THE UNIVERSITY OF IOWA MLB Winning Percentage vs Team Payroll Philip Hawbaker Mark Kaiser Daniel Murray 5 5 2008 MLB Winning vs Payroll Introduction The baseball industry is a multi billion dollar business encompassing a wide array of teams and people from a variety of locations The game itself baseball is a game of statistics with every play every hit every error and every single act on the field recorded and kept track of in the form of a statistic The most prominent of these statistics among every sport is the winning percentage Representing the number of winning games out of every game played the ratio is a numeric representation of the team s success Additionally another common fascination among sports fans is the pay earned by the athletes Some of the best athletes in the world command seven and eight figure yearly salaries justifiable by their outstanding athletic performance However with athletes who aren t known as the best in the game yet still receive large paychecks or above average athletes who receive low salaries it becomes unclear whether or not there is a direct relationship between pay and athletic performance Through a database of baseball statistical information on www baseballalmanac com information was found regarding both types of data dating back to 1995 The primary concern of the testing was to determine if in fact there was a positive relationship between the winning percentage of the overall baseball team and the payroll of the team for the entire year The payroll only included the salaries of the players the managers payroll was excluded from the analysis Data For the collection of data the group analyzed thirteen American League teams For each team thirteen years were analyzed 1995 2007 noting the yearly payroll and the winning percentage Overall this collection of data resulted in 169 observations covering each of the thirteen teams for thirteen years Each year the payroll changed for every team as did the winning percentage However to properly analyze the value of the payroll rather than specific dollar amount adjustments to the payroll amount had to be made A payroll of 50 million in 1995 has significantly more value than a payroll of 50 million in 2007 due to economic inflation In order to account for this decrease in the value of the currency adjustments were made to reflect the monetary value of the payrolls rather than simply dollar amounts This was accomplished by utilizing the compound interest formula where x the inflation rate in decimal format n years after 1995 This formula was utilized on a large scale in an excel spreadsheet and the numbers were reported in a separate list Once these data were calculated and gathered the numbers were analyzed using the SAS software Only the winning percentage and inflation adjusted team payrolls were utilized in the analysis Results The following chart is a scatterplot representing the imputed data in its raw form 43 observations were omitted because of the similarity between some of the data points Because the display of the SAS scatterplot is somewhat limited several data points that are similar from a more macro viewpoint are omitted even though they differ when scrutinized more closely Additionally because of the large scale of the payrolls involved all payroll amounts are in millions of dollars Plot of winpct payroll Symbol used is Winpct 0 8 0 7 0 6 0 5 0 4 0 3 0 2 0 50 100 150 200 payroll The REG Procedure Model MODEL1 Dependent Variable winpct Number of Observations Read Number of Observations Used 169 169 Analysis of Variance Sum of Mean DF Squares Square F Value Pr F Source Model 1 0 17306 0 17306 Error 167 0 77179 0 00462 Corrected Total 168 0 94485 37 45 0001 Root MSE 0 06798 R Square 0 1832 Dependent Mean 0 50737 Adj R Sq 0 1783 Coeff Var 13 39890 Parameter Estimates Variable Parameter Standard DF Estimate Error Intercept payroll 1 1 0 44038 0 00130 t Value 0 01213 0 00021314 36 30 6 12 Pr t 0001 0001 The above chart represents some of the basic statistics regarding the baseball data The most important information represented in the chart is the parameter estimates for both the Intercept and payroll variables Utilizing the information given the regression line equation is Winning percentage 0 44038 0 00130 Payroll in millions The REG Procedure Model MODEL1 Dependent Variable winpct Number of Observations Read Number of Observations Used 169 169 Analysis of Variance Sum of Mean DF Squares Square F Value Pr F Source Model 1 0 17306 0 17306 Error 167 0 77179 0 00462 Corrected Total 168 0 94485 37 45 0001 Root MSE 0 06798 R Square 0 1832 Dependent Mean 0 50737 Adj R Sq 0 1783 Coeff Var 13 39890 Parameter Estimates Variable Parameter Standard DF Estimate Error Intercept payroll 1 1 0 44038 0 00130 t Value 0 01213 0 00021314 36 30 6 12 Pr t 0001 0001 Parameter Estimates Variable DF Intercept payroll 1 1 95 Confidence Limits 0 41642 0 00088351 0 46433 0 00173 The following chart represents the data gathered using a 95 confidence interval on the regression line This states the range at which we are 95 confident that the regression line lies within given a random sample size of 169 The graph of this regression line and the corresponding 95 confidence interval is in shown in the appendix Additional analysis was done to find a residual scatterplot using the SAS software This chart reveals the ability of the regression line to relate the two variables winning percentage and team payroll The figure located in the appendix is a horizontal line with the data points distributed around it The majority of the points lie within 0 1 of the regression line However several points lie outside of that range and a few lie outside the 0 2 range Though these values are not very well described by the regression line they are acceptable considering the variability of the data Conclusion We determined that there is very little correlation between the winning percentage of the teams and how much their payroll was From our regression data the value was 0 1832 This means there is only an 18 32 correlation between the payroll of one team and their winning percentage The slope of the regression line was 0 00130 This data reveals that for every additional million dollars spent on payroll team winning percentage increases by only 00130 or 13 From this data it is clear that paying the players more does not really lead to an increase in winning percentage Additionally it is clear that payroll alone is not the sole factor in