Abstract
Weekly box office revenues for motion pictures show a pattern where peak revenues often appear in the first week, and then new revenues slowly die out. This paper proposes a simple model to describe such box office revenues. The new model assumes that there are two types of adopters, with the first being the moviegoers who are aroused to go to a movie based on intrinsic motivation, possibly aroused by trailers, advertising and social media content, and a second type of moviegoers who enjoy shared consumption. A second key feature of the simple model, which involves basic logistic diffusion patterns, is that the first type starts adopting already before the launch of a movie, but can only go a movie when it is launched, while the second type starts to adopt right from the launch onwards. The sum of the two S-shaped diffusion processes only gets observed from the launch of a movie onwards. Parameter estimation turns out to be easy as is illustrated for forty top lifetime grosses (as per 2020) for the USA.
Highlights
Introduction and motivationThis paper deals with modeling the diffusion in the motion picture industry, here in particular and as an illustration, the USA market with a focus on the weekly box office data for the forty top movies .1 Typical cumulative revenues observations look like those as inFig. 1, which depicts the cumulative revenues forStar Wars: Episode VII The Force Awakens
The present paper proposes a simple model to describe box office revenues
In words, is the total amount of moviegoers who adopt a movie before its launch smaller than the total amount of the second type of adopters? given the different motivations to go to the movies, it may be that γ2 > γ1
Summary
This paper deals with modeling the diffusion in the motion picture industry, here in particular and as an illustration, the USA market with a focus on the weekly box office data for the forty top movies The focus of the present paper is not on (pre-launch) forecasting nor on features of the movies that moderate the patterns, but instead it is on describing the data like in Fig. 1 using a model that allows for an interpretation concerning two types of adopters (consumers). For forecasting purposes, one may decide to fit a simple Weibull model to the data, see for example Moe and Fader (2002) or a logarithmic function These models do not have an interpretation in terms of two types of adopters, which is pursued in the present paper. At first sight it seems that the data concern a truncated diffusion process. This section proposes a simple model that incorporates underlying S shaped diffusion processes with straightforward interpretation, which can exactly describe the patterns in the data. No hard proof can be given to the two labels, but it
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