# Income Inequality in Professional Sports

It’s no secret that professional athletes have seen massive increases in compensation over the past decade or two. It seems like every offseason we’re breaking down the next record contract to see what absurd amount of money a player is making every day or hour. Our sports franchises have evolved into these tremendous corporations that epitomize American Capitalism. US sports leagues (except MLS) act as their own closed economies with sets of rules and policies designed to maximize output. Since these output maximizing policies are similar to those in a traditional economy, discrepancies among labor wages are bound to happen.

I was curious to see which policies adopted by the different professional sports leagues have led to more disparity in player wages. To do this, I analyzed the salaries of the five biggest American sports leagues in terms of revenue which included the NFL, NBA, MLB, NHL, MLS, as well as the English Premier League for international context.

## League Review

Before I get into any of the data, I wanted to give a brief overview of the source of salary inequities in sports and some strategies used to combat the inequities.

Free Agency

For what has become a standard practice today, free agency was a pivotal moment for professional athletes that didn’t come around until the 1970’s for the MLB, the 1990’s for NFL, NBA, NHL, and 2015 for MLS. Free agency changed the whole framework of labor relations in sports. Before, a player’s value was subject only to the team that drafted or originally signed them but free agency recognized the right for players to sell their labor on the open market to whatever team was willing to pay.

Securing this bargaining power over the owners has dramatically increased the cost of labor. Not only has free agency shifted labor costs onto owners, but it has played an imperative role in undermining competitiveness and exacerbating income inequality in sports.

Free agency is a necessity for the athletes employed, but it also presents an advantage to the franchises bringing in the most revenue. The policies adopted by each league in response to free agency have led to different levels of inequality in player salaries.

Competitive Balance

To combat the unfair advantages derived from free agency, the league committees and player associations of each sport agree on a set of rules and policies for redistributing income among teams. Since sports franchises can make decisions about player compensation that either focus on maximizing wins or maximizing profits, the leagues take it upon themselves to make sure there is a balance between the two.

This idea of competitive balance is crucial for the health and longevity of professional sports leagues. For instance, fans of the home side want to see their team win no matter what, but for the game to be valuable to a neutral observer, an assured level of uncertainty in the outcome is required. This is the foundation of competition and what drives people to spend money on sporting events.

To support competitive balance, sports leagues use similar principles that western economies use such as price ceilings, minimum wage, and revenue sharing. For example, these leagues all have some form of a salary cap that limits the amount a team can spend on its players. They also configure revenue-sharing models where they pool up portions of their revenue and distribute it equally among their teams. Each league uses a different combination of rules to preserve parity between its teams.

This is particularly interesting to me because these rules have a direct impact on the money players make and I wanted to show the effect of each league’s strategy on how income is distribution among players.

## Data Overview

Like I stated before, the main focus of this report is to figure out how much income inequality is present in each professional sports league. I used a variety of statistical measures to determine which leagues had the most disparity in wages which included simple measures like mean, median, and quartile ranges. I also used more intuitive metrics: average variances, variance coefficients, Lorenz curves, and Gini indexes.

I gathered salary numbers from the 2018–2020 seasons on spotrac.com which tracks the salaries and all related info on players and teams. I compiled a list of all the player salaries and transformed them into logarithmic values to account for the skewness.

I excluded players that were not signed for the whole year and had salaries below the minimum to ensure integrity in the results. I used the “average salary” figure which equals the contract value divided by the number of years on the contract. I felt this was the most standardized number across the leagues because the “cash” earned figure is too noisy with some leagues using large upfront signing bonuses. I also didn’t want to use the “cap hit” number because of how different each league’s cap structure is.

Under the average salary figure, all bonuses are prorated across the lifetime of the contract. Additionally, using the average salary eliminates majority of the effects that Covid-19 had on player compensation in each league.

## Analysis

Bar Chart

The first item I wanted to display is a simple clustered bar chart that consist of the mean and median salaries. This gives us an idea of type of money players make in each league.

The first points I noticed were that NBA players get paid remarkably more than any other league and MLS player compensation is far off the pack. We can also see that the average salaries in the MLB and NFL differ greatly to their median salaries while the EPL and NHL show the smallest differences.

I used a straightforward mean-median ratio to quantify how much larger the mean salaries were than the median salaries. The larger the ratio value, the more skewed the mean average becomes by outliers. As we can see above, NFL and MLB salaries are seriously skewed by top earners with their mean average salaries being 3.21 and 2.72 times greater than their median salaries over the last three seasons. The EPL and NHL sit at the bottom of this list with ratios of 1.38 and 1.72 respectively.

Violin Plot

The next way I visualized the data was by creating a violin chart. A violin chart combines a box and whisker plot with a kernel density plot and with this we can look at the mean, median, inner quartile range (IQR), and density distribution of the untransformed salaries from 2020.

The IQR is the width of the box and where all the salaries from the 25th percentile up to 75th percentile land (The middle 50%). The whiskers that extend out from the box indicate the minimum and maximum salaries that are within 1.5 times the IQR on either side. Any salaries that fall outside this range are considered outliers.

