predicting box office revenues
DESCRIPTION
I examined two models of predicting box office revenue for my Senior Comps Project in Mathematics.TRANSCRIPT
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Predicting Box Office Predicting Box Office RevenuesRevenues
Allison TamakiAllison Tamaki
22
33
I.I. Revenue Patterns of High-Yielding Revenue Patterns of High-Yielding FilmsFilms
II.II. Time-to-Decide and Time-to-Act Time-to-Decide and Time-to-Act ModelModel
III.III. ““Determinant” ModelDeterminant” Model
Outline
44
Revenue Patterns
TYPE 2 Sleeper
• Wide release
• High yields upon release
• Build slowly to Wide release
• Slow revenue at start, build to high revenues
TYPE 1 Blockbuster
55Release Date: July 18, 2008 11
The Dark Knight
$0
$20,000,000
$40,000,000
$60,000,000
$80,000,000
$100,000,000
$120,000,000
$140,000,000
$160,000,000
$180,000,000
0 5 10 15 20 25 30 35 40
Weekends Since Release
Gro
ss p
er W
eeke
nd
66Release Date: April 19, 2002 11
My Big Fat Greek Wedding
$0
$2,000,000
$4,000,000
$6,000,000
$8,000,000
$10,000,000
$12,000,000
$14,000,000
$16,000,000
0 10 20 30 40 50 60
Weekends Since Release
Gro
ss
pe
r W
ee
ke
nd
↑
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Eliashberg and Sawhney’s Eliashberg and Sawhney’s
Time-to-DecideTime-to-Decide & & Time-to-Time-to-ActAct Model Model• Focuses on understanding consumer behavior
• Two steps for an individual to see a movie:
1. Individual exposed to influential information, decides to see the movie (T)
2. Individual acts on decision to go see movie (τ)
The time for an individual to see a movie is t = T + τ
• Varies over consumer population: treat T, τ as independent random variablesEliashberg, Jehoshua, Mohanbir S. Sawhney. (1996). A Parsimonious Model Eliashberg, Jehoshua, Mohanbir S. Sawhney. (1996). A Parsimonious Model
for for Forecasting Gross Box-Office Revenues of Motion Pictures. Forecasting Gross Box-Office Revenues of Motion Pictures. Marketing Science, Marketing Science, 15:2, 113-131.15:2, 113-131.
88
Distributions of Time-to-Distributions of Time-to-DecideDecide
0
)(][ dTTTxTE
• Time-to-Decide, T ~ Exponential Distribution [λ]
• Probability to decide by time T:
• Expected time to decide:
0][ dTeTTE T
1
][ TE
TeTXTx )(')(
99
Distribution of Time-to-ActDistribution of Time-to-Act
0;1)( eY eYy )(')(
• Time to act, τ ~ Exponential Distribution [γ]
• Probability to act by time τ:
• Expected time to act:
1
][ E
1010
tt eetZ
1
),|(
duutyuXtZt
0
)()()(
• T, τ are independent random variables, so can calculate Z(t) as:
t utu dueetZ0
)(1)( ey )(
Recall:
• t = T + τ
• Can’t observe T or τ directly
• Can observe Z(t) = Probability that the movie will be seen by the individual by time t
Probability of Seeing Movie by time t
1111
Estimating Estimating λλ and and γγ
• Observe: Ž(tk) is the actual probability that the movie will be seen by time tk. We know this from revenue records.
