2011-2019 MLB Payroll and Performance

Recently, I have blogged about MLB.  First, I looked at competitive balance between the American League and the National League.  Then I blogged regarding 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 2019.  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 0.0788935.  This number is interpreted as follows:  a one unit increase in relative payroll on average yields a 0.0788935 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 2019 seasons, relative payroll equals $129,404,591.  So the regression tells us that if a team increases their team payroll by $129,404,591 that the average team’s regular season winning percent increases from 0.500 to 0.508, which over a 162 game regular season means that teams would win an additional 12.78 games. Another way of looking at it, is that each win would result in an additional $10,124,963 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 0.1365, which I interpret as relative payroll “explains” only 13.65% 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 14% chance of rain, will you wear rain boots, a rain coat and carry an umbrella for just a 14% chance?  I would not.  In the same way, should MLB general managers spend an additional $129 million dollars to increase winning percent nearly 8%, when the “weather forecast” of rain is 14%?

2011-2019 MLB Team Payroll Inequality

Yesterday, I took a look at competitive balance in MLB and found that MLB competitiveness was declining this season as compared to last season.  So now, what I want to look at is the level of team payroll inequality using team payroll data.

In the chart below is the MLB Team Payroll Gini coefficients from 2011 to 2019.  As you can see, team payroll is highly unequal.  Want to know how to calculate the Gini coefficient?  Look here.

2018 NFL Payroll and Performance

Yesterday, I blogged about competitive balance in the NFL for the 2018 season.  Today I will look at the relationship between payroll and performance in the NFL for the 2018 season.  The basic idea is that teams that pay higher salaries to their players will perform better.  As sports economists, we tend to be highly skeptical of this hypothesis, but it is a persistent topic - especially in baseball.  So let's see what happens.

To do this, first I need the data.  Payroll data is from spotrac and performance data is from profootball reference.   Once that is done, the first thing I did was to calculate the correlation coefficient between payroll and performance, and the correlation between payroll and performance is NEGATIVE!!  That is a first for me.  Now, one thing we know statistically is that you should not draw conclusions from descriptive statistics, but there are those that do.  If one was to draw a conclusion (again this is not statistically valid, then those who do this would have to conclude that lower pay results in better performing NFL teams).  I doubt you will hear much from the pay and performance crowd about the 2018 NFL season.

Running a regression between performance and payroll (with robust standard errors), I get that the coefficient on payroll is negative and statistically significant as well.  This is a problem for the payroll and performance hypothesis holders.  Additionally, just for the 2018 season, payroll "explains" only 17% of team performance, so this seems to be not only the wrong sign, but also the not a lot.

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%?

2017 MLB Pay and Performance

Last week I blogged about competitive balance in MLB.  Now I want to turn to the relationship between MLB payroll and MLB performance.  I have looked at this using USA Today MLB team payroll data in the past (2015 and 2016), but now I want to use data from spotrac.com for MLB.  I find that the data from spotrac is excellent and probably more accurate than the USA Today MLB team payroll data.  The data from spotrac starts in 2011, so I have a smaller time frame to work with, but I thought it would be good to see if the relationship between payroll and performance differs using a different set of MLB team payroll data.  If you are interested in doing this type of analysis, here is a step-by-step guide to payroll and performance analysis.

So, after collecting and organizing the 2011 through 2017 MLB team payroll and team performance data, I ran the regression on team performance using relative payroll as the independent variable.  I use a software package called Stata for the statistical analysis and found that relative payroll is positive and statistically significant with respect to MLB team performance, just like I have found in each previous time I have done this type of statistical analysis using data from USA Today.  The coefficient on relative payroll is 0.06868, which means that a one unit increase in relative payroll will lead to a 0.06868 increase in team winning percent.  In terms of wins, the regression results show that a one unit increase in relative payroll would result in just over 11 additional wins.  In order to get those wins, a MLB team would have to increase team payroll by one unit of relative payroll, which is the same thing as average payroll.  For the 2017 MLB season, that is an increase of $152,327,084 using data from spotrac.  So those approximately 11 wins would cost about $13,690,875 per win.  That is a rather costly amount to pay for each win.

Finally, the regression results show that while the relationship between MLB team performance and relative payroll is positive and statistically significant, the amount that relative payroll "explains" of MLB team performance is not that much.  In this case, using data from spotrac, the explanatory power of the regression is rather weak, with an adjusted r-squared equal to 0.127.  Another way of saying that is that relative payroll only "explains" 12.7% of MLB team performance.  I will let you decide if you think that is good enough.  But will state that there are other variables that explain a greater amount of MLB team performance than relative payroll.

2016 MLB Payroll and Performance

Yesterday, I looked at how competitive MLB was using the Noll-Scully measure of competitive balance and today I want to look at the relationship (and its magnitude) between regular season MLB team payroll and MLB regular season team performance.  If you are interested in doing this type of analysis, here is a step-by-step guide to payroll and performance analysis.

