Maths of Moviemaking

Hollywood films increasingly use shot lengths of a particular pattern that best holds our attention.

Spanning over 75 years of filmmaking, what is common to The 39 Steps, Rebel Without a Cause and The Revenge of the Sith? In these films, filmmakers have used shot lengths that replicate a pattern also found in studies of the attention spans of humans, a pattern designed to hold our attention. Moreover, over the years, Hollywood films have evolved to match this pattern far better than they did in the medium’s earlier years.

This 1/f pattern occurs in diverse fields of study such as neurosciences, physics, music and even a study of the flooding of the Nile! While there is no clear explanation of its ubiquity, its occurrence in music holds some clues. White noise is sound wherehearing one unit will not help you predict what will follow; it is completely random. Brown noise is where one unit completely determines the next, but this rigidity is uninteresting to the ear. In pink noise, sound units follow this 1/f pattern that is not completely predictable but is pleasing to the ear. In case of cinema shots, this would imply that shot lengths are related to each other in much the way that units of sound are related to each other in pink noise.

A study led by Cornell Psychologist James Cutting has studied shot lengths in 150 Hollywood movies from 1935 to 2005. The paper explains that the typical ‘Hollywood film has become increasingly clustered in packets of shots of similar length. For example, action sequences are typically a cluster of relatively short shots, whereas dialogue sequences (with alternating shots and reverse-shots focused sequentially on the speakers) are likely to be a cluster of longer shots.’

The authors clarify that, ‘In no way do we claim that there is any intention on the part of filmmakers to develop a 1/f film style… Instead … as explorations and crafting of film have proceeded for at least 70 years, film narrative has fallen naturally into 1/f shot structure…’ Cutting adds that while the technique may grab viewer attention, it does nothing to improve the quality of movies; after all, he finds The Revenge of the Sith, which adheres closely to the 1/f ideal, just ‘dreadful’.

About The Author

Hartosh Singh Bal

Hartosh Singh Bal turned from the difficulty of doing mathematics to the ease of writing on politics. Unlike mathematics all this requires is being less wrong than most others who dwell on the subject.