• Given λ and γ, our model predicts probability Z(tk
| λ, γ)
• Least Squares Regression: find values of λ and γ to Minimize Q(λ, γ)
m
kkk tZtZQ
1
2)],|()([),(
1212
EstimatingEstimating λλ andand γγ forfor thethe DarkDark KnightKnight
• Use Mathematica function NMinimize to
estimate λ= 0.455738 and γ = 5.947
1313
0.0000000
0.2000000
0.4000000
0.6000000
0.8000000
1.0000000
1.2000000
0 10 20 30 40
Weeks
Z_k
22.2455738.0
11][
TE 168.0
947.5
11][
E
1414
Revenue “Determinants”Revenue “Determinants”
DETERMINANDETERMINANTT
POSITIVEPOSITIVE NEGATIVENEGATIVE
GenreGenre Action Science Action Science FictionFiction
Horror ThrillerHorror Thriller
Children’s Children’s ComedyComedy
Documentary Documentary DramaDrama
Release DateRelease Date SummerSummer(Memorial Day-Labor (Memorial Day-Labor Day)Day)
Not SummerNot Summer
MPAA RatingMPAA Rating G PG PG-13G PG PG-13 R NC-17 UR NC-17 U
AwardsAwards Academy Award Academy Award Wins/NominationsWins/Nominations
Best/Top Best/Top ActorsActors
Entertainment Weekly’s 25 Entertainment Weekly’s 25 Best Actors of the 90sBest Actors of the 90s
The Movie Times’ Top 20 The Movie Times’ Top 20 ActorsActors
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Using “Determinants” to Using “Determinants” to Predict Gross RevenuePredict Gross Revenue
• Simonoff and Sparrow used linear regression model to Simonoff and Sparrow used linear regression model to predict gross revenue using many of the determinantspredict gross revenue using many of the determinants
• Used a sample of movies to determine the coefficientsUsed a sample of movies to determine the coefficients
• The determinants included in the model are:The determinants included in the model are:• GenreGenre• MPAA RatingMPAA Rating• Summer ReleaseSummer Release• Best ActorsBest Actors• Top Dollar ActorsTop Dollar Actors
Simonoff, Jeffrey S., Ilana R. Sparrow. (2000). Predicting Movie Grosses: Simonoff, Jeffrey S., Ilana R. Sparrow. (2000). Predicting Movie Grosses: Winners and Winners and losers, blockbusters and sleepers. losers, blockbusters and sleepers. Stern School of Business, Stern School of Business, New York University.New York University.
n
jijjni xG
10010 ),...,(log
1616
““DETERMINANT”DETERMINANT” CATEGORYCATEGORY COEFFICIENT COEFFICIENT ((ββijij))
CONSTANTCONSTANT 0.3940.394
GENREGENRE ActionAction 0.4010.401
Children’sChildren’s -0.030-0.030
ComedyComedy -0.189-0.189
DocumentaryDocumentary -1.248-1.248
DramaDrama -0.408-0.408
HorrorHorror 0.5130.513
Science FictionScience Fiction 0.6930.693
ThrillerThriller 0.2670.267
MPAA RatingMPAA Rating GG 0.5340.534
PGPG 0.3800.380
PG-13PG-13 0.3120.312
RR -0.079-0.079
NC-17NC-17 -0.118-0.118
U (unrated)U (unrated) -1.028-1.028
SUMMER RELEASESUMMER RELEASE NoNo -0.150-0.150
YesYes 0.1500.150
BEST ACTORSBEST ACTORS 0.4000.400
TOP DOLLAR ACTORSTOP DOLLAR ACTORS 0.7120.712
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Predicting Gross Revenue for The Predicting Gross Revenue for The Dark KnightDark Knight
• Constant (0.394)Constant (0.394)• Genre: Action/Adventure (0.401)Genre: Action/Adventure (0.401)• MPAA Rating: PG-13 (0.312)MPAA Rating: PG-13 (0.312)• Summer Release?: Yes (0.150)Summer Release?: Yes (0.150)• Best Actors: Gary Oldman #18 (0.4)Best Actors: Gary Oldman #18 (0.4)• Top Dollar Actors: Gary Oldman (0.712)Top Dollar Actors: Gary Oldman (0.712)
712.04.15.0312.0401.0394.0log10 G
369.2log10 G
1818
457.2
369.210
884.233
The Dark Knight would be predicted to make $233.88 million
Actual Gross = $533 million
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Limitations of Gross Revenue Limitations of Gross Revenue Prediction ModelPrediction Model
• Accuracy Accuracy • Previous filmsPrevious films• Budget – production, advertising, etc. Budget – production, advertising, etc. • Director/ProducerDirector/Producer
• PublicityPublicity• Best Actors and Top Actors aren’t up to Best Actors and Top Actors aren’t up to
datedate• Multiple genresMultiple genres
2020
What’s Next…What’s Next…
• Improve accuracy of the modelImprove accuracy of the model• Update Best and Top Actor listsUpdate Best and Top Actor lists• Incorporate other determinantsIncorporate other determinants
• Look at foreign box office to model Look at foreign box office to model worldwide box office revenueworldwide box office revenue
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SourceSourcess1. Arnold, Jesse C., J.S. Milton. 1. Arnold, Jesse C., J.S. Milton. Introduction to Probability and Statistics Principles and Introduction to Probability and Statistics Principles and
Applications for Engineering and the Computing Sciences.Applications for Engineering and the Computing Sciences. New York: McGraw-Hill, New York: McGraw-Hill, 1990. 1990.
