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The Demand for Baseball Tickets 2005

Frank Francis

Brendan Kach

Joseph Winthrop

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Overview

• Objectives • Hypothesis/Variables Examined• Software • Approach• Model• Variable • Statistics• Results• Policy Implications

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Objectives

•To develop an econometric model that explains what factors drove the demand for baseball tickets in 2005

•To provide forecasters with a working model that can be used to make predictions about the future demand for baseball tickets

•To provide baseball management with a solid foundation upon which to make policy decisions based on objective reasoning

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Hypotheses

•Ho: The demand for baseball tickets is explained by average ticket price

•H1: The demand for baseball tickets is explained by the cost of parking

•H2: The demand for baseball tickets is explained by stadium seating capacity

•H3: The demand for baseball tickets is explained by winning percentage

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Variables Examined

Price VariablesAverage ticket priceParking priceBeer price FCI: Fan Cost Index

Demand Variable: Demand for baseball tickets

Performance Variables2005 WINS2005 Losses2005 Win / Loss Percentage2005 Runs Scored2005 Runs Allowed 2005 Homeruns

Other VariablesHome Game Average AttendanceRoad Game Average AttendanceHome Game Occupancy PercentageStadium Seating CapacityPopulation Census Data

Team Economic VariablesTotal RevenueOperating IncomeTotal Payroll ExpenseCurrent Worth

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•WinORS was used to formulate the model

•Ease of Use

•Ability to handle large data sets

•Ability to change model and recalculate results in a timely fashion

Software

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Approach

• Baseball team cross sectional data set from 2005

• Developed an industry demand model

• Stepwise regression was used to determine the most significant variables

• Ordinary Least Squares regression was used to test variables for Multicollinearity, homoscedasticity, serial correlation, and normality

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Variable Identification and Definition

Variable TYPE Hypothesized Sign

Home Game Average Attendance END Dependent

Average Ticket Price END Negative

Home Game Occupancy Percentage END Positive

Home Game Seating Capacity EXG Positive

Team Payroll EXG Positive

Operating Income END Positive

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Cross Sectional Linear Additive Demand Model

QX = -27408.907 - 149.537(PX ) + 446.93(hX)

+ 0.638(sX) + 0.00003(tX) + 0.00002(oX)

QX =Demand for Baseball Tickets

PX = Average Ticket Price

hX = Home Game Occupancy Percentage

sX = Stadium Seating Capacity

tX = Total Team Payroll

oX = Operating Income

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Predictive Ability of Model

Regression Predictive AbilityDependent Variable: 2005 Home Game Average Attendance

Actual Predicted

Observation333231302928272625242322212019181716151413121110987654

Act

ual &

Pre

dict

ed

58,00056,000

54,000

52,000

50,000

48,00046,000

44,000

42,000

40,00038,000

36,000

34,000

32,000

30,00028,000

26,000

24,000

22,00020,000

18,000

16,000

14,000

12,000

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Overall Significance

• The P-value (0.00001) is well below 0.05

• This shows that the model is statistically significant at better than the 99% confidence level.

F-Value825.032

P-Value0.00001

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Coefficient of Determination

• Demonstrates that a high degree of variability in ticket sales that can be explained by variation in the independent variables

Association TestRoot MSE 731.018SSQ(Res) 12825310.950Dep.Mean 30590.833Coef of Var (CV) 2.390

R-Squared 99.422%Adj R-Squared 99.301%

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Multicollinearity

• The first of four regression assumptions is the absence of collinearity or that independent variables must be independent from other independent variables.

• The test for multicollinearity is determined by the value for variance inflation factor (VIF) with a value below 10 indicating an absence of collinearity.

AVERAGE VIF = 1.998

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Parameter VIFs

Variable Variance Inflation Factor

Average Ticket Price 2.291

Home Game Occupancy Percentage 2.546

Home Game Seating Capacity 1.450

Team Payroll 2.532

Operating Income 1.172

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Constant Variance

• The second of four regression assumptions is the expectation of constant variance across the residual terms.

• The White’s test is used to test the null hypothesis and determine if the residual error terms are homoskedastic.

White's Test for Homoscedasticity ====> 25.800P-Value for White's ====> 0.17254

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Constant Variance

Regression Constant Variance TestDependent Variable: 2005 Home Game Average Attendance

Predicted50,00045,00040,00035,00030,00025,00020,00015,000

Res

idua

l

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

-200

-400

-600

-800

-1,000

-1,200

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Auto Correlation

• The third of four regression assumptions is the absence of serial (auto) correlation

• The Durbin-Watson statistic is used to test for the existence of positive and negative serial correlation with time series data.

• Constant Variance plot provides an indication of positive or negative serial correlation.

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Normality of Error Terms

Normal Probability PlotDependent Variable: 2005 Home Game Average Attendance

Expected Residual1,4001,2001,0008006004002000-200-400-600-800-1,000-1,200-1,400

Sor

ted

Res

idua

l

1,800

1,600

1,400

1,200

1,000

800

600

400

200

0

-200

-400

-600

-800

-1,000

-1,200

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Elasticities

Variable Average Elasticities

Average Ticket Price - 0.10778

Home Game Occupancy Percentage 1.02480

Home Game Seating Capacity 0.99879

Team Payroll 0.06168

Operating Income 0.00523

• Elasticity represents a percentage change in the dependent variable given a percentage change in the independent variable.

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Price Elasticity Implications

• Existing demand for baseball tickets is price inelastic

• A 10% increase in the average price of tickets will on lead to a 1% decrease in demand

• Baseball teams can raise prices and it will lead to an overall increase in revenue.

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Conclusion

• We accept Ho, that states the demand for baseball tickets is explained by average ticket price, because it is significant at the 99% confidence level.

• We reject H1, because price of parking is not significant at the 90% confidence level.

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Conclusion

•We accept H2 because stadium seating capacity is significant at the 99% confidence level

•We reject H3 because the winning percentage of the team is not significant at the 90% confidence level