Friday, January 13, 2012

Finding free information

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What could be more American than a Major League Baseball Game? Can¡¦t most people identify with the experience of visiting a Major League Baseball park? General Motors used to market its Chevrolet line of vehicles with a jingle that equated baseball, hot dogs, apple pie and Chevrolet. It¡¦ our national past time that invokes fond memories of our youth and fosters dreams of young boys and girls everywhere. Certainly Major League Baseball is a pure form of entertainment meant to be afforded by all and free of business controversy, right? Not quite!


These days, Major League Baseball (MLB) has had its share of economic woes that make the business side of baseball all too real. In August of this year, the owners and player¡¦s union narrowly averted another work stoppage that many people felt could have driven baseball fans all around the country out of the parks for good. Strikes in 184 and 14 brought out the ugly side of baseball that most just don¡¦t wish to see. After all, people still want to hum the Chevrolet tune and dream the dreams of the boys of summer. But, for the sake of argument and the fulfillment of a class assignment, this investigation of that very real business side will provide an understanding of the impact it has on the average Major League Baseball patron.


In contrast to the idealistic nature that Americans typically wish to bestow upon the sport, the real issues of player salaries, average ticket prices and attendance shape the economic framework of the business. Player strikes have brought ballooning player salaries into the spotlight and the inevitable comparison between salaries and average attendance has been editorialized thoroughly (1). In fact, after the most recent strike in 14 and 15, attendance at Major League Baseball games dropped 0 percent () and speculation on the future of the business was much in question. Only a home run title chase that eventually broke the single season home run record seemed to bring fans trickling back into the parks. That chase between Mark McGwire and Sammy Sosa jump-started the National League¡¦s attendance with the American League following close behind.


In addition to skyrocketing player salaries and lackluster attendance following the strike, the spotlight on new baseball stadiums with their hundreds of million dollar price tags has had some asking about baseball revenues and the survival of small market teams. The good news is that most Major League Baseball teams who have either moved into a brand new stadium or undergone significant face lifts to their old facilities have enjoyed modest increases in average attendance ().


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So, the question has been posed, ¡§How does player salaries, negative sentiment toward the game, the price tag of new stadiums and, of course, increased ticket prices effect the average MLB attendance?¡¨ One Los Angeles Times report (5) takes a very demand-side economic stance. In short the article states that every MLB team sets prices in the inelastic portion of the demand curve, meaning higher than normal price equilibrium. The writer argues that the reason ticket prices are increasing is because fans are willing to pay the price. He goes on to say that because fans are willing to pay higher prices, baseball players are able to command higher salaries. The silver lining in this cloud is that even with increasing ticket prices, MLB prices are still a bargain when compared to other professional sports (4).


On top of it all, the most recent MLB economic woe is the suggestion of the contraction of the leagues by two teams. This has only fueled the growing argument that large market teams will succeed while small market teams will not be able to survive. Certainly a detailed analysis on the cause and effect of the MLB demand, namely average MLB attendance, should reveal some insight into state of the business and might be used to predict the future behavior of MLB fans.


A literature search revealed two sources of regression analysis available to the public on the Internet (6). One model attempts to explain attendance as a function of salaries, ticket prices and the presence of a new stadium. The other model adds location to the mix (7). In this paper, a new model of average MLB attendance will be built including ticket price, team salary, location and economic factors other models have omitted. Finally, with a stable model of attendance in hand, MLB fans might be able to forget the business and concentrate on the seventh inning stretch while enjoying a good pennant race.


In order to evaluate the most recent state of the business following the latest strike, data from 15 through 001 were used. The first model that was evaluated is a model that assumes average attendance is a function of the team¡¦s winning percentage, the number of All Stars, the number of awards, the total salary, the average ticket price, the distance to the next nearest MLB team, the annualized unemployment rate for the city, the disposable income and a dummy variable indicating the presence of a new stadium. For the purposes of this model, teams that either move into a new stadium or significantly remodel their existing stadium are given a value of 1.0 under the dummy variable for five years. The number of awards is a count of the actual awards a team accrues including such acknowledgements as the Cy Young Award, Rookie of the Year, Manager of the Year as well as many others.


Null hypotheses were developed for all of the independent variables and they were tested with the t-statistic using a one tailed test. The confidence interval used for the model evaluation was 5% (5% t-statistic significance). The following table summarizes the null hypotheses for the original model.


Variable Null Hyppothesis Description


Pct �� GE 0 A team¡¦s winning percentage positively influences the average attendance


AllStars �� GE 0 A team¡¦s number of All Star players positively influences the average attendance


Awards �� GE 0 A team¡¦s number of awards positively influences the average attendance


Total Salary �� GE 0 A team¡¦s total salary positively influences the average attendance


Ticket Price �� LE 0 As average ticket prices increase, average attendance should decrease


Distance �� GE 0 As the distance to the next alternative MLB team increases, average attendance increases


Unemployment �� LE 0 As the city¡¦s unemployment rate increases, the average attendance decreases


Disposable Income �� GE 0 As the average per capita state income increases, average attendance increases


New Stadium �� GE 0 The presence of a new stadium increases average attendance


A second model was analyzed that also included one other independent variable. The previous year¡¦s attendance was added to compensate for the trend that typically teams that draw low numbers continually draw low numbers and teams that draw high numbers typically continue to draw high numbers. The hypothesis tested with the addition of this variable is tabulated.


