Saturday, July 24, 2010

More Econometric Fun With The Saw Movies (This Blog Article is in 3D)

Last year, I attempted to predict the box office success of Saw 6 using regression analysis aided by statistical software. Since the gruesome Halloween tradition of the Saw franchise will continue this year with "Saw 7: 3D" I'm going to try it again and see if I can improve on my powers of prognostication.
To help the non-econometrically inclined understand what's going on, here's the same basic explanation of regression analysis I included on my James Bond article:
For those unfamiliar with regression analysis, it's a statistical method that searches for correlation among phenomena. It uses calculus to find the mathematical equation that best fits a group of numerical data. This type of math is really labor intensive, and for large data sets was near impossible before the computer age. I don't know how the calculus works, but that's OK for my purposes. I just think of statistical software as a "magic box" that spits out predictive functions when I put numbers into it.
This is the method I shall use to try to predict how much money Saw 7 will make at the domestic box office.
So let's get started. Here is the data of how much money each Saw film has made:

Saw 1 - $55,185,045 (2004)
Saw 2 - $87, 039,965 (2005)
Saw 3 - $80,238,724 (2006)
Saw 4 - $63,300,095 (2007)
Saw 5 - $56,746,769 (2008)
Saw 6 - $27,693,292 (2009)

To improve the analysis, as I did with the James Bond article, I am going to adjust for inflation by putting everything into 2004 dollars. This will automatically remove the inflation that distorts the comparability of year to year data.
Here's the same data converted into 2004 dollars:

Saw 1 - $55,185,045
Saw 2 - $84,177,916
Saw 3 - $75,707,623
Saw 4 - $58,098,757
Saw 5 - $50,177,182
Saw 6 - $24,585,575

Here it is on a chart:

As you can see, after a sizable jump from the first movie to the second, I think due to the built in publicity of the first film, the box office has declined with each new release. I think this represents the economic principle of diminishing marginal returns, as film viewers get tired of seeing the same thing year after year (in this case, viewers are getting tired of seeing people get tortured by sadistic Rube Goldberg contraptions.)
So what does regression analysis predict for Saw 7? Let's plug in the data and find out.
I will use the same econometric model I used in my earlier Saw article. This model will use only two variables to mathematically predict how Saw 7 will do. The model will be "explaining y in terms of x and z." These explanatory variables are:
1. The numerical order of the release of the films (1,2,3,4,5, and 6)
2. A "sequel dummy" variable (a value of 0 or 1 depending on if the film is the first in the series. So when I plug in the data, Saw 1 will get a 0, and Saw 2 through 6 will each get a 1) This "sequel dummy" isolates the positive effect on the box office that is the result of the built in publicity created by the first film.
And here it goes. Plugging in the data, the statistical software gives me the following function:
Boxoffice[t] = -14471512.3 order[t] +46778902.5 sequeldummy[t] +69656557.3 + e[t]
To translate this statement into English, it says:
The box office of a Saw movie decreases by an average of around $14 million with each new Saw film that is released:
(-14471512.3 order[t])
The box office also increases by around $46 million just from the built in publicity of being part of a franchise, as is the case with Saw 2-6: (46778902.5 sequeldummy[t])And at the end of the function there's: (+69656557.3).
This $69 million figure is the y-intercept, so if you could break the laws of both reality and filmmaking, and release "Saw Zero" this is how much money it would make at the box office (order and sequeldummy would both be 0 in this case leaving just the intercept.)
So what does this mean for Saw 7? Lets plug it in. For Saw 7:
Order = 7
Sequeldummy = 1
So our model will be:
BoxOffice(saw 7) = -$14,471,512*(7) + $46,778,902*(1) + $69,656,557
= -$101,300,584 + $46,778,902 + $69,656,557
= $15,134,875 (in 2004 $s)
Adjusting to current dollars, (2009 is the best I can get)
BoxOffice(saw 7) = $17,047,984

So, this model predicts Saw 7 to make around $17,047,984 at the U.S. box office.
To me, this seems like a very low number, if only for one reason:
Saw 7 will be in 3D!
So there are going to be body parts and blood flying at the audience, which will certainly add to its appeal. (Though I'm not much of a fan of the series, I might even see it because it's in 3D.) Adding the 3d-ness of the film into the model would have been tricky, and I prefer to keep this as simple as possible. However I just found a statistic online saying that 3D movies gross on average 4 times as much as 2d movies. If this is true, does it mean that Saw 7 will gross around $70 million dollars? No. Most 3d movies are big budget, family friendly spectacles like Avatar, or the Pixar films, which tend to get higher grosses in the first place. Nonetheless, I would expect Saw 7, just from the fact that it will be in 3 dimensions, to earn more, maybe significantly more, than $17 million. Especially if there is extra blood and guts flying in the audience's face.

Wessa, P. (2010), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r6, URL

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