## Tuesday, October 22, 2013

### MLB Payroll & Performance from 1988 to 2013

Last week I wrote about the 2013 MLB regular season's team payroll and performance relationship and found that their is zero statistically significant amount of common variation between team payroll and team performance in the regular season.  Problem with this is that it takes into account only one season (hence the use of team total payroll) and one season is a limited sample size.  That I will correct.

In analyzing the relationship between payroll and performance, first let's think about what MLB regular season performance looks like during a season.  As you know, winning percent has an average of 0.500 for each season - thus winning percent as a variable is stationary, meaning that the average of all the teams winning percent over time does not change.  Here is the graph for winning percent.  As you can see, the average of winning percent remains the same over time.

Again, I use relative payroll since relative payroll is a stationary variable in that the mean is one for each season.  Here is graph of relative payroll from 1988 to 2013.  Yes, those spikes are the New York Yankees (smaller ones on the right are the Phillies, Dodgers and Red Sox's).

When looking at a longer time period (1988-2011), I find that relative payroll (a team's total payroll divided by the MLB season average payroll for all teams) is positive and statistically significantly related to team performance.  I use relative payroll and winning percentage since both variables are stationary and thus the amount of variation that is in common for both will give a better picture as to how well payroll and performance are related.

So, here are the updated results using data from 1988 to 2013 for the regular MLB season.  I find that relative payroll is positive and statistically significant.  The "explanatory power" of relative payroll for the 1988-2011 time period was 17.6%.  Now adding two more seasons I find that it has fallen to 16.4%, indicating that relative payroll and team regular season performance is weakening.

What if instead of using relative payroll I used total payroll?  Since total payroll have been increasing, then this will give weaker statistical results compared to using relative payroll, since total payroll is non-stationary.  As you can see below the variable is increasing from left to right.

Running the regression reveals that the amount of variation that is in common between total payroll and team regular season performance is now 5.9%.