Variable Null Hyppothesis Description


PrevAttend �� GE 0 As a team¡¦s previous year¡¦s attendance increases, average attendance for the current year increases


Most of the MLB data in the model is annual per calendar year season. The unemployment rate for the city and the disposable per capita income were annualized for the model. Data for this model was limited to the MLB teams in the United States. There are two teams that are located in Canada. Data for the Toronto Blue Jays and the Montreal Expos were omitted for the simplicity of the model. Unemployment rate data was available for the Canadian cities, but that data was not published free of charge. The per capita disposable income and the average ticket price would have had to be converted annually to US dollars using the average exchange rate. For these reasons these teams were excluded from the data sets. A complete listing of the entire data used is included in Appendix B. A total of 10 data sets were evaluated in this model.


The Initial Model


The first model that was analyzed to predict average MLB attendance was


Ave Attend = A + ��1 (Pct) + �� (AllStars) + �� (Awards) + ��4 (Total Salary) + ��5 (Ticket Price) + ��6 (Distance) + ��7 (UnEmployment) + ��8 (Disposable Income) + �� (New Stadium)


Ind. Variable Coefficient Standard Error t-statistic


Intercept (A) 748.87 657.48 1.401


Pct (��1 ) 0178.6 5.7 .187


AllStars (�� ) 10.40 411.6 .178


Awards (�� ) 1.0 441.01 0.


Total Salary (��4 ) 0.00014 .756 E-05 5.708


Ticket Price (��5 ) 56. 184.7 0.05


Distance (��6 ) .40 .47 1.401


UnEmployment (��7 ) -76.5 48.5 -.086


Disposable Income (��8 ) -0.150 0.678 -0.561


New Stadium (�� ) 507.04 17.4 4.151


The full Microsoft Excel analysis of this model is included in Appendix C.


A logical evaluation of the model


The first step in evaluating the model is always to check to see if the model is logical. A check of the signs of the coefficients is evaluated to see if the direction of the impact of the independent variables makes sense. In this model two of the independent variables are suspect immediately. The average ticket price is the first independent variable that is not logical in the model. A positive coefficient on this variable would indicate that raising ticket prices would increase average MLB attendance. While this is not logical to the model, a previous discussion about teams pricing their tickets in the inelastic portion of the demand curve is supported. The second independent variable that is not logical to model is Disposable Income. The negative sign on the coefficient would suggest that as per capita Disposable Income decreases, average MLB attendance will increase. Again, this is not logical to the model. The coefficients for the remaining independent variables all reflect the direction of the null hypotheses developed in each case. These values make logical sense to the model.


Evaluation of the slope terms


The next step in evaluating the model is to determine whether the slope terms on all of the independent variables are significantly positive or negative. This is accomplished by testing the slope terms with a t-statistic. The t-statistic is calculated by subtracting the null hypothesis value from the coefficient and dividing by the standard error of the variable. The t-statistics are included in the evaluation table on page 7 for this model. These calculated t values are compared with the critical table value to see if they are significant. The critical t-statistic value for this model is 1.645. This is found by looking up the appropriate degrees of freedom (180= 10-(+1)) at �� = .05 (one tailed test).


In this model, Awards, Ticket Price, Distance, and Disposable Income all do not have significant calculated t-values so the null hypotheses for these coefficients cannot be rejected. The other values of the t-statistic for Pct, AllStars, Total Salary, UnEmployment, and New Stadium are significant and the null hypotheses for these coefficients can be rejected. The alternative hypotheses for these coefficients are accepted.


The Explanatory Power of the Model


According to the regression statistics provided by Excel for this model, the adjusted R-squared value is 0.601. This means that the model can explain roughly 60% of the variation. While adjusted R-Squared values closer to 1.0 are more desirable in explaining models, this value is interpreted as a strong correlation between the dependent and the independent variables for the model. A graph of the actual verses the predicted values for this model is included in Appendix A.


Serial Correlation


Because the data for this model was annualized, no serial correlation is suspected. A check of the Durbin-Watson statistic verifies this with a value of .10. Typically the Durbin-Watson statistic is between 1.5 and .5 when there is no serial correlation of the data with an ideal value of .0.


Multi-Colinearity


The final check for the model is to evaluate the existence of multi-colinearity between the independent variables. This is done by evaluating the correlation coefficient matrix between the independent variables and looking for values above 0.7. The full correlation matrix Excel table is included in Appendix D. Pct has correlation values of 0.68 and 0.6 for AllStars and Awards. AllStars has a correlation coefficient of 0.57 with Awards. It is easy to see how these might be correlated as it would be suspected that a higher number awards and All Stars should mean a team has a higher winning percentage. But because none of these values are above the 0.7 threshold and because Awards has a non-significant t-statistic, the possible correlation in these variables will be ignored. The one significant correlation that does exist is between Ticket Price and Total Salary. While a discussion of ticket price has already concluded that teams typically price tickets at whatever the market will bear, it is evident by this correlation that teams tend to continue to raise ticket price in relationship to their total salary. This correlation, too, will be ignored since Ticket Price has already been targeted with a low t-statistic.