After combining the data and performing the statistical analysis, one finds the following.  First, for the 2016 MLB regular season, there is a positive and statistically significant (t-statistic is greater than two in absolute value) relationship between team payroll and team performance.  In fact, the relationship is that an additional increase of ten million dollars in one teams payroll would move an average team (i.e. the Kansas City Royals) from a winning percentage of 0.500 to 0.509 and an additional increase in team payroll equal to the average team payroll ($126 million) would move the average performing team from 0.500 to 0.614, which is basically an increase in 18 wins over the regular season or almost $7 million for each additional win.  While for the average team this moves them from not making the playoffs to being a World Series contender, for teams like the Minnesota Twins, this moves them from being the worst team in MLB with a winning percent of 0.364 to a winning percent of 0.478 and still out of playoff contention.

Second, the performance of the regression is better than in years past, with the amount that the variation in team payroll "explains" the variation in team performance being around 39%.

2015 MLB Pay and Performance

Yesterday I posted on competitive balance in the MLB and showed that competitive balance in the MLB is getting slightly better in the 2015 season.  So the next step is to look at payroll and performance in MLB during the 2015 season.  I have looked at payroll and performance previously and here is a blog from the end of last season in MLB.  As you can see from that blog that the payroll and performance relationship has been declining since the mid-1990's.  In fact, just taking a look at last season, there is no statistically significant relationship between team payroll and team regular season performance in MLB for the 2014 season.  So, was 2014 a fluke or a trend.  Let's find out by looking at the 2015 MLB regular season.

To do so, first i need the two variables: MLB regular season winning percent, which I grabbed from ESPN and MLB team payrolls which I got from USA Today's MLB team payroll page and second, I need to run the payroll and performance statistical analysis.  (If you are interested in performing your own payroll and performance analysis, here is a step-by-step guide to analyzing payroll and performance.)

What I find is that team payroll for the 2015 MLB season is statistically insignificant, meaning that MLB team payroll has zero effect on MLB team regular season performance during this last season, just like in the 2014 season.

2015 NBA Payroll and Performance

Today I am going to look at NBA payroll and NBA performance.  Over the last few years, NBA payroll has not been a very good predictor of NBA regular season performance.  Let's see if that trend holds up for the last two NBA regular seasons.  Thus I have grabbed data from the internet on NBA payrolls  for 2013/14 regular season and the 2014/15 regular season and NBA performance and run a regression on how well relative payroll is related to regular season performance.

What I find is that over the last two NBA regular seasons is that relative payroll is positive and statistically significant, but only explains about 12.6% of regular season winning percentage.

2014 NFL Payroll and Performance

With the NFL regular season in the books, let me turn my attention to the relationship between team payrolls and team performance.  As we discuss in our book The Wages of Wins, while there tends to be a positive and statistically significant relationship between relative payroll and team performance, the relationship is not really very large enough to conclude that spending by teams is related to on-field performance.  While the book was published in 2006 (and updated in 2007), I like to try to keep up to date on these topics and thus the reason for this blog post.

So, I downloaded the NFL regular season team standings data and NFL team payroll data to run this analysis for just the 2014 season.  Before I present the results, I want to discuss the payroll data.  Using the link above you can see that I am using "cash" and not there salary cap option.  The reason is that I want to focus on actual spending by the team on the players as opposed to how money is attributed to payroll regulations.  For those interested in doing this on there own, here is a step-by-step guide to payroll and performance analysis in Microsoft Excel.

So for the 2014 NFL regular season team payroll and performance is positive and statistically significant, but the amount that payroll explains team performance is about 25%.  Meaning that there is 75% unexplained.  If I wanted to know why teams wins, using only payroll seems to be a limited resource.

Payroll and Performance in MLS

One of the ideas that we focus on in our book The Wages of Wins is the relationship between team payroll and team performance.  We focus primarily on Major League Baseball as that is the sport that the payroll and performance discussion tends to get the most talk.  What we find is that using team performance (regular season winning percentage) and team payroll (relative payroll when comparing multiple seasons or total payroll for one season) we find that there is a positive relationship between team performance and team payroll.  Additionally, we find that that relationship is statistically significant over multiple seasons, meaning that from a statistical viewpoint the two variables are different from zero.  Each of these we find evidence for.  Yet in terms of the amount that the two variables have in common, we find is less than 20% over most time periods.

So, let's take a look at MLS for just the 2014 regular season.  First let me note that since there are only 19 teams in MLS this season, the number of observations is suspect.  So take the following with a statistical "grain of salt".  Eventually, I will like to come back and analyze this over a much longer time period, but it will take some time for me to get the salary data cleaned up from the pdf's on the internet. 

