Blockbusters, Bombs & Sleepers The Income Distribution of Movies Sitabhra Sinha The Institute of Mathematical Sciences Chennai (Madras), India

A Pareto Law for Movies Why look at Movie Income ? Movie income is a well-defined quantity; Income distribution can be empirically determined Asset exchange models for explaining Pareto Law in wealth/income distribution cannot be applied ! Movies don’t exchange anything between themselves !! “There’s no business like show business” Pareto exponent for Movie Income :   2 But

Popularity of Products/Ideas  Movies: S Sinha & S Raghavendra (2004) Eur Phys J B, 42, 293  Scientific Papers: S Redner (1998) Eur Phys J B, 4, 131  Books: D Sornette et al (2004) Phys Rev Lett, 93, Movies popularity distribution → a prominent member of the class of popularity distributions

1+  = 3 The Popularity of Scientific Papers 1/   0.48 Measure of popularity : citation distribution Relation between exponents for  : Cumulative probability (Pareto Law) 1+  : Probability distrn (Power law) 1/  : Rank distribution (Zipfs Law)  Pareto exponent  2 ISI Phys Rev D

The Popularity of Books Measure of popularity : Book sales at amazon.com  Pareto exponent  2

A ‘ Hit ’ is Born: The Dynamics of Popularity Conjecture: Universality Pareto exponent for popularity distributions   2

Outline of the Talk  Empirical : Distributions SS & S Raghavendra (2004) Eur Phys J B, 42:  Empirical : Time evolution SS & R K Pan, in preparation  Model SS & S Raghavendra (2004) SFI Working Paper SS & S Raghavendra (2005) to appear in Practical Fruits of Econophysics, Proc 3 rd Nikkei Econophysics Symposium, Springer-Tokyo

Outline of the Talk  Empirical : Distributions SS & S Raghavendra (2004) Eur Phys J B, 42:  Empirical : Time evolution SS & R K Pan, in preparation  Model SS & S Raghavendra (2004) SFI Working Paper SS & S Raghavendra (2005) to appear in Practical Fruits of Econophysics, Proc 3 rd Nikkei Econophysics Symposium, Springer-Tokyo

Measuring Popularity However, these are for movies released long ago: lot of information available for people to decide What about newly released movies still running in theatres ? Popularity of a movie can be estimated in various ways: e.g., Number of votes received from registered users in IMDB database Or, DVD/Video rentals from Blockbuster Stores What’s the income, dude ?

Income Distribution Snapshot Too few data points, too much scatter Each week, about movies running in theatres across USA Hard to make a call on the nature of the distribution !

The Movie Year: Seasonal Fluctuations in Movie Income over a Year Makes sense to look at income distribution over a year: we can ignore seasonal variations

Popularity Distribution of movies released in USA during acc to weeks in Top 60 Gaussian distribution Long tail: the most popular movies do not fit a Gaussian! Rank distribution of movies: explores the tail of the distribution containing the most popular movies Data for all years fall on the same curve after normalizing !! slope 

Gross Income Distrn of movies released in USA during Opening Gross Kink indicating bimodality Bimodal distribution of opening gross Movies either do very badly or very well on opening ! Distribution scaled by average gross to correct for inflation

Gross Income Distrn of movies released in USA during Opening Gross Total Gross Unimodal 1/   0.5  Pareto exponent  2 at opening week and remains so through the entire theatre lifespan The only contribution of movies which perform well long after opening (sleepers) Distribution scaled by average gross to correct for inflation

Relation between longevity at Top 60 & Total Gross IMAX movies Slope ~ 2.14 G Total ~ T 2

Outline of the Talk  Empirical : Distributions SS & S Raghavendra (2004) Eur Phys J B, 42:  Empirical : Time evolution SS & R K Pan, in preparation  Model SS & S Raghavendra (2004) SFI Working Paper SS & S Raghavendra (2005) to appear in Practical Fruits of Econophysics, Proc 3 rd Nikkei Econophysics Symposium, Springer-Tokyo

