1

Film Franchises and the Edwards-Buckmire Model: An Examination of the Financial

Performance of Movie Sequels

Jacob Ortega-GingrichAdvisor: Ron Buckmire

2

Objectives

Two Parts of Project Confirm that Edwards-Buckmire Model in its current

unmodified state is is capable of modeling the post-release behavior of sequels with the same degree of accuracy as with original non-sequels.

Examine how observed trends between the performance of sequels and their parent films can allow for better a priori prediction of the behavior of hypothetical future sequels

3

Edwards-Buckmire Model

dGdt

=SA

dSdt

=−S S−S *

AAmax

dAdt

=−A

D 1[ SS M

P

G H %2 ]A

4

Typical Solution Curves

5

Part I: EBM and Sequels

Comparing the accuracy of EBM in modeling sequels and non-sequels

6

Non-sequel Film

7

Non-Sequels

Film Title Final Gross Revenue Predicted Gross Revenue (EBM) Percent ErrorAre we there yet? 82674398 98000000 18.54

Diary of a Mad Black Woman 50633099 66000000 30.35

Fantastic Four 154696080 176000000 13.77Chronicles of Narnia: The Lion . . . 291710957 269000000 -7.79

Batman Begins 205343774 217000000 5.68Madagascar 193595521 259000000 33.78

Sisterhood of the Traveling Pants 39053061 42000000 7.55Average: 14.55

8

Sequel

9

Sequels

Film Title Final Gross Revenue Predicted Gross Revenue (EBM) Percent ErrorAre we done yet? 46911611.27 49000000 4.45

60942138.73 111000000 82.14

Fantastic Four: Rise of the . . . 124614290 238000000 90.99Chronicles of Narnia: Prince . . . 126956814.4 207000000 63.05

Dark Knight 478118311.1 803000000 67.95Madagascar 2 161371108.1 251000000 55.54

Sisterhood of the Traveling Pants 2 39524519.73 43000000 8.79Average: 53.27

Madea's Family Reunion

10

Part II: Predicting the behavior of Sequels

How observed trends between the performance of parent and sequel films can allow for improved a priori prediction of the behavior of sequel films

11

Edwards-Buckmire Model

dGdt

=SA , G 0=0

dSdt

=−S S−S *

AAmax

, S 0=S 0

dAdt

=−A

D 1[ SS M

P

G H %2 ]A , A0=A0

12

Awareness and A0

A0=b W

W: awareness level of the film

A0: initial value of Ab: film-specific parameter

13

2005 non-sequels

Film Title A(0) Awareness (W) bThe Chronicles of Narnia: The Lion, the Witch and the Wardrobe 22492.25 25 899.69War of the Worlds 34418.93 42 819.5King Kong 24473.86 100 244.74Wedding Crashers 18701.35 21 890.54Charlie and the Chocolate Factory 22760.09 26 875.39Batman Begins 25530.51 52 490.97Madagascar 17493.96 44 397.59Mr. & Mrs. Smith 20636.96 12 1719.75Hitch 16311.95 27 604.15The Longest Yard 19181.14 9 2131.24The Fantastic Four 21491.53 32 671.61Chicken Little 13340.97 21 635.28Robots 11928.44 27 441.79Walk the Line 11166.81 13 858.99The Pacifier 11601.83 4 2900.46Fun with Dick and Jane 14261.23 4 3565.31The 40 year old virgin 11350.47 8 1418.81

9084.78 3 3028.26Monster-in-Law 8710.24 4 2177.56Flightplan

14

b values in parent-sequel pairs

15

b in sequel-parent pairs

A0sequel=b sequel W sequel

bsequel

b parent

≈1

A0sequel≈ b parent W sequel

16

b and time lag

17

b and reception of parent

18

b and reception of sequel

19

b and cast continuity

20

Project Summary

Confirmation that EBM models sequels with a similar degree of accuracy as non-sequels

confirms that post-release behavior of sequels is identical to that of original non-sequels

Method of a priori approximation of a sequel's behavior

relationship between A(0) and W A(0) can be estimated for a sequel using the value of b

from the parent film.

21

References

Edwards, David A., and Ron Buckmire. "A differential equation model of North American cinematic box-office dynamics." IMA Journal of Management Mathematics. 12. (2001): 41-74. Print.

Hennig-Thurau, Thorsten, Mark B. Houston, and Torsten Heitjans. "Conceptualizing and Measuring the Monetary Value of Brand Extensions: The Case of Motion Pictures." Journal of Marketing. 73.

(2009): 167-183. Print.

Data Taken From:

Box-office Mojo (www.boxofficemojo.com): all weekly and final financial figures

Rotten Tomatoes (www.rottentomatoes.com): H% figures

Numerical solutions to the EBM generated using Wolfram Mathematica 7