chakrabarti, A Chakraborti, and A Chatterjee (eds.) Econophysics and Sociophysics: Trends and Perspectives. Berlin: Wiley: 417-447. (here)
Posted on June 3, 2010, in British Cinema, Film Industry, Film Studies, Motion Picture Production and tagged Box Office, British Cinema, Film Analysis, Film Studies, Motion Picture Exhibition. Bookmark the permalink. Leave a comment.