A Movie Bestiary Classifying Movies according to the time evolution of their income  Blockbusters: High Opening Gross, High Total Gross Intermediate to long theatre lifespan  Bombs: Low Opening Gross, Low Total Gross Short theatre lifespan  Sleepers: Low Opening Gross, High Total Gross Long theatre lifespan

Spiderman (2002) A classic blockbuster Peaks on weekends Daily earnings Weekend earnings Exponential decay

Spiderman 2 (2004) A blockbuster … but like most sequels, earned less & ran fewer weeks than the original !

The Blockbuster Strategy “If it doesn’t open, you are dead !” - Robert Evans, Hollywood producer The opening is the most critical event in a film’s commercial life FACT: > 80 % of all movies earn maximum box-office revenue in the first week after release Jaws (1975) : the first movie to be released using the (now classic) blockbuster strategy :  Heavy pre-release advertising  Presence of star/stars with name recognition  Wide release Underlying assumption : ‘Herding’ effect among movie audience A large opening will induce others to see the movie !

BLOCKBUSTERS: Examples  Very high opening gross  Exponential decay in subsequent earnings

Lord of the Rings 3: Return of the King (2003) Top grosser of the year !

Harry Potter and the Sorcerer’s Stone (2001)

The Sixth Sense ( 1999) Blockbuster…. but behaved like a sleeper very late in its theatre lifespan ! (longest time at top 60 for non-IMAX movie - 40 weeks)

BOMBS: Examples  Very low opening gross  Exponential decay in subsequent earnings  Earns significantly less than budget

Bulletproof Monk (2003) Spectacular flop ! Production budget: $ 50 Million Advertising budget: $ 25 Million

American Psycho (2000)

SLEEPERS: Examples  Very low opening gross  Sudden rise in subsequent earnings before eventual exponential decay before eventual exponential decay

My Big Fat Greek Wedding (2002) A classic sleeper ! Produced outside Hollywood Extremely long theatre lifespan Gradual rise in income Subsequent exponential decay

The Blair Witch Project (1999) Another Hollywood outsider sleeper

Mystic River (2003) Publicity Buildup to Oscar Awards A Hollywood insider sleeper ! Unusual: Multiple rises in income during theatre lifespan

To compare 2004 Spiderman Lord of the Rings 3: Return of the King Mystic River Bulletproof Monk 2002Spiderman My Big Fat Greek Wedding 2001 Harry Potter and the Sorcerers' Stone 2000 American Psycho 1999 The Sixth Sense Blair Witch Project Color code: BlockbusterSleeperBomb

Scaled by opening gross Income of most movies decay exponentially with the same decay rate < 5 weeks Comparing the Income Growth / Decay of Movies

Outline of the Talk  Empirical : Distributions SS & S Raghavendra (2004) Eur Phys J B, 42:  Empirical : Time evolution SS & R K Pan, in preparation  Model SS & S Raghavendra (2004) SFI Working Paper SS & S Raghavendra (2005) to appear in Practical Fruits of Econophysics, Proc 3 rd Nikkei Econophysics Symposium, Springer-Tokyo

Puzzle The Pareto tail appears at the opening week itself Asset exchange models don’t apply Can’t be explained by information exchange about a movie through interaction between people Need a different approach The Pareto tail appears at the opening week itself Asset exchange models don’t apply Can’t be explained by information exchange about a movie through interaction between people Need a different approach

Popularity = Collective Choice Process of emergence of collective decision in a society of agents free to choose in a society of agents free to choose constrained by limited information constrained by limited information having heterogeneous beliefs. having heterogeneous beliefs. Example: Example: Movie popularity. Movie popularity.

