Movie Money
Making
There’s a lot of math in
movies. I’m 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. We’re talking money. (Data from thenumbers.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
Let’s begin by looking at the data for some
recent blockbusters. The chart is from
thenumbers.com.
One
quick thing to notice is how well the graph shows us what is going on with the
movie grosses. Let’s 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.
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 don’t use commas in your numbers on the
calculator. That’s 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 612 in L1 and L2. Go to your graph. Which function is the best fit?
Which is the worst? Why?
So let’s 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 510.
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 


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 


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 movie’s profitability are…well, 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.
Let’s close with that. The chart
below is from midsummer 2003.
10) Make some predictions: did Matrix Reloaded break 300 million? Can Nemo catch up to Spiderman’s
400 million? Between which two movies will Pirates of the Caribbean finish
between in terms of total gross?