Thus given I am only looking at the 2014 regular season the statistical results are not very promising.  For the 2014 regular season neither base salary nor guaranteed salary are statistically significant with respect to standings points.  In other words, from a statistically viewpoint either base salary or guaranteed salary do not explain end of regular season standings points.

MLB Pay and Performance 1988 to 2014

With the MLB regular season in the books and the playoffs underway, I thought that I would get back to looking at MLB pay and performance.  As we state in our book, The Wages of Wins, while there is a positive and statistically significant relationship between relative payroll and team performance (as measured by winning percent); the variation that is common between the two variables is not a lot.  So what I will do here is measure both the relationship and the amount of common variation (using r-squared) for the MLB regular season over a few different time periods.

If you are interested in performing your own payroll and performance analysis, here is a step-by-step guide to analyzing payroll and performance.

First, the two variables are MLB regular season winning percent, which I grabbed from ESPN and MLB team payrolls which I got from USA Today's MLB team payroll page. 

Second, as I have explained previously, I am using relative payroll because average payrolls have been increasing over time and average winning percent is constant over time.  Hence if I use total payroll instead of relative payroll, I will find a weaker relationship since MLB total payrolls are increasing and MLB winning percent is constant.  If I use relative payroll (a team's total payroll divided by that seasons average payroll) then I will be comparing two variables that are stationary to each other and get better results.

How much in common is the variation in relative payroll and the variation in winning percent by season?

1995-2014:  18.1%
2000-2014:  14.8%
2005-2014:  13.7%
2010-2014:    8.4%
2014:  relative payroll is statistically insignificant.

Over different time periods we see that the explanatory power of relative payroll on team winning percent has been declining since 1995.

MLB Payroll Visualized

The LA Times has a nice article showing MLB payrolls!

NBA Payroll and the Playoffs

Last year (November 14) I wrote about being skeptical that payroll and performance are significantly related in the NBA.  Kristi Dosh (ESPN writer) is not skeptical about the relationship between pay and performance in the NBA and predicted that the top 10 payrolls will make the playoffs.  So, how did that work out?

Dosh predicts that the following teams will make the 2013-14 NBA playoffs:  Nets, Knicks, Heat, Bulls, Lakers, Raptors, Clippers, Celtics, Thunder and Pacers and the teams in bold did not actually make the playoffs.  As I have written previously, "I think this would be much more convincing if the top 16 teams in terms of payroll made the playoffs for say ten NBA seasons.  That would give much more credibility to this type of statement.  Since this statement only looks at ten of the possible sixteen playoff spots the prediction is only 62.5% accurate - or leaves 37.5% of the playoffs teams unexplained.  For statisticians this is a large error."  Now the error is compounded with three of the teams in the top ten of payroll not making the playoffs, which is a forecast error of 30%!

As we have written in The Wages of Wins, relative payroll is not a good predictor of team performance in the sense that it does not have a lot of commonality between the two variables.
Here is a look at the statistical relationship between NBA payroll and NBA regular season performance over different time periods.

Since the 2004/05 NBA season (i.e. the last decade) the relationship between relative payroll and regular season performance is statistically significant (95% level), but relative payroll only "explains" 7.2% of the variation in regular season performance (which is statistically called r-squared) adjusted for heteroskedasticity in the data (unequal scatter).  If we look at the adjusted r-squared that falls slightly to 6.9%.

Taking the time period of Mrs. Dosh (2011/12 to now) the statistical relationship between relative payroll and regular season performance is statistically significant (95% level) and the amount that relative payroll is in common with regular season performance is higher with an r-squared of 0.188 and an adjusted r-squared of 0.179.  Still relative payroll misses over 80% of the variation in regular season performance.  I will let you decide if that is a good predictor or not.

Finally, just taking this season into account, now the statistical relationship between relative payroll and regular season team performance is statistically insignificant at the 95% level.  Meaning from a statistical viewpoint that payroll is NOT related to team regular season performance.

NHL Pay and Performance

Yesterday I blogged about competitive balance in the NHL, and today I want to extend that to take a look at pay and performance in the NHL during the regular season.  Recently a new website has emerged which focuses on the payroll cap in the NHL, called capgeek.com.  It is excellent and I know of no better website for salary and team payroll information on the internet.  So, I am going to use their information to estimate the relationship between regular season payroll and regular season performance from the 2009/10 NHL regular season to the 2013/14 regular season.

To do that, I will run a linear regression on relative payroll and team points (team performance measure).  For those interested, here is a step-by-step guide as to how to do this yourself.  You may be wondering why I use relative payroll and why I am focusing on the statistical measure called r-squared.  I answer (or link) to those directly below.