Collective Choice: A Naive Approach Each agent chooses randomly independent of all other agents. Each agent chooses randomly independent of all other agents. Collective decision: sum of all individual choices. Collective decision: sum of all individual choices. Example: YES/NO voting on an issue Example: YES/NO voting on an issue For binary choice For binary choice Individual agent: S = 0 or 1 Individual agent: S = 0 or 1 Collective choice: M = Σ S Collective choice: M = Σ S Result: Normal distribution. Result: Normal distribution. NOYES 0 % Collective Decision M 100%

Modeling emergence of collective choice Agent’s choice depends on Personal belief (expectation from a particular choice)Personal belief (expectation from a particular choice) Herding (through interaction with neighbors)Herding (through interaction with neighbors) 2 factors affect the evolution of an agent’s belief Adaptation (to previous choice):Adaptation (to previous choice): Belief changes with time to make subsequent choice of the same alternative less likely Belief changes with time to make subsequent choice of the same alternative less likely Learning (by global feedback through media):Learning (by global feedback through media): The agent will be affected by how her previous choice accorded with the collective choice (M). The agent will be affected by how her previous choice accorded with the collective choice (M).

The Model: ‘Adaptive Field’ Ising Model Binary choice :2 possible choice states (S = ± 1). Binary choice :2 possible choice states (S = ± 1). Belief dynamics of the i th agent at time t: Belief dynamics of the i th agent at time t: where is the collective decision μ: Adaptation timescale μ: Adaptation timescale λ: Learning timescale λ: Learning timescale Choice dynamics of the ith agent at time t: Choice dynamics of the ith agent at time t: for square lattice

Results Long-range order for λ > 0Long-range order for λ > 0

Initial state of the S field: 1000 × 1000 agents

λ = 0: No long-range order μ =0.1 N = 1000, T = itrns Square Lattice (4 neighbors)

μ =0.1 λ > 0: clustering λ = 0.05 N = 1000, T = 200 itrns Square Lattice (4 neighbors)

Results Long-range order for λ > 0Long-range order for λ > 0 Self-organized pattern formationSelf-organized pattern formation

μ =0.1 λ = 0.05 Ordered patterns emerge asymptotically

Results Long-range order for λ > 0Long-range order for λ > 0 Self-organized pattern formationSelf-organized pattern formation –Multiple ordered domains –Behavior of agents belonging to each such domain is highly correlated –Distinct ‘cultural groups’ (Axelrod).

Results Long-range order for λ > 0Long-range order for λ > 0 Self-organized pattern formationSelf-organized pattern formation –Multiple ordered domains –Behavior of agents belonging to each such domain is highly correlated –Distinct ‘cultural groups’ (Axelrod). Phase transitionPhase transition –Unimodal to bimodal distribution as λ increases.

Bimodality with increasing λ

Results Long-range order for λ > 0Long-range order for λ > 0 Self-organized pattern formationSelf-organized pattern formation –Multiple ordered domains –Behavior of agents belonging to each such domain is highly correlated –Distinct ‘cultural groups’ (Axelrod). Phase transitionPhase transition –Unimodal to bimodal distribution as λ increases. Similar results for agents on scale-free networkSimilar results for agents on scale-free network

OK… but does it explain reality ? Rank distribution: Compare real data with model US Movie Opening Gross Model Model: randomly distributed λ

Rank Distribution according to Ratings A DeVany & W D Walls (2002) J Business 75:425 Rank distrn of G-rated movies similar to that for = 0 Rank distrn of PG, PG-13 and esp R-rated movies similar to that for > 0

Conclusion Movie income distribution is Gaussian but with a power law tail having Pareto exponent  ~ 2 Possibly universal for popularity distributions ! True for opening gross income as well as total gross income distribution Pareto tail cannot be explained by information exchange through interaction among agents Bimodality in opening gross distribution can be explained by a collective choice model Movie income distribution is Gaussian but with a power law tail having Pareto exponent  ~ 2 Possibly universal for popularity distributions ! True for opening gross income as well as total gross income distribution Pareto tail cannot be explained by information exchange through interaction among agents Bimodality in opening gross distribution can be explained by a collective choice model