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A Mathematical Investigation of the Financial Performance of Movie Sequels

This study explores the financial performance of movie sequels using mathematical models and actual movie data. The research identifies important variables and equations, as well as modifications to existing models. Numerical results are provided, and future research questions are discussed.

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A Mathematical Investigation of the Financial Performance of Movie Sequels

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  1. A Mathematical Investigation of the Financial Performance of MovieSequels Ron Buckmire, Occidental College David Edwards, University of Delaware Jacob Ortega-Gingrich‘13, Occidental College A Preliminary Report Joint Math Meetings (Boston, MA; 1/6/2012)

  2. Outline Introduction to Cinematic Box-Office Dynamics Important variables, concepts and equations Graphs of typical movie data The Edwards-Buckmire Model (EBM) Drawbacks of EBM Modified EBM Preliminary Numerical Results Future Work Joint Math Meetings (Boston, MA; 1/6/2012)

  3. Introduction to Cinematic Box-Office Dynamics Important variables G(t) : cumulative gross receipts of the movie S(t) : number of screens movie is exhibited A(t) : normalized weekly revenue ($ per screen average) t : time in number of weeks Important concepts • A and S have quasi-exponential profiles Joint Math Meetings (Boston, MA; 1/6/2012)

  4. Actual Movie Data: The Expendables (2010) Joint Math Meetings (Boston, MA; 1/6/2012)

  5. Actual Movie Data: Taken (2009) Joint Math Meetings (Boston, MA; 1/6/2012)

  6. The EBM (Edwards & Buckmire, 2001) where Joint Math Meetings (Boston, MA; 1/6/2012)

  7. EBM Parameters Joint Math Meetings (Boston, MA; 1/6/2012)

  8. Typical numerical solutions of EBM Joint Math Meetings (Boston, MA; 1/6/2012)

  9. Reasons Why EBM Needs Modifying Fails to allow H% to vary with time Movie-specific parameter () estimates are difficult to make and somewhat arbitrary Most movies have a contract period (2-4 weeks) in which screens is constant, i.e. S’=0 S and A actual data more erratic than first thought; G is relatively smooth Joint Math Meetings (Boston, MA; 1/6/2012)

  10. Modifying the EBM (J. Ortega-Gingrich) Uses an Economics-inspired “demand” model where G’(t)=μ(S)D(t) and assumes D(t) decreases exponentially over time Incorporates fixed contract periods when screens are constant Greatly modifies the A equation Modified EBM has 3 parameters, 2 of which are movie-independent (or global) Joint Math Meetings (Boston, MA; 1/6/2012)

  11. Modified EBM (EBM 2) Joint Math Meetings (Boston, MA; 1/6/2012)

  12. Screen Availability Function μ(S) a=1/T,T is total number of movie theaters in North America (~4,000) The functionμ(S) should satisfy the following conditions:

  13. Numerical Calculations with EBM 2 Analyzed119 movies from 2005-2010 (minimum final gross $50m) All dollars adjusted for inflation to 2005 Used Mathematica to generate numerical solutions to the modified EBM Found “global” values of parameters that would minimize the difference between computed G∞ and actual G∞ while also minimizing standard deviation Joint Math Meetings (Boston, MA; 1/6/2012)

  14. Numerical Results: (N=119) Joint Math Meetings (Boston, MA; 1/6/2012)

  15. Numerical Results: (N=119) Distribution of G Computed/G Actual as Histogrammean=1.0389, std. dev.=0.158 Joint Math Meetings (Boston, MA; 1/6/2012)

  16. Numerical Results: Using Global Parameters The Expendables (2010) Joint Math Meetings (Boston, MA; 1/6/2012)

  17. Numerical Results: Using Global Parameters Taken (2009) Joint Math Meetings (Boston, MA; 1/6/2012)

  18. Numerical Results: Using Chosen Parameters The Expendables (2010) Joint Math Meetings (Boston, MA; 1/6/2012)

  19. Numerical Results: Using Chosen Parameters Open Season (2006) Joint Math Meetings (Boston, MA; 1/6/2012)

  20. Open Questions (Future Work) “The Holy Grail”: Predict the opening weekend gross before the movie is released The sequel problem: predict the gross of a sequel based on characteristicsof the parent film (considered an easier version of the a priori Holy Grail problem if one can find a relationship between sequel and parent films) Joint Math Meetings (Boston, MA; 1/6/2012)

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