## A Quick Look at the Relationship between Payroll & Winning Across Leagues

Note: This post is related to work currently being done in a class called “Predictive Sports Analytics” at Emory University.

This week, we are taking a (simple) look at the relationship between payrolls and winning across the four major professional sports league.  We begin today with a quick look at the strength of the payroll-winning relationship across the leagues.

The payroll variable that we use in this analysis is relative payroll.  To construct this variable, we simply divide each team’s payroll by the league average that year.  For example, if a team has double the league average the relative payroll measure would be 2, and if they had a payroll of exactly the league average, the variable would equal 1.

Please note that we did say this is a simple look.  The analysis could be extended in a variety of ways (such as using a division average as the denominator).  But, we are using this analysis as a discussion point for our Predictive Sports Analytics class here at Emory, and we want to keep the analysis clean.

So, let’s compare some basic descriptive statistics across leagues.  The tables below list measures of payroll and winning rate dispersion across leagues (we are doing this analysis using data from 2001 to 2013).  The first table includes data on relative payrolls.  The standard deviation (std. dev.) is a measure of spread in which higher values indicate greater variation and lower values indicate a tighter range.

The league with the greatest dispersion (variance) in payrolls is MLB.  Baseball is followed by the NHL and the NBA.  The NFL has the smallest amount of variability.  These results are not surprising given the differences in collective bargaining agreements, and revenue sharing policies across leagues.

Payroll Dispersion

 League Std. Dev. Minimum Maximum MLB .408 .19 2.85 NBA .195 .42 1.82 NHL .238 .13 1.80 NFL .126 .59 1.46

The next table shows the variability in winning rates across leagues.  This is potentially important information for league commissioners and media companies.  It is unclear what the right level of competitive balance is for generating maximum fan interest.  But, at least at some level, fans probably want to see more even match-ups, and small market residents want their team to have a chance to be a winner.

Interestingly, we find the greatest dispersion in winning rates in the NFL – the league known for parity.  This is likely due to the fact that we are studying one year winning rates, and the NFL has a relatively short season.  The league with the most balance is MLB – the league with the least revenue sharing, and the most concerns about large market dominance.

Winning Percentage Dispersion

 League Std. Dev. Minimum Maximum MLB .073 .265 .716 NBA .151 .106 .817 NHL .099 .292 .837 NFL .193 0 1

This brings us to the real reason for today’s post: A look at the “strength” of the relationship between spending and winning across leagues.  This is done by computing the correlation between relative payroll and winning, and also by estimating a linear regression of winning as a function of relative payroll.  The table below contains the results.

 League Correlation Equation MLB .44 Win% = .42 + .08 * Rel_Pay NBA .32 Win% = .25 + .25 * Rel_Pay NHL .45 Win% = .35 + .20 * Rel_Pay NFL .17 Win% = .25 + .25 * Rel_Pay

We see that the relationship between winning and payroll is the strongest in MLB and the NHL.  While the “hard” salary cap leagues have the weakest relationship.

One more note: this is just the start.  As the weak progresses, we are going to examine the most efficient and least efficient teams in each league.  In other words, we are going to see what front offices get the most bang for their buck and who struggles.  Stay tuned.

Mike Lewis & Manish Tripathi, Emory University 2014.