math in the news: 7/4/11

7/4/11

Data Analysis at the Movies

• Hollywood makes its money from movie ticket sales.

• Some of the most popular movies in history have generated over a billion dollars in sales.

Data Analysis at the Movies

• This table shows the top 10 movies in terms of how much money they have earned lifetime.

• Source for all data: http://www.the-numbers.com/

Released Film Name Total Box Office

1 2009 Avatar $2,783,918,982

2 1997 Titanic $1,842,879,955

3 2003The Lord of the Rings: The Return of the King $1,119,027,325

4 2010 Toy Story 3 $1,064,404,880

5 2006Pirates of the Caribbean: Dead Man's Chest $1,060,615,812

6 2010 Alice in Wonderland $1,024,391,110

7 2008 The Dark Knight $1,001,945,358

8 2011Pirates of the Caribbean: On Stranger Tides $985,387,226

9 2001Harry Potter and the Sorcerer's Stone $974,775,550

10 2007Pirates of the Caribbean: At World's End $960,996,492

Data Analysis at the Movies

• One of the biggest indicators of how well a film will do is how much it earns during its opening weekend.

Data Analysis at the Movies

• One of the biggest indicators of how well a film will do is how much it earns during its opening weekend.

• For example, The Dark Knight (2008) had one of the biggest opening weekends in history.

• Over subsequent weekends the numbers decreased dramatically, but the movie earned over $1 billion!

Data Analysis at the Movies

• The same pattern can be seen in the box office receipts for Titanic, one of the most popular movies of all time.

Data Analysis at the Movies

• Even movies that don’t do well show a similar pattern. One of the biggest-hyped and biggest disappointments of 2008 was a film called Speed Racer. Here is the graph of its box office receipts.

Data Analysis at the Movies

• In each case, the data give the appearance of an exponential graph of the form shown here. This is an example of exponential decay, where the base, b, is less than 1.

• We can perform an exponential regression on each of the data sets whose graphs we reviewed.

Data Analysis at the Movies

• Here is the exponential regression graph based on the box office receipt data for The Titanic.

• Note that the base is less than 1.

Data Analysis at the Movies

• Here is the exponential graph based on the box office receipt data for The Dark Knight.

Data Analysis at the Movies

• Here is the exponential graph based on the box office receipt data for Speed Racer.

Data Analysis at the Movies

• Here are the three regression graphs together: f1 is for Titanic; f2 is for Dark Knight; and f3 is for Speed Racer.

• Note the similarities to the three shapes.

Data Analysis at the Movies

• With each of these exponential functions, the value of a is related to the box office receipts during the opening weekend of a movie.

• This makes sense, since in the case of exponential decay, a is the maximum value (in Quadrant 1) when x = 0.

Data Analysis at the Movies

• With each of these exponential functions, the value of a is related to the box office receipts during the opening weekend of a movie.

• This makes sense, since in the case of exponential decay, a is the maximum value (in Quadrant 1) when x = 0.

Data Analysis at the Movies

Take 5

1. What kind of exponential function would model a blockbuster film?

2. What kind of exponential function would model an unsuccessful film?

Data Analysis at the Movies

• Here is the data for the first ten weeks of box office receipts for the movie Rio.

• Try to develop an exponential model using this data.

WeekendBox Office Receipts

0 $75,436,796

1 $142,239,105

2 $103,983,924

3 $61,378,823

4 $30,312,005

5 $25,300,074

6 $13,160,316

7 $8,491,748

8 $4,581,205

9 $4,487,143