Another example of misleading time-based correlation

On my sister blog last week, I wrote about how to screw up a column chart. The chart designer apparently wanted to explore whether Rotten Tomato Scores are correlated with box office success, and whether the running time of a movie is correlated with box office success. In either case, the set of movies is a small one, those directed by Chris Nolan. Here is a better view of the data:

There were a few questions on Twitter, which I will address in this post. Someone complained about the horizontal axis thinking that year data is continuous and the axis should not be discrete. That would be true if the data is truly continuous. The way I interpret the year data here is ordinal: Chris Nolan only makes a movie once every 1 to 3 years; his career is also developing during this period of time; so I think of the horizontal axis as ordinal, that is, his first film, his second film, etc.

Another Twitter user tried a scatter plot. It's very satisfying to see the following chart. It shows a strong positive correlation between the running time of a movie and the box office receipts.

In fact, a hockey-stick line fits the data even better. This implies a multiplicative relationship between running time and box office receipts. We can fit this by first taking the logarithm of box office receipts. So, the following
chart showing how good this fit is:

 If you run a regression, the R-squared is 90 percent, and the effect of running time is extremely significant (p < 0.0002). So we have proved that Chris Nolan should make longer movies because the longer the running time of his movies, the bigger the box office.

 ***

Now, re-consider the last lines of last week's blog (link):

You might have noticed that both running time and box office numbers have gone up over time. (That is to say, running time and box office numbers are highly correlated.) Do you think that is because moviegoers are motivated to see longer films, or because movies are just getting longer?

And these items:

1) Chris Nolan's career experienced a hockey-stick growth during this time.

2) Movies have become longer and longer in general.

3) Rotten Tomatoes also experienced a hockey-stick growth in users during this time period. In January 2000, the site had 250K visitors, at which point the founders said they "started in earnest as a company". (link) Today, according to Wikipedia, they had almost 20 million monthly visitors. In other words, several of the early movies by Chris Nolan came out before RT came into its own.

 

 

 

 

Comments

[Nate]

Wow, it sounds like he needs to make a 50 hour movie! According to the model it will suck up all the money in the world!

[Jegar]

There are other factors that could be causing this correlation, in particular marketing budget.

The way studios market films is to pick a 'blockbuster' for that year out of the set of scripts they have selected, then buzz the hell out of it.

If Chris Nolan's film is chosen to be the blockbuster for that year, his film will get more money in its budget - meaning it is easier to make a longer movie.

It will also have more money dedicated to its advertising, meaning a higher box office take and potentially a higher RT rating.

As Nolan's career continues and he gets more films under his belt (delivered on time and to budget hopefully), the budget dedicated to his films will naturally increase because his projects are now less risky.

So all these features and their trends- length of film, box office take and RT rating can all be explained by the fact that they all reflect greater investment in the films over time due to his name reducing the risk that the film will never be released.

All of this will be blown out of the water if we look at his actual budgets I'm sure, but that could easily be due to the 'creative accounting' the studios do to prevent making a profit and therefore having to pay royalties to the cast and crew, or paying tax on their blockbusters.