Why relative payroll?  This is for statistical purposes, but simply stated - the average of team payrolls are rising over the time period and the average of team performance is remaining relatively constant.  So if you just take a look at payroll and performance you are comparing a variable that is increasing to one that is constant (or stationary) and you will get a lower statistical relationship that what is truly taking place.  In fact the correlation coefficient (called r) between payroll and performance falls dramatically over this time period as opposed to the coefficient of determination (r-squared).  For this time period, for payroll and performance r = 0.034 while for relative payroll and performance r = 0.235, and thus for payroll and performance r-squared = 0.001 and for relative payroll and performance r-squared = 0.055.

Why do I use r-squared?  I have answered that here.

So, what is the relationship between team relative payroll and team regular season performance?  For the the 2009/10 NHL season to the 2013/14 NHL regular season that I have data from capgeek, relative payroll is statistically significant (at the 99% confidence level) with respect to team points. Yet, in terms of the common variation between the two variables, there is not much with the R-squared = 0.055.  If I include payments of long-term injured reserve and also include bonuses, the r-squared actually decreases.  Thus relative payroll "explains" less than 6% of NHL team regular season performance since 2009/10.

Hence, I conclude that NHL regular season team payrolls are not a good indicator of NHL regular season performance.

MMA Monopsonist and Labor Supply

Bleacher Report has a great article on the business of MMA and has a link to Eddie Alvarez's contract.  Given that MMA does not have a "players" union, we see some similar labor market behavior to the time period in other professional sports before collective bargaining.  This is an example of a monopsonist facing a competitive labor supply market, where the profit maximizing solution is to set the wage in the competitive labor supply market below what would occur in a competitive labor market.

EPL Pay and Performance

The Economist has a nice article on pay and performance in the English Premier League, making some interesting arguments as to why points per pound (UK currency) is different for different teams.

NBA Payroll and Performance

In our book The Wages of Wins we talk about when performing statistical analysis; for samples, size matters. Specifically, the larger the sample size (more relevant data), the more accurate (smaller the standard error) are the statistical results.  Thus looking at a team over a few games or a league over a couple of years and making definitive statements about the team or the league is a highly dubious endeavor.

How do we come up with such a conclusion?  Here is a guide for further reading:

Why are small sample sizes a problem, and thus need to use a longer time period?
A step-by-step guide on how to perform the payroll and performance analysis.
Why do I use relative payroll (3rd paragraph)?
Why do I use R-squared (or adjusted R-squared) as our measuring stick?

Recently I read the following:  NBA teams in the top 10 of payroll for the past two years have all made the playoffs, and thus the author concludes that the following teams will make the playoffs this year:  Nets, Knicks, Heat, Bulls, Lakers, Raptors, Clippers, Celtics, Thunder and Pacers.  Others looking at on-court performance have left out some of the teams in the payroll top 10 in their predictions.

So payroll "predicts" ten of the sixteen NBA playoff teams.  I think this would be much more convincing if the top 16 teams in terms of payroll made the playoffs for say ten NBA seasons.  That would give much more credibility to this type of statement.  Since this statement only looks at ten of the possible sixteen playoff spots the prediction is only 62.5% accurate - or leaves 37.5% of the playoffs teams unexplained.  For statisticians this is a large error.

So, what I thought I would do was look at the relationship between NBA (relative) payroll and NBA regular season performance.  To do that I need to get NBA payroll data, which is provided at University of Michigan Professor Rodney Fort's website (direct NBA payroll link) and since I was already there, I used his data for NBA regular season winning percentage (direct NBA winning percentage link) to perform this statistical analysis.

Starting with the 1990-91 NBA regular season and finishing with the most completed NBA regular season (2012-2013), performing a linear regression (controlling for heteroskedastity) on the plus side the statistical analysis results in relative payroll to be positive and statistically significant but on the down side reveals that relative payroll and winning percent have almost 11% of common variation, meaning that relative payroll fails to explain about 90% of regular season winning percentage.  Frankly, that is rather poor if you are using payroll to "predict" performance.  If we take a look at the last two NBA seasons (which one was a lockout season), we see that the relationship between relative payroll and regular season winning percent improves to about 23% using adjusted R-squared.  Again, for the last two seasons (one with a lockout) the variation in relative payroll doesn't even explain a quarter of the variation in NBA team winning percent.

If we use a bigger recent sample (five years which covers the 2008-09 to 2012-13 NBA regular seasons) we see that the amount of variation in common between relative payroll and regular season winning percent is still about 23%.  Taking the five years before that (2003-04 to 2007-08 seasons) things are vastly different.  Relative Payroll is statistically insignificant, or in other words, statistically has ZERO impact on winning percent.  Even if you can overlook that the amount of variation in common between the two is 1%.  Hence the relationship between relative payroll and winning percent has improved in the past five years as compared to the previous five year period.  Again, to me not that convincing of a relationship.

As always, the proof is in the pudding - so I will come back to this at the end of the 2013-14 NBA regular season, let's take a look at how well payroll relates to getting into the NBA playoffs.

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%.