How the Avengers assemble: Ecological modelling of effective cast sizes for movies

The number of characters in a movie is an important feature. However, it is non-trivial to measure directly, for example naive metrics such as the number of credited characters vary wildly. Here, we show that a metric based on the notion of ecological diversity as expressed through a Shannon-entropy based metric can characterise the number of characters in a movie, and is useful in taxonomic classification. We also show how the metric can be generalised using Jensen-Shannon divergence to provide a measure of the similarity of characters appearing in different movies, for instance of use in recommendation systems, e.g., Netflix. We apply our measures to the Marvel Cinematic Universe (MCU), and show what they teach us about this highly successful franchise of movies. In particular, these measures provide a useful predictor of success for films in the MCU, as well as a natural means to understand the relationships between the stories in the overall film arc.