Saturday, September 26, 2009

The Saw Movies, and Diminishing Marginal Returns

Every year, around halloween, horror movie fans are treated to the release of the next Saw movie. For those who aren't familiar, this is a series of films about diabolical killers and mechanical deathtraps. It's a gory formula that has proven successful in attracting viewers so far. With five films made already, and a sixth coming out this October, it seems that there will be a new Saw movie released every halloween, forever. But economic wisdom tells us that this can't be true. There are bound to be diminishing marginal returns for the Saw movies, right?
Let's take a look at the data. The following are the domestic box office results for all five of the Saw movies so far:

Saw 1 - $55,185,045
Saw 2 - $87,039,965
Saw 3 - $80,238,724
Saw 4 - $63,300,095
Saw 5 - $56,746,769

After the initial jump from the first film to the first sequel, we do see diminishing box office with every film. My theory is that sequels to successful films already have a level of built in publicity, almost like a brand name. So, what will the next Saw movie gross (no pun intended) at the box office? Using an awesome piece of free online statistical software, I have built a multiple regression model to predict the box office results of the next Saw movie. Here it is.

(This is a very simple model, based upon on a sample of only 5 occurrences, and not taking many important variables into consideration. I don't seriously believe it will predict the box office of Saw VI, But it sure would be cool if it did.)

I used two variables to explain the box office of these movies:
1. The order of their release, meaning a value of 1 - 5
2. A dummy variable (1 or 0) applied if the film is a sequel. This is used to explain the "Sequel Bump" I have seen here.

Thanks to the miracle of statistical software, we have the following model:

SawBoxOffice =
$65966866.70 + $43600897.50*(sequel dummy) - $10781821.70*(film#) + e[t]

So, using the model, lets predict the box office for Saw VI:

Saw6BoxOffice = $65966866.70 + $43600897.50*(1) - $10781821.70*(6)
= $44,876,834

So, I predict that Saw 6 will make $44,876,834 at the box office. We'll find out if my prediction is close at all when the halloween spooky movie season is over.


Wessa, P. (2009), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r4, URL