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: Math modeling handbook now available

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.

Related Stories

Blockbuster 'Avatar' to accelerate 3D revolution

Jan 06, 2010

The runaway success of science fiction blockbuster "Avatar" will accelerate the 3D movie revolution, which has already powered Hollywood to a record year at the box office, analysts say.

Site offers movie ratings with a twist

Sep 10, 2009

There's no shortage of Internet sites and services that rate movies. RottenTomatoes.com and Metacritic.com compile critics' reviews; while IMDB.com lets users pick the Top 250 movies of all time. If you want to know what ...

AMD64 Is The Force Behind Star Wars

Aug 09, 2004

At Siggraph today, AMD (NYSE: AMD) announced that AMD Opteron™ processor-based servers and workstations are providing the digital backbone for the final Star Wars prequel, Episode III: “Revenge of the Sith.” The AM ...

Recommended for you

Not just the poor live hand-to-mouth

13 hours ago

When the economy hits the skids, government stimulus checks to the poor sometimes follow. Stimulus programs—such as those in 2001, 2008 and 2009—are designed to boost the economy quickly by getting cash ...

Math modeling handbook now available

16 hours ago

Math comes in handy for answering questions about a variety of topics, from calculating the cost-effectiveness of fuel sources and determining the best regions to build high-speed rail to predicting the spread ...

Archaeologists, tribe clash over Native remains

16 hours ago

Archaeologists and Native Americans are clashing over Indian remains and artifacts that were excavated during a construction project in the San Francisco Bay Area, but then reburied at an undisclosed location.

Male-biased tweeting

18 hours ago

Today women take an active part in public life. Without a doubt, they also converse with other women. In fact, they even talk to each other about other things besides men. As banal as it sounds, this is far ...

User comments : 12

Adjust slider to filter visible comments by rank

Display comments: newest first

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.
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.

More news stories

Male-biased tweeting

Today women take an active part in public life. Without a doubt, they also converse with other women. In fact, they even talk to each other about other things besides men. As banal as it sounds, this is far ...

Not just the poor live hand-to-mouth

When the economy hits the skids, government stimulus checks to the poor sometimes follow. Stimulus programs—such as those in 2001, 2008 and 2009—are designed to boost the economy quickly by getting cash ...

Archaeologists, tribe clash over Native remains

Archaeologists and Native Americans are clashing over Indian remains and artifacts that were excavated during a construction project in the San Francisco Bay Area, but then reburied at an undisclosed location.

When things get glassy, molecules go fractal

Colorful church windows, beads on a necklace and many of our favorite plastics share something in common—they all belong to a state of matter known as glasses. School children learn the difference between ...

SK Hynix posts Q1 surge in net profit

South Korea's SK Hynix Inc said Thursday its first-quarter net profit surged nearly 350 percent from the previous year on a spike in sales of PC memory chips.

FCC to propose pay-for-priority Internet standards

The Federal Communications Commission is set to propose new open Internet rules that would allow content companies to pay for faster delivery over the so-called "last mile" connection to people's homes.