2. Butler, Michael, Neil Terry, De’Arno De’Armond. (2003). The Determinants of Domestic 2. Butler, Michael, Neil Terry, De’Arno De’Armond. (2003). The Determinants of Domestic Box Office Performance in the Motion Picture Industry. Box Office Performance in the Motion Picture Industry. Southwestern Economic Southwestern Economic ReviewReview, 137-148., 137-148.
3. Butler, Michael, Neil Terry, De’Arno De’Armond. (2003). Determinants of the Box Office 3. Butler, Michael, Neil Terry, De’Arno De’Armond. (2003). Determinants of the Box Office Performance of Motion Pictures. Performance of Motion Pictures. Proceedings of the Academy of Marketing StudiesProceedings of the Academy of Marketing Studies, , 8:2, 23-28.8:2, 23-28.
4. Chintagunta, Pradeep, Ramya Neelamegham. (1999). A Bayesian Model to Forecast 4. Chintagunta, Pradeep, Ramya Neelamegham. (1999). A Bayesian Model to Forecast New Product Performance in Domestic and International Markets. New Product Performance in Domestic and International Markets. Marketing Science, Marketing Science, 18:2, 115-136. 18:2, 115-136.
5. De Vany, Arthur, W. David Walls. (1996). Bose-Einstein Dynamics and Adaptive 5. De Vany, Arthur, W. David Walls. (1996). Bose-Einstein Dynamics and Adaptive Contracting in the Motion Picture Industry. Contracting in the Motion Picture Industry. The Economic Journal, The Economic Journal, 106, 1493-1514.106, 1493-1514.
6. Eliashberg, Jehoshua, Mohanbir S. Sawhney. (1996). A Parsimonious Model for 6. Eliashberg, Jehoshua, Mohanbir S. Sawhney. (1996). A Parsimonious Model for Forecasting Gross Box-Office Revenues of Motion Pictures. Forecasting Gross Box-Office Revenues of Motion Pictures. Marketing Science, Marketing Science, 15:2, 15:2, 113-131.113-131.
7. Peck, Roxy, Chris Olsen, and Jay L. Devore. 7. Peck, Roxy, Chris Olsen, and Jay L. Devore. Introduction to Statistics and Data AnalysisIntroduction to Statistics and Data Analysis. . New York: Duxbury P, 2004. New York: Duxbury P, 2004.
8. Shugan, Steve, Joffre Swait. (2008). Enabling Movie Design and Cumulative Box Office 8. Shugan, Steve, Joffre Swait. (2008). Enabling Movie Design and Cumulative Box Office Predictions Using Historical Data and Consumer Intent-to-View. Predictions Using Historical Data and Consumer Intent-to-View.
9. Simonoff, Jeffrey S., Ilana R. Sparrow. (2000). Predicting Movie Grosses: Winners and 9. Simonoff, Jeffrey S., Ilana R. Sparrow. (2000). Predicting Movie Grosses: Winners and losers, blockbusters and sleepers. losers, blockbusters and sleepers. Stern School of Business, New York University.Stern School of Business, New York University.
10. IMDB; 11. Box Office Mojo; 12. The Movie Times; 13. Entertainment Weekly 10. IMDB; 11. Box Office Mojo; 12. The Movie Times; 13. Entertainment Weekly
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THANK YOU!THANK YOU!
• Professor BuckmireProfessor Buckmire• Professor KnoerrProfessor Knoerr• LionsGate International DepartmentLionsGate International Department• Malee AlexanderMalee Alexander