Movie Money Making

 

Thereís a lot of math in movies.Iím not talking about A Brilliant Mind, nor even all the coordinate geometry in computer generated imagery (CGI) or the fractal geometry in the animation programs.Weíre talking money.(Data from the-numbers.com, very cool movie site, and rich with data.).Information on this presentation is at faculty.gvsu.edu/goldenj/movies.html along with a few other

 


Letís begin by looking at the data for some recent blockbusters.The chart is from the-numbers.com.

 


One quick thing to notice is how well the graph shows us what is going on with the movie grosses.Letís start with some quick interpretation questions.

 

1)      Despite its relatively slow start, Titanic went on to become the number one box office hit of all time.What phenomenon led to this?

 

 

 

 

 

 

2)      Judging from the graph, the gross functions (did I really just write that?) seem to belong to the same family.What sort of function might model this data?

 

 

 


To get a better answer to the second question, we need some hard data.

 

Spiderman:fastest to 100 million, 200 million and 300 million.Tied for 400 million with Titanic.

Date

Rank

Gross

Theaters

Total Gross

Days

Week #

Weekly Gross

weekly ratio

5/3/2002

1

$114,844,116

3,615

$114,844,116

3

1

$114,844,116

 

5/10/2002

1

$71,417,527

3,615

$223,040,031

10

2

$108,195,915

0.942111087

5/17/2002

2

$45,036,912

3,615

$285,573,668

17

3

$62,533,637

0.57796671

5/24/2002

2

$28,508,104

3,876

$333,641,492

24

4

$48,067,824

0.768671491

5/31/2002

3

$14,317,411

3,646

$353,823,544

31

5

$20,182,052

0.419866146

6/7/2002

5

$10,311,062

3,235

$370,428,183

38

6

$16,604,639

0.822742851

6/14/2002

7

$7,515,984

2,702

$382,537,669

45

7

$12,109,486

0.729283305

6/21/2002

10

$4,555,932

2,278

$390,382,313

52

8

$7,844,644

0.647809824

6/28/2002

11

$3,130,214

1,810

$395,874,471

59

9

$5,492,158

0.700115646

7/5/2002

13

$2,204,636

1,502

$400,058,357

66

10

$4,183,886

0.761792723

7/12/2002

18

$890,372

574

$401,991,818

73

11

$1,933,461

0.462120861

7/19/2002

22

$403,186

265

$402,770,278

80

12

$778,460

0.402625137

7/26/2002

25

$251,065

177

$403,142,910

87

13

$372,632

0.478678416

8/2/2002

25

$234,714

228

$403,505,336

94

14

$362,426

0.972611048

8/9/2002

40

$84,383

85

$403,620,726

101

15

$115,390

0.318382235

8/16/2002

44

$67,390

74

$403,706,375

108

16

$85,649

0.742256695

 

Calculator time!

 

Set your calculator window for x to go from 0 to 12, y to go from 0 to 120,000,000 with yscl=10,000,000.

(Note:you donít use commas in your numbers on the calculator.Thatís for us humans.)

 

Enter the data for the first five weekend grosses in L2, and the weekend numbers in L1.Turn on a stat plot with unconnected dots.

3)      What kind of function does the pattern look like?

 

 

 

 

4)      Do linear regression on the data.What function do you get?(Enter this in Y1).

 

 

 

5)      Do quadratic regression on the data.What function do you get?(Enter this in Y2).

 

 

 

6)      Do exponential regression on the data.What function do you get?(Enter this in Y3).

 

 

 

7)      Enter data from weeks 6-12 in L1 and L2.Go to your graph.Which function is the best fit?Which is the worst?Why?

 


So letís start predicting.Three of the top movies for 2003 were Finding Nemo, The Matrix Reloaded and Pirates of the Caribbean.The data is given below for their first four weeks.Use exponential regression to predict weekly grosses for weeks 5-10.

 

Finding Nemo

Date

Rank

Gross

Total Gross

Days

Week #

Weekly Gross

5/30/2003

1

$70,251,710

$70,251,710

3

1

$70,251,710

6/6/2003

2

$46,589,649

$144,043,789

10

2

$73,792,079

6/13/2003

1

$28,384,483

$191,487,211

17

3

$47,443,422

6/20/2003

2

$21,138,752

$228,549,216

24

4

$37,062,005

Predictions:

Week

Weekly Gross

Total Gross

 

Week

Weekly Gross

Total Gross

5

 

 

 

8

 

 

6

 

 

 

9

 

 

7

 

 

 

10

 

 

 

 

Matrix Reloaded

Date

Rank

Gross

Total Gross

Days

Week #

Weekly Gross

5/16/2003

1

$91,774,413

$134,282,716

4

1

$134,282,716

5/23/2003

2

$39,904,034

$203,773,759

11

2

$69,491,043

5/30/2003

4

$15,687,241

$232,701,046

18

3

$28,927,287

6/6/2003

5

$9,186,342

$247,778,753

25

4

$15,077,707

Predictions:

Week

Weekly Gross

Total Gross

 

Week

Weekly Gross

Total Gross

5

 

 

 

8

 

 

6

 

 

 

9

 

 

7

 

 

 

10

 

 

 

 

Pirates of the Caribbean

Date

Rank

Gross

Total Gross

Days

Week #

weekly

7/11/2003

1

$46,630,690

$70,625,971

5

1

$70,625,971

7/18/2003

2

$34,034,597

$133,007,414

12

2

$62,381,443

7/25/2003

2

$23,136,029

$176,838,155

19

3

$43,830,741

8/1/2003

3

$18,844,044

$209,531,292

26

4

$32,693,137

Predictions:

Week

Weekly Gross

Total Gross

 

Week

Weekly Gross

Total Gross

5

 

 

 

8

 

 

6

 

 

 

9

 

 

7

 

 

 

10

 

 

 

 


While the press tends to report just the highest weekend gross, and dote on whose film is one or two, the two factors that really determine a movieís profitability areÖwell, that actually makes a good question.

 

8)      If you are a movie executive, what two pieces of data are you going to look at to determine a movies long term profitability?And perhaps use to decide whether to put more money into advertising or not?How do those factors determine profitability?

 

 

 

 

9)      Out of the movies we have considered, what data point for Finding Nemo is the most surprising?Give your reasoning.

 

 

 

 


There are many fine statistical points that can be brought up through consideration of this data.Prediction value of a few points vs. more data (what unlikely result would have been predicted after week two for Nemo?), looking for anomalies (what happened in week 5 to Spiderman?) and the power of graphical representation for qualitative reasoning.Letís close with that.The chart below is from mid-summer 2003.

10)  Make some predictions:did Matrix Reloaded break 300 million?Can Nemo catch up to Spidermanís 400 million? Between which two movies will Pirates of the Caribbean finish between in terms of total gross?