joint math meetings (boston, ma; 1/6/2012) 1 a mathematical investigation of the financial...
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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 profilesTRANSCRIPT
Joint Math Meetings (Boston, MA; 1/6/2012)1
A Mathematical Investigation of the Financial Performance of Movie Sequels
Ron Buckmire, Occidental CollegeDavid Edwards, University of DelawareJacob Ortega-Gingrich ‘13, Occidental College
A Preliminary Report
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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
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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
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Actual Movie Data: The Expendables (2010)
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Actual Movie Data: Taken (2009)
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The EBM (Edwards & Buckmire, 2001)
SA
dtdG
ASdtdS
AGS
SdtdA
~
~~
where
*
~SM )1(
1~
DS
A
SPASH
max*
2%~
0)0( G 0)0( AA 0)0( SS
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EBM Parameters
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Typical numerical solutions of EBM
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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
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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)
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Modified EBM (EBM 2)
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)
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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
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Numerical Results: (N=119)
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Distribution of G Computed/G Actual as Histogrammean=1.0389, std. dev.=0.158
Numerical Results: (N=119)
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Numerical Results: Using Global ParametersThe Expendables (2010)
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Numerical Results: Using Global ParametersTaken (2009)
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Numerical Results: Using Chosen ParametersThe Expendables (2010)
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Numerical Results: Using Chosen ParametersOpen Season (2006)
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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)