A Parsimonious Model for Forecasting Gross Box-Office Revenues of Motion Pictures
Authors: Sawhney Mohanbir S. , Eliashberg Jehoshua 
Published: October 2008

The primary objective of this paper is to develop a parsimonious model for forecasting the gross box-office revenues of new motion pictures based on early box office data. The paper also seeks to provide insights into the impact of distribution policies on the adoption of new products. The model is intended to assist motion picture exhibitor chains (retailers) in managing their exhibition capacity and in negotiating exhibition license agreements with distributors (studios), by allowing them to project the box-office potential of the movies they plan to or currently exhibit based on early box-office results. It is also of interest to practitioners in other software industries (e.g., music, books, CD-ROMs) where the distribution intensity is highly variable over the product life cycle and is an important determinant of new product adoption patterns. The model and its extensions are of interest to academic researchers interested in modeling distribution effects in new product adoption, as well as forecasters looking for ways to leverage historical data on related products to forecast the sales of new products.

We draw upon a queuing theory framework to conceptualize stochastically the consumer's movie adoption process in two steps—the time to decide to see the new movie, and the time to act on the adoption decision. The parameter for the time-to-decide process captures the intensity of information intensity flowing from various information sources, while the parameter for the time-to-act process is related to the delay created by limited distribution intensity and other factors. Our conceptualization extends existing new product forecasting models, which assume that consumers act instantaneously on the motivating information they receive about the new product. The resulting model is parsimonious, yet it accommodates a wide range of adoption patterns. In addition, the stochastic formulation allows us to quantify the uncertainty surrounding the expected adoption pattern. In the empirical testing, we focus on the most parsimonious version of the modeling framework. BOXMOD-I, a model that assumes stationarity with respect to the two shape parameters that characterize the adoption process. The model produces fairly accurate early forecasts using at most the first three weeks of data for calibration, and the predictive performance of the model compares favorably with benchmark models. We propose extensions of the basic model that account for more realistic non-stationary distribution intensity patterns—including a “wide release” pattern that relies on intensive distribution and promotion, and a “platform release” pattern that involves a gradual buildup of distribution intensity. Finally, we present an adaptive weighing scheme that combines initial parameter estimates obtained from a meta-analysis procedure with estimates obtained from early data to produce forecasts of box-office revenues for a new movie when little or no box-office data are available.

An important finding from the empirical testing is that motion picture box-office revenue patterns display remarkable empirical regularity. We find that there are only three classes of adoption patterns, and these can all be represented within the basic model by using a two-parameter. Exponential or Erlang-2 probability distribution, or a three parameter Generalized Gamma distribution. We also find that cumulative box-office revenues can be predicted with reasonable accuracy (often within 10% of the actual) using as little as two or three data points. However, our attempts to predict revenue patterns without any sales data meet with limited success. While the scale parameter can be estimated reasonably well from a historical database of parameter values, we find that it is considerably more difficult to predict the shape parameters using historical data.

The parsimony we seek in developing the model comes at the cost of several limiting assumptions. We assume that the time-to-decide subprocess and the time-to-act subprocess are independent, which may not be the case if decisions on continued exhibition by retailers are endogenously related to box-office revenues over the life cycle. In the basic model formulation, we also assume that the time-to-act process can be represented by an exponential distribution, which may not always be the case. While we provide some empirical evidence to support these assumptions, further research could relax these and other assumptions to enrich the basic model, although this would entail some loss in parsimony.