Post on 24-Dec-2015
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Film Franchises and the Edwards-Buckmire Model: An Examination of the Financial
Performance of Movie Sequels
Jacob Ortega-GingrichAdvisor: Ron Buckmire
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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
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Edwards-Buckmire Model
dGdt
=SA
dSdt
=−S S−S *
AAmax
dAdt
=−A
D 1[ SS M
P
G H %2 ]A
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Typical Solution Curves
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Part I: EBM and Sequels
Comparing the accuracy of EBM in modeling sequels and non-sequels
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Non-sequel Film
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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
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Sequel
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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
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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
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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
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Awareness and A0
A0=b W
W: awareness level of the film
A0: initial value of Ab: film-specific parameter
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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
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b values in parent-sequel pairs
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b in sequel-parent pairs
A0sequel=b sequel W sequel
bsequel
b parent
≈1
A0sequel≈ b parent W sequel
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b and time lag
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b and reception of parent
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b and reception of sequel
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b and cast continuity
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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.
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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