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

2. 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

3. 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

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

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

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

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

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

9. 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

10. 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)

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

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

13. Joint Math Meetings (Boston, MA; 1/6/2012) 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

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

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

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

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

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

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

20. 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 characteristics of 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)