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

and

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.

Sources:

www.BoxOfficeMojo.com

http://www.westegg.com/inflation/

Wessa, P. (2010), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r6, URL http://www.wessa.net/

http://www.slideshare.net/DigitalCinemaMedia/2d-vs-3d-box-office

Free Samples and Diminishing Marginal Utility

Have you ever been at a grocery store and tried a free sample of some food, maybe some potato chips, and thought, "Wow! I could eat a million of these"? You then bought the product, took it home and realized after the second handful of chips that you really didn't want to eat a million of them anymore? If this has happened to you, you've helped to illustrate a very important concept in economics: diminishing marginal utility.

Diminishing marginal utility is the economic and psychological fact that in general, when people consume more of any item (not just food, but other things such as movies as I've explored in earlier articles), their desire to consume more of that item decreases. So one might really enjoy that first potato chip, but after eating a certain number of them, not want to eat any more, even to the point that one might get disgusted by the thought of eating more chips.
There are important biological reasons for human psychology to be this way. If people never got tired of eating potato chips no matter how many they consumed at one time, they would make themselves very sick. The same goes for non-food items, though perhaps to a lesser extent. I'm sure some people out there would be happy with an infinite number of shoes (Imelda Marcos or the Sex and the City girls perhaps?) Nonetheless a certain level of moderation exists in our psychology, and for some very good reasons.
Anyway, the point of my writing this article is to provide a word of advice to consumers: Know your own utility function.
For those who don't know what a utility function is, it's a mathematical or graphical representation of how much satisfaction one gets from consuming more of an item. Though I won't get into the tricky situation of trying to quantify utility, which is an abstract, personal and subjective thing, it is clear that utility diminishes with more units consumed. To make the right purchases for themselves, consumers should realize that the free sample they taste is unique. The next unit of the product will not taste the same, because utility is diminishing with every unit.
But the grocery store doesn't want you to be aware of this. The grocery store wants you to think that every potato chip will be as good as that first one, and that when making your purchase, you will think that your utility function will not decrease, as in this utility function graph:



If one's utility function were like this, every potato chip would be just as good as that first one. Grocery stores would thrive for a while, but humanity would eat itself into extinction. Thankfully this is not the case. In reality, people's utility functions decrease, like this one:





(Notice that just before 50 chips, utility is actually about to go negative. This means the person would get negative utility from more chips, probably due to physical discomfort. Not good for your stomach.)
So when you're at the grocery store and you try a free sample, remember that those tasty potato chips are hitting your taste buds at the very tippy top of your utility function. It's going to be downhill from there. And though at that moment you might feel like you can eat a million chips, if you bought these million chips, you might end up wasting 999,950 of them.

The Social Premium on Alcoholic Beverages

Ever sit and have a drink at a fancy bar and wonder "why am I paying $8 for a glass of wine?" The answer to this question, of why a glass of wine at a bar might sell for more than an entire bottle of wine at the grocery store, can be uncovered by economic principles.

There are three forces at work here pushing the price up.

1. The extra costs that must be incurred by the bar in order to serve you that drink. In particular, unlike a grocery store purchase, where consumption is a self-serve process, in its pricing, a bar must cover all of the costs of serving drinks, from bartender's wages to dishwashing detergent.

2. Individual drinks are smaller in quantity than what is usually sold at the grocery store, which eliminates the possibility of a quantity discount for a larger purchase.

3. What I call "the Social Premium" on these drinks. This premium arises from the social benefits of drinking at a bar as opposed to drinking elsewhere. These extra benefits to drinkers at bars make it rational for them to pay more per drink. Some of the social benefits may include: Interaction with the opposite sex, a hopping dance-floor, an epic game of pool with a complete stranger, and countless other things that are easier (in economics-speak "less costly") to find at a bar than other places. It's true that one can plan a party to gain these same social benefits with cheaper drinks, but that entails its own costs.

Many of these extra social benefits are not guaranteed to happen. But the mind of the consumer constructs an expected value of all things that might happen, and factors this into his/her decision of whether or not to purchase a drink at a certain price. The greater the customer's expected benefits of purchasing that drink at the bar, the higher the price can go. This logic holds for all products, not just alcohol. Alcohol just provides a particularly useful example of a social premium, because it is greatly associated with social interaction.

A group of economists should get together for a giant pub-crawl and econometrically study the ratio of the price of drinks sold at bars with the equivalent drinks bought from local grocery stores. My guess is that the results would show the perceived possibility of sexual relations to be an important driver of the price. This could be quantitatively studied through such metrics as male/female ratios at different bars. If this does drive the price of drinks, in a sense (and a very cynical sense), many bar patrons are "paying for sex", they just don't realize it.