Film Franchises and the Edwards-Buckmire Model: An Examination of the Financial Performance of Movie Sequels

Abstract

The Edwards-Buckmire Model (EBM) is a mathematical model which utilizes a system of three nonlinear coupled ordinary differential equations to model the box-office dynamics of films released theatrically in North America. This research project seeks to examine the performance of film sequels in the context of the existing EBM and to find relationships between the performance of parent and sequel films, particularly in how the former may affect the latter, with the purpose of enabling accurate a priori predictions of the financial performance of future sequels using the EBM. First, we use data from previously released sequels to confirm that the EBM is capable of modeling the performance of sequels with the same degree of accuracy as it would in modeling the behavior of an original movie. Next, we examine various trends which have been observed, indicating connections between the performance of parent and sequel films, particularly in how the former may affect the latter. We do this by examining data concerning awareness, attendance, and gross revenue to date for pairs of parent and derivative films. Finally, we discuss what these observed trends indicate about the relationship between the performance of sequels and their parents, particularly in how known data about a potential parent film can be used to better predict how a hypothetical future sequel would perform under various conditions, utilizing the EBM.