Blockbusters, Bombs & Sleepers
The Income Distribution of Movies
Sitabhra Sinha
The Institute of Mathematical Sciences
Chennai (Madras), India
“There’s no business like show business”
Why look at Movie Income ?
Movie income is a well-defined quantity;
Income distribution can be empirically determined
A Pareto Law for Movies
Pareto exponent for Movie Income :   2
But
Asset exchange models for explaining Pareto Law in
wealth/income distribution cannot be applied !
Movies don’t exchange anything between themselves !!
Movies popularity distribution → a prominent
member of the class of popularity
distributions
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, 228701
The Popularity of Scientific Papers
Measure of popularity : citation distribution
ISI
1+ = 3
Phys Rev D
 Pareto exponent  2
Relation between exponents for
 : Cumulative probability (Pareto Law)
1+: Probability distrn (Power law)
1/  : Rank distribution (Zipfs Law)
1/  0.48
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: 293-296

Empirical : Time evolution
SS & R K Pan, in preparation

Model
SS & S Raghavendra (2004) SFI Working Paper 04-09-028
SS & S Raghavendra (2005) to appear in Practical Fruits of
Econophysics, Proc 3rd Nikkei Econophysics Symposium,
Springer-Tokyo
Outline of the Talk

Empirical : Distributions
SS & S Raghavendra (2004) Eur Phys J B, 42: 293-296

Empirical : Time evolution
SS & R K Pan, in preparation

Model
SS & S Raghavendra (2004) SFI Working Paper 04-09-028
SS & S Raghavendra (2005) to appear in Practical Fruits of
Econophysics, Proc 3rd Nikkei Econophysics Symposium,
Springer-Tokyo
Measuring Popularity
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
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 ?
What’s the income, dude ?
Income Distribution Snapshot
Each week, about 100-150
movies running in theatres
across USA
Too few data points,
too much scatter
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
Gaussian distribution
Popularity Distribution
of movies released in
USA during 1999-2003
acc to weeks in Top 60
Long tail: the most popular
movies do not fit a Gaussian!
slope  - 0.25
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 !!
Opening Gross
Gross Income Distrn
of movies released in
USA during 1997-2003
Distribution scaled by average
gross to correct for inflation
Kink indicating bimodality
Bimodal distribution of
opening gross
Movies either do very badly
or very well on opening !
Opening Gross
1/  0.5
Gross Income Distrn
of movies released in
USA during 1997-2003
Distribution scaled by average
gross to correct for inflation
Total Gross
1/  0.5
Pareto exponent  2
at opening week and
remains so through the
entire theatre lifespan
Unimodal
The only contribution of
movies which perform well
long after opening (sleepers)
Relation between longevity at Top 60 & Total Gross
GTotal ~ T 2
IMAX movies
Slope ~ 2.14
Outline of the Talk

Empirical : Distributions
SS & S Raghavendra (2004) Eur Phys J B, 42: 293-296

Empirical : Time evolution
SS & R K Pan, in preparation

Model
SS & S Raghavendra (2004) SFI Working Paper 04-09-028
SS & S Raghavendra (2005) to appear in Practical Fruits of
Econophysics, Proc 3rd 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)
Peaks on
weekends
Daily earnings
Exponential decay
A classic blockbuster
Weekend earnings
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

My Big Fat Greek Wedding (2002)
Gradual rise in income
Subsequent exponential decay
A classic sleeper !
Produced outside Hollywood
Extremely long theatre lifespan
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
2004
Spiderman 2
To compare
2003
Lord of the Rings 3: Return of the King
Mystic River
Bulletproof Monk
2002
Spiderman
My Big Fat Greek Wedding
2001
Harry Potter and the Sorcerers' Stone
2000
American Psycho
1999
The Sixth Sense
Blair Witch Project
Color code:
Blockbuster
Sleeper
Bomb
Comparing the Income
Growth / Decay of
Movies
Scaled by opening gross
Income of most movies
decay exponentially
with the same decay
rate < 5 weeks
Outline of the Talk

Empirical : Distributions
SS & S Raghavendra (2004) Eur Phys J B, 42: 293-296

Empirical : Time evolution
SS & R K Pan, in preparation

Model
SS & S Raghavendra (2004) SFI Working Paper 04-09-028
SS & S Raghavendra (2005) to appear in Practical Fruits of
Econophysics, Proc 3rd 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
Popularity = Collective Choice
Process of emergence of collective decision
 in a society of agents free to choose
 constrained by limited information
 having heterogeneous beliefs.

Example:
Movie popularity.
Collective Choice: A Naive Approach


Each agent chooses randomly independent of all
other agents.
Collective decision: sum of all individual choices.
Example: YES/NO voting
on an issue
 For binary choice
Individual agent: S = 0 or 1
Collective choice: M = Σ S
 Result: Normal distribution.

NO
YES
0 % Collective Decision M 100%
Modeling emergence of collective
choice
Agent’s choice depends on
• Personal belief (expectation from a particular choice)
• Herding (through interaction with neighbors)
2 factors affect the evolution of an agent’s belief
• Adaptation (to previous choice):
Belief changes with time to make subsequent choice
of the same alternative less likely
• Learning (by global feedback through media):
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).
 Choice dynamics of the ith agent at time t:

for square lattice

Belief dynamics of the ith agent at time t:
is the collective decision
where
 μ: Adaptation timescale
 λ: Learning timescale
Results
• Long-range order for λ > 0
Initial state of the S field: 1000 × 1000 agents
μ =0.1
λ = 0: No long-range order
N = 1000, T = 10000 itrns
Square Lattice (4 neighbors)
μ =0.1
λ = 0.05
λ > 0: clustering
N = 1000, T = 200 itrns
Square Lattice (4 neighbors)
Results
• Long-range order for λ > 0
• Self-organized pattern formation
μ =0.1
Ordered patterns emerge asymptotically
λ = 0.05
Results
• Long-range order for λ > 0
• Self-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 > 0
• Self-organized pattern formation
– Multiple ordered domains
– Behavior of agents belonging to each such domain is
highly correlated
– Distinct ‘cultural groups’ (Axelrod).
• Phase transition
– Unimodal to bimodal distribution as λ increases.
Bimodality with increasing λ
Results
• Long-range order for λ > 0
• Self-organized pattern formation
– Multiple ordered domains
– Behavior of agents belonging to each such domain is
highly correlated
– Distinct ‘cultural groups’ (Axelrod).
• Phase transition
– Unimodal to bimodal distribution as λ increases.
• Similar 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: randomly distributed λ
Model
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