MLB Payroll & Performance

The last two days I wrote about Major League Baseball.  First, I took a look at competitive balance between the American League and the National League and noted that while the National League (in historical terms) was fairly competitive, the American League was not.  The following post looked at MLB team payroll inequality and I showed that since 2011, MLB team payroll inequality is rather large and increasing. So are those two facts related?  Specifically, I am looking at team performance (as measured by each team’s regular season winning percent) and each team’s relative payroll from 2011 to 2018.  Data is found here.  In order to analyze this, I run a linear regression with team regular season winning percent (the dependent variable) on team relative payroll (the independent variable), using robust standard errors.  I find the following:  first, relative payroll is positive and statistically significant, meaning that an increase in a team’s relative payroll leads to an increase in the team’s regular season winning percent; and statistically significant means that I am at least 95% confident that this relationship between team performance and relative payroll was not a random result (assuming that the underlying hypothesis is true).  That is great that we can know the these two variables are related.  But it would also be helpful to know the size and by how much they are related.

In terms of the amount, we can use the estimated coefficient from the regression to answer this question.  In the regression that I ran, I find that the coefficient (marginal effect) is equal to 0.072997.  This number is interpreted as follows:  a one unit increase in relative payroll on average yields a 0.072997 increase in regular season winning percent.  So how much is a one unit increase in relative payroll?  Relative payroll is average payroll during each season.  Over the 2011 to 2018 seasons, relative payroll equals $128,432,967.  So the regression tells us that if a team increases their team payroll by $128,432,967 that the average team’s regular season winning percent increases from 0.500 to 0.507, which over a 162 game regular season means that teams would win an additional 11.82 games. Another way of looking at it, is that each win would result in an additional $10,860,711 spent on payroll.  Now for an average team that does not seem like a good deal, but for teams “on the bubble” of making or not making the post-season, this might be a serious consideration. 

Finally, how much does relative payroll explain regular season winning percentage?  In other words, even if relative payroll is positive and statistically significant, how much does the variation in relative payroll relate to the variation in regular season winning percent?  To answer that question, we use the regression’s R².  From the regression results, the R2 is equal to 0.1302, which I interpret as relative payroll “explains” only 13.02% of regular season winning percent.  Hence, the explanatory power of relative payroll seems to be not very strong.  Think of it this way, if the weather forecast states there is a 13% chance of rain, will you wear rain boots, a rain coat and carry an umbrella for just a 13% chance?  I would not.  In the same way, should MLB general managers spend $128 million dollars to increase winning percent 7%, when the “weather forecast” of rain is 13%?