1. The Determinants of Major League Baseball Attendance Numbers Jason Cohenford, Rebecca Fan, Mark Rauckhorst, Ujjayanee Roy MBA555, Dec. 6 2011 Professor Gordon H. Dash

2. Overview Objective Hypotheses Software and Data Model Variables Examined Statistical Details Results Conclusions

3. 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.

4. Hypotheses H 1 : Season attendance levels are dependent upon previous years number of wins. H 2 : Season attendance levels are dependent on the average ticket price. H 3 : Season attendance levels are dependent on the average summer rainfall. H 4 : Season attendance levels are dependent on the teams city population. H 5 : Season attendance levels are dependent on the team making the playoffs in the previous year.

5. 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: ESPN Standings MLB.com Salary Information Country Studies.us/Weather Forbes Wikipedia

6. Approach 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.

7. 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 = AL K where: Y = total production (the monetary value of all goods produced in a year) L = labor inputlabor K = capital inputcapital A = total factor productivitytotal factor productivity α and β are the output elasticities of labor and capital, respectively. These values are constants determined by available technology.output elasticities

8. 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

9. Significant Variables ParameterStandard t for Ho:P-valueVIF VariableEstimateErrorEst = 0 (95% = 0.05) Intercept 1505985.829167071.9399.0140.00001n/a 2011 Salary0.010.0023.9550.000733.745 Highest Player Salary0.0380.0142.7210.010713.298 AL-345954.603103092.029-3.3560.00261.02 Playoffs342044.726121222.9992.8220.008541.109 City Population-0.0350.015-2.4280.020671.685 Average Summer Rainfall-27041.9019405.151-2.8750.007561.046 Dependent2011 total attendance

10. 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

11. 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.

12. 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. Highest player salary P value =.01071 AL P-value =.00260 Playoffs P-value =.00854 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

13. VIF and Homoscedasticity (Whites Test) The p value of homoscedasticity =.59026. Homoscedasticity = 14.114 Average VIF =1.984

14. Normality For normal data the points plotted in the quantile-quantile plot should fall approximately on a straight line, indicating data is normally distributed.

15. Returns to Scale Log Normal Parameter Estimates for Selected Attributes: 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

16. Elasticities The following elasticities indicate the percentage change in the attendance that would be expected from a 1% change in the given variable.

17. Results Accept H 3 : Season attendance is dependent on the average summer rainfall in the home city. H 4 : Season attendance is dependent on the home city population. H 5 : Season attendance is dependent on the team making the playoffs in the previous year. Do Not accept H 1 : Season attendance is dependent on the number of wins a team had in the previous year. H 2 : Season attendance is dependent on the average ticket price.

18. 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.