Transcript The Determinants of Major League Baseball Attendance Numbers

The Determinants of Major League
Baseball Attendance Numbers
Jason Cohenford, Rebecca Fan,
Mark Rauckhorst, Ujjayanee Roy
MBA555, Dec. 6 2011
Professor Gordon H. Dash
Overview
Objective
 Hypotheses
 Software and Data
 Model
 Variables Examined
 Statistical Details
 Results
 Conclusions

Objective

To identify the variables that are
statistically significant at the 95%
confidence level in the determining the
attendance levels of major league baseball
teams in 2011.
Hypotheses
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H1: Season attendance levels are dependent
upon previous years number of wins.
H2: Season attendance levels are dependent
on the average ticket price.
H3: Season attendance levels are dependent
on the average summer rainfall.
H4: Season attendance levels are dependent
on the teams city population.
H5: Season attendance levels are dependent
on the team making the playoffs in the
previous year.
Software and Data
WinORS software was used for data
manipulation.
 Cross sectional data was compiled for all 30
major league baseball teams for 2010 and
2011.
 Sources of Information:
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◦
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ESPN Standings
MLB.com Salary Information
Country Studies.us/Weather
Forbes
Wikipedia
Approach
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Data for 2010 and 2011 related to all 30 major league
baseball teams was converted into scalar and dummy
variables and entered into WinORS.
Stepwise regression was used to identify the most
significant variables.
Ordinary Least Squares analysis was used to refine
the model, test for Multicolinearity, Homoscedasticity
and Normality.
Dummy Variables were created to account for
American League versus National League, whether
the team had made the playoffs in the previous year,
and whether the team plays in an indoor stadium.
Erroneous outlier data points were identified and
removed.
Model
Cobb Douglass functional form of production has been used to
represent the relationship of output to input.
In its most standard form for production of a single good with
two factors, the function is
Y = ALaKb
where:
Y = total production (the monetary value of all goods produced in
a year)
L = labor input
K = capital input
A = total factor productivity
α and β are the output elasticities of labor and capital,
respectively. These values are constants determined by
available technology.
Model for Baseball
The use of the Cobb Douglas model with respect to the
success of the baseball team :

Output Y was measured by Team Attendance
Input from six different categories were included in the
model:
– 2011 salary
– Highest player salary
– American League vs. National League
– Playoffs
– City Population
– Average Summer Rainfall

Significant Variables
Variable
Parameter
Standard
Estimate
Error
t for
Ho:
P-value
(95% =
Est = 0 0.05)
VIF
Intercept
1505985.829
167071.939
9.014
0.00001 n/a
2011 Salary
0.01
0.002
3.955
0.00073
3.745
0.038
0.014
2.721
0.01071
3.298
-345954.603
103092.029
-3.356
0.0026
1.02
342044.726
121222.999
2.822
0.00854
1.109
-0.035
0.015
-2.428
0.02067
1.685
-27041.901
9405.151
-2.875
0.00756
1.046
Highest Player Salary
AL
Playoffs
City Population
Average Summer Rainfall
Dependent
2011 total attendance
Variables Not Found to be
Significant
2010 Wins
 2010 Team Value
 2010 Team Revenue
 2010 Operating
Income
 Age of Stadium
 2011 Average ticket
price
 2011 Runs Scored

2011 Runs Allowed
 2011 Home Runs
 2011 All Stars
 Indoor Stadium
 Average Summer
temp.
 Highest Salary as %
of Total
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Statistical Details
Cross sectional regression analysis has been conducted.
The dependent variable = 2011 Total Attendance
R Squared = 86.221,
Adjusted R Square = 86.221% which is not high
The F statistic is 23.987 and the P Value for it is .00001
The probability of observing a value greater than or
equal to 23.987 is less than 0.0001. The P Value is
less than .05. Therefore the probability of incorrectly
rejecting the null hypothesis is very small.
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Statistical Details Continued
Statistical Significance of Each Individual Variable at the
95% confidence level or higher
2011 SALARY P value = .00073 Null Hypothesis rejected P is Less
than .01,result is statistically highly significant.
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Highest player salary P value = .01071
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AL P-value = .00260

Playoffs P-value = .00854
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City Population = .02067

Average summer rainfall P-value = .00756

In all the above cases the P is less than .05, hence the Null
Hypothesis is rejected and the Results are statistically significant

VIF and Homoscedasticity (White’s
Test)
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The p value of homoscedasticity = .59026.
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Homoscedasticity = 14.114
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Average VIF =1.984
Normality
For normal data the points plotted in the quantile-quantile plot should fall
approximately on a straight line, indicating data is normally distributed.
Returns to Scale
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Log Normal Parameter Estimates for Selected
Attributes:
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2011 Salary: 0.490
Highest Player Salary: 0.169
AL: -0.008
Playoffs: 0.010
City Population: -0.090
Average Summer Rainfall: -0.090
Sum: 0.490+0.169-0.008+0.010-0.090-0.090 =
0.481
 Result is Diminishing Returns to Scale: Total
Attendance increases proportionally less than the
inputs
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Elasticities
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The following elasticities indicate the
percentage change in the attendance that
would be expected from a 1% change in
the given variable.
Team Salary Highest Player American League 2010 Playoffs City Population Average Summer
2011
Salary
Rainfall
0.362
0.228
-0.076
0.035
-0.085
-0.115
Results

Accept
◦ H3: Season attendance is dependent on the
average summer rainfall in the home city.
◦ H4: Season attendance is dependent on the home
city population.
◦ H5: Season attendance is dependent on the team
making the playoffs in the previous year.

Do Not accept
◦ H1: Season attendance is dependent on the
number of wins a team had in the previous year.
◦ H2: Season attendance is dependent on the
average ticket price.
Conclusions
The number of previous season wins
does not influence the attendance of
current season.
 The average ticket price does not
significantly affect the attendance levels.
 Total season attendance is dependent on
home town population, but inversely.
 There is a correlation between making
the playoffs in the previous year and
season attendance levels.
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