Pay and Performance in MLB

I have written previously about pay and performance in a variety of sports leagues included Major League Baseball. We have written about this in our book - The Wages of Wins - and have stated repeated that payroll (or over time relative payroll) statistically has very little relationship with regular season performance using a statistic called r-squared. I have also explained why r-squared is a superior statistical measure.

So, let's take a look how well this holds for just the 2011 MLB regular season. Using data from the USAToday's MLB salary database and the 2011 MLB regular season standing, I ran a linear regression with the dependent variable 2011 regular season winning percent and the independent variable 2011 team payroll. I find that team payroll is statistically significant at the 95% confidence level. While that is supportive of the hypothesis that teams with higher payroll will have higher performance, there are two other problems. Let's take a deeper look.

First, r-squared (which measures the relationship between the variation in the dependent and independent variables) is 0.168. This means that variation in team payroll "explains" about 16.8% of the variation in regular season performance for the 2011 MLB season. Our problem is that those that hold to the payroll-performance hypothesis, payroll should have a much greater effect on team performance than about 17%. Given this low relationship, I conclude that while payroll and performance are related, it is not that strong.

The other issue is the effect that payroll has on regular season performance. The payroll coefficient from the regression of wins and team payroll is 0.000000114375468825704, which is a very small number. In other words to generate one more win, a MLB team would need to increase their payroll by $8.743 million (and no other team change their payroll or increase their payroll by $8.743 million more than the average increase in payroll). Given that the average payroll last season was $92.872 million an average team (81 wins) results in spending $1.147 million per win. Thus teams would have to spend nearly 8 times the average cost for each win.

Yet, what about the post season? Of the eight teams that made the playoffs this post-season, New York and Philadelphia were in the top payroll quartile, Detroit, St. Louis and Texas were in the second quartile, Milwaukee was in the third quartile and Arizona and Tampa Bay were in the bottom payroll quartile. Here's the percentage of wins for the League Division Series (LDS), League Championship Series (LCS) and the World Series (WS).

Quartile	LDS	LCS	WS
1	21.05%	0.00%	0.00%
2	47.37%	83.33%	100.00%
3	15.79%	16.67%	0.00%
4	15.79%	0.00%	0.00%

While not definitive, teams in the top half of the regular season have won a greater percentage of post-season games, yet the hypothesis would have a higher winning percentage than observed. Now I admit, that one season is not a large enough sample to make a definitive conclusion, and that different seasons will have different results, it does ask for more research on the payroll and performance hypothesis in MLB. This I will return to in the future.