Hollywood movies follow a mathematical formula

Feb 19, 2010 by Lin Edwards report
Image: James E. Cutting, Psychological Science, DOI: 10.1177/0956797610361679.

(PhysOrg.com) -- Hollywood movies have found a mathematical formula that lets them match the effects of their shots to the attention spans of their audiences.

Psychologist Professor James Cutting and his team from Cornell University in Ithaca, New York, analyzed 150 high-grossing Hollywood released from 1935 to 2005 and discovered the shot lengths in the more recent movies followed the same mathematical that describes the human attention span. The pattern was derived by scientists at the University of Texas in Austin in the 1990s who studied the attention spans of subjects performing hundreds of trials. The team then converted the measurements of their attention spans into wave forms using a mathematical technique known as the Fourier transform.

They found that the magnitude of the waves increased as their frequency decreased, a pattern known as pink noise, or 1/f fluctuation, which means that attention spans of the same lengths recurred at regular intervals. The same pattern has been found by Benoit Mandelbrot (the chaos theorist) in the annual flood levels of the Nile, and has been seen by others in air turbulence, and also in music.

Cutting made his discovery by measuring the length of every shot in 150 comedy, drama and action films, and then converted the measurements into waves for every movie. He found that the more recent the films were, the more likely they were to obey the 1/f fluctuation, and this did not just apply to fast action movies. Cutting said the significant thing is that shots of similar lengths recur in a regular pattern through the film.

Cutting believes obeying the 1/f law makes films “resonate with the rhythm of human attention spans,” and this makes them more gripping. Films edited in this way would then tend to be more successful and the style of shooting and editing more likely to be copied. Films of Cutting’s own favorite genre, the Film Noir, do not generally follow the 1/f law, with shot lengths tending to be more random. By contrast The Empire Strikes Back (1980) and the 2005 blockbuster movie Star Wars Episode III (which Cutting considers to be “just dreadful”) both follow 1/f rigidly.

The researchers concluded that over the next few decades film makers may take more care to follow the 1/f law to try to boost audience engagement.

Explore further: Mathematical model tackles 'Game of Thrones' predictions

More information: Attention and the Evolution of Hollywood Film; James E. Cutting, Jordan E. DeLong and Christine E. Nothelfer, Psychological Science published online 5 February 2010. DOI:10.1177/0956797610361679 . Full text of the paper is available here.

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User comments : 12

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Skeptic_Heretic
4.9 / 5 (7) Feb 19, 2010
The formula,

If $movie.revenuestream gt $movie.expenditure append $_.success=1
else append $_.success=0
If $movie.success=1 wait years=5
then repeat
If $movie.success=0 rename $movie.title
then repeat

End
CLS
mjc
3 / 5 (2) Feb 19, 2010
what the....! the comment above makes NO sense
dallas27
5 / 5 (1) Feb 19, 2010
Actually, it's hilarious!

Think Mission Impossible I, II, III or the James Bond series.....and then think Freaky Friday, The Hot Chick, and Being John Malkovich.
Skeptic_Heretic
5 / 5 (2) Feb 19, 2010
what the....! the comment above makes NO sense

It's a pseudo powershell script for "If we made money, put out a remake in 5 years. If we didn't make money, recycle the story with new actors and characters."

I thought it was humorous.
mjc
Feb 19, 2010
This comment has been removed by a moderator.
Parsec
5 / 5 (1) Feb 19, 2010
Another typical example of evolution in action. I doubt very much if producers are timing each shot to correspond to the 1/f law. Most of them probably think the moon is made of cheese and the idea that they have the mathematical understanding to describe shot lengths according to an underlying principle is pretty unlikely.

I find the explanation offered in the article far more likely. The community of film editors is pretty small, and those associated with successful movies get more work. This moves editors with the 'style' of cutting towards the 1/f law into more and more movies, gradually replacing those that do not.

They will probably soon be teaching this law to film editors in school. Nothing wrong with it, the 1/f law can be followed even for quite original and unique scripts.
kasen
not rated yet Feb 20, 2010
Having engaged in some heavy movie-watching lately, of the order of tens, maybe hundreds of films in a few months, I have experienced the evolution described above.

Moreover, there is a serious conditioning factor at work. Growing up with post-90s films, I find it harder to watch films the older they are, because of the slower pace. It's not that I can't focus, it's that I get easily bored by the strenuous plot progression.

My generation has been conditioned to process a lot of information really fast and as such, we're quite impatient when it comes to entertainment. I just wonder how will the post-2000 kids look at things. I feel we're approaching some sort of asymptote.
Yes
not rated yet Feb 20, 2010
If your formula stops working, then you rewrite it in Fortran 77 or some other old long forgotten mysterious language like clipper or so.
That scheme of old forgotten, ancient and mysterious seems to be popular in Hollywood, and you will make even more $ out of less movie.
magpies
not rated yet Feb 20, 2010
They have to make things faster because of the lack of plot...
Neurons_At_Work
not rated yet Feb 20, 2010
Sounds like natural selection playing out in the film industry. Reminiscent of the samurai crab...
canuckit
not rated yet Feb 20, 2010
I guess they forgot to include in their formula
the amount of explosives for each movie.
Paradox
not rated yet Feb 21, 2010
My generation has been conditioned to process a lot of information really fast and as such, we're quite impatient when it comes to entertainment. I just wonder how will the post-2000 kids look at things. I feel we're approaching some sort of asymptote.


It is probably that you are more "conditioned" to the loud noises and flashing lights, with little regard for the story. I have no problem "processing" any film, whether it be new or old, as long as the storyline is halfway decent. I would bet that after you have seen enough movies, you will find that the flash and bang aspect loses some of it's appeal.
Nune
not rated yet Mar 21, 2010
what the....! the comment above makes NO sense

It's a pseudo powershell script for "If we made money, put out a remake in 5 years. If we didn't make money, recycle the story with new actors and characters."

I thought it was humorous.


It was.
Patterns in your script helped me decipher it, but maybe Klingon would have been more familiar language to use.