predicting box office revenues

22
1 Predicting Box Office Predicting Box Office Revenues Revenues Allison Tamaki Allison Tamaki

Upload: atamaki

Post on 26-Jan-2015

125 views

Category:

Documents


2 download

DESCRIPTION

I examined two models of predicting box office revenue for my Senior Comps Project in Mathematics.

TRANSCRIPT

Page 1: Predicting Box Office Revenues

11

Predicting Box Office Predicting Box Office RevenuesRevenues

Allison TamakiAllison Tamaki

Page 2: Predicting Box Office Revenues

22

Page 3: Predicting Box Office Revenues

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

Page 4: Predicting Box Office Revenues

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

Page 5: Predicting Box Office Revenues

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

Page 6: Predicting Box Office Revenues

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

Page 7: Predicting Box Office Revenues

77

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.

Page 8: Predicting Box Office Revenues

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 )(')(

Page 9: Predicting Box Office Revenues

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

Page 10: Predicting Box Office Revenues

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

Page 11: Predicting Box Office Revenues

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)],|()([),(

Page 12: Predicting Box Office Revenues

1212

EstimatingEstimating λλ andand γγ forfor thethe DarkDark KnightKnight

• Use Mathematica function NMinimize to

estimate λ= 0.455738 and γ = 5.947

Page 13: Predicting Box Office Revenues

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

Page 14: Predicting Box Office Revenues

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

Page 15: Predicting Box Office Revenues

1515

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

Page 16: Predicting Box Office Revenues

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

Page 17: Predicting Box Office Revenues

1717

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

Page 18: Predicting Box Office Revenues

1818

457.2

369.210

884.233

The Dark Knight would be predicted to make $233.88 million

Actual Gross = $533 million

Page 19: Predicting Box Office Revenues

1919

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

Page 20: Predicting Box Office Revenues

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

Page 21: Predicting Box Office Revenues

2121

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

Page 22: Predicting Box Office Revenues

2222

THANK YOU!THANK YOU!

• Professor BuckmireProfessor Buckmire• Professor KnoerrProfessor Knoerr• LionsGate International DepartmentLionsGate International Department• Malee AlexanderMalee Alexander