A Revised Model


With the analysis of the initial model in hand, another model was proposed to remove those independent variables that did not contribute to the overall prediction of average attendance. The revised model also included one other independent variable that might help increase the adjusted R-squared value and help with the overall explanatory value of the model.


The revised model that was analyzed to predict average MLB attendance was


Ave Attend = A + ��1(Pct) + ��(AllStars) + ��(Total Salary) + ��4(UnEmployment) + ��5(New Stadium) + ��6(PrevAttend)


Ind. Variable Coefficient Standard Error t-statistic


Intercept (A) -4118.75 675.78 -1.5


Pct (��1 ) 150.65 555.5 4.17


AllStars (�� ) 4. 70.6 1.586


Total Salary (�� ) 6.56E-05 1.7E-05 .660


UnEmployment (��4 ) -418.85 4.80 -1.86


New Stadium (��5 ) 171.5 77. .17


PreAttend (��6 ) 0.64 0.0416 15.6


Revised Model Evaluation


The logical nature of the revised model is in tact. The coefficients of Pct, AllStars, Total Salary, UnEmployment and New Stadium all stayed the same. PreAttend (Previous Year¡¦s Average Attendance) is positive suggesting that as a team¡¦s previous year average increases, the average attendance for the current year will increase as well. All of the slope terms are significant as each has t-values is greater than the critical t-statistic of 1.645. Every null hypothesis for each coefficient in the revised model can be rejected in favor of the alternative. The explanatory nature of the revised model is better with an adjusted R-squared value of 0.85. In the revised model, the model itself explains 8.5% of the error. The Durbin-Watson statistic for this revised data calculates to be 1.5. There should not be any serial correlation with annual data and the calculated statistic does confirm this. Durbin-Watson values between 1.5 and .5 suggest no serial correlation of the data. A final check for multi-colinearity can be performed by analyzing the correlation matrix in Appendix D. The two variables that are the closest to exhibiting multi-colinearity are Pct and AllStars. The calculated correlation coefficient between the two is 0.67. Values less than 0.7 are accepted and since this does make logical since, and because both are significant to the model, they will each be accepted as part of the revised model.


The revised model developed for Average MLB Attendance does meet all five criteria for evaluating a model outlined in class. The overall R-squared value explains greater than 80% of the variation in this model and by most accounts seems to be a reasonable fit of the data. With Major League Baseball attendance almost back to pre-strike levels, it seems this model could be useful in predicting the average attendance at Major League Baseball Games.


The intercept value at ¡V4118 merely shows a negative value when the actual data is interpolated back to zero. Since zero values for every independent variable are out of the reasonable realm of possibility, the intercept is accepted. The following table summarizes in somewhat real terms what the coefficients mean to the revised attendance equation.


Ind. Variable Coefficient Implication


Pct 160.65 For every percentage point a team can increase, they should get more fans on average


AllStars 4. Each All Star player on a team¡¦s roster contributes about 4 more fans on average


Total Salary 6.56E-05 For every $1 million dollars a team spends, they should average another 7 fans on average


UnEmployment -418.85 Each percentage point drop in the unemployment rate contributes about 41 more fans on average


New Stadium 171.5 The presence of a new stadium contributes about 1,71 more fans per game on average


PrevAttend 0.64 For every 1000 fans a team had on average in the previous year, the current year¡¦s average will be increased by 64 fans


It must be remembered that this model was built without using Canadian team data. This model should not be used to predict average attendance for those teams. The nature of the model is independent of the actual teams. Each data point was analyzed without regard for which team contributed to that data. Major League baseball has 0 teams now in varying markets with varying salary budgets. Teams who wish to aggressively increase their attendance numbers should develop a model for their particular circumstances including promotions and advertising spending.


It seems that building a new stadium will increase a team¡¦s attendance. Spending more money in player salaries should increase attendance as well. And as long as ticket prices are in some reasonable realm, raising ticket prices has little affect on average attendance.


1. Fisher, Eric (000, April 5). Baseball Ticket Prices Soar Out of the Park.


The Washington Times.


. Fisher, Eric (000, July v16 i5 p8). New Ball Parks Help Boost MLB Attendance. Insight on the News


. Lahman, Sean. (00) The Baseball Archive. Web Site http//www.baseball1.com


4. The Seattle Times (00, February 1) Ticket Prices Up, But Below Other Sports.


5. Shaikin, Bill. (1, April 1 p). Experts Say Demand, Not Higher Salaries, Drives Up Baseball Ticket Prices. Los Angeles Times.





6. Stoner, Brian. (000) A Model for Attendance at Major League Baseball Games. Downloaded /7/00. http//www.econ.washington.edu


7. Winfree, Jason A., McCluskey, Jill J., Mittelhammer, Ron C., Fort, Rodney (001, December 14) Location and Attendance in Major League Baseball. Downloaded /7/00. http//users.pullman.com


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