The kernel density plot highlights the frequency distribution of the salaries. These are the colored bands that seem to wrap the box and whiskers. For example, if you look at the bottom of these plots you will see the bands extend wider than they do at the top. This is because there are significantly more players making less than $5 million than there are making $40 million.

Insights

- From looking at the box plot we can see that the NFL actually has a mean that sits outside of its IQR. This means that there are players that earn in the top 25% that still make less than the average salary. This is a sure sign of high inequality.
- Given the MLS is a much younger league, it makes sense majority of MLS players sit at the bottom of this distribution. Only 9% of their players make over a million dollars and the nearly 30% make less than $100k. The top earner in the MLS for the 2020 season was Carlos Vela who made $6.3 million.
- We can see that the NHL is relatively equally distributed with half of its players earning around $1–$4.8 million. This is also true for the EPL where a handful of players that make $15+million but 50% of the league makes between $1.4 and $5.4 million.

Lorenz Curve and Gini Index

The Lorenz Curve and Gini index make it easier to visualize and compare varying levels of inequality. The Lorenz Curve shows how income is distributed in a population and compares it to perfect equality.

To create this, we can plot the cumulative percentage of the population on the x-axis and the cumulative percentage share of income made on the y-axis. Perfect equality would be shown on the graph as a linear line where each percentage increase in cumulative population is equal to the same percentage increase in cumulative income earned.

If income was perfectly distributed, 20% of the population would make 20% of the income, 50% of the population would make 50% of the income, and so on.

The Lorenz Curve is a great way to visualize how much inequality exists in a population and even more so where the inequality is happening. Populations with curves that deviate farther away from the line of perfect equality have more apparent inequality. The curves on this graph can also be converted into numbers for a more practical comparison. This is called a Gini Index.

The Gini index is a universal coefficient between 0 and 1 that represents the area between the line of perfect equality and the line plotted from the population’s actual income distribution. Since the plotted lines for populations with high inequality deviate further away from the line of perfect equality, they also have a larger area between them.

Gini indexes closer to 1 indicate higher inequality. This standardized coefficient gives us the ability to make relative comparisons between the leagues. Below are the Gini Indexes of each league for the 2020 season.

The inequality trend continues with this analysis as the MLB and NFL lead the sports leagues in variance and Gini index, both measures of inequality. It’s also no surprise that the NHL and EPL are at the bottom of this list.

In addition to the absolute variance calculations, I used a coefficient of variation(CV) that measures relative variation. The higher the CV, the more dispersion around the mean. With this statistic we can see that the MLS actually had the most average variance on a percentage basis among player salaries over the last three years.

Below is a breakdown of each team’s salary variances in all the leagues. These tables are sorted by the coefficient of variation. The teams with the most variance in player salaries are at the top.

As you might have guessed before, the bigger market teams who spend more money on player salaries have more inequality in their payrolls. This is visualized below with a scatterplot that compares each team’s average salary with their coefficient of variance from the 2020 season.

There is clearly a linear relationship between the two variables, especially in the American leagues. Big market teams with major money players like the Yankees, Warriors, Rams, Galaxy, Penguins, and Manchester City are all the driving forces of income inequality in their respective leagues.

Conclusions:

- Using the mean average is a faulty way to look at how much players make in sports. Using the median salary paints a more accurate picture.
- The MLB is certainly the most inequitable league examined as they ranked first or second in every statistical analysis used to measure income inequality. This is due to their large roster sizes and luxury tax structure. There is no cap to what a team can spend on players but when they do spend over a certain limit, a 20% tax is implemented on all additional money spent. Only a handful of teams have actually paid into the luxury tax system but since the taxing point is set so high and there is no salary floor, the system is fundamentally useless. To give you an example from 2019, the Red Sox spent $165 million on its 25-man payroll as opposed to the Pirates who spent just $30 million. The MLB’s set of policies has led to the most league wide disparity and most income inequality between players.
- The use of a “soft cap” and luxury tax in the NBA has gained them the number one spot for disparity among team performance. Big market teams dominate the league year after year because the soft cap and luxury tax allow them to attract and pay for the best talent. Although the league lacks parity between its teams, its use of high minimum contracts and set maximum contracts has curbed wage inequality slightly more than the NFL and MLB. It’s also important to note that the NBA is one of the most selective leagues in the world with only roughly 450 players. This helps make it the most lucrative sports league in the world, and it’s not even close. Half of their players earn at least $4 million dollars while some make upwards of $40+ million a season.
- The NHL’s use of a ‘hard cap” is a major reason they have the least amount of wage inequality as it sets a strict limit on the amount teams can spend on players. The NHL is the only league that succeeds at limiting wage inequality and sustaining parity among its teams at the same time. I think the NFL’s hard cap does its job in maintaining league wide parity but fails at decreasing wage inequality. However, this could be attributed to the huge roster sizes and the necessary premium put on certain positions like QB, WR, DE, and DT.
- The inequities of the MLS could be attributed to the age and nature of the league. Since soccer in America is so overshadowed by the bigger sports leagues, their business model has adjusted accordingly. MLS owners have it relatively easy actually. The MLS operates as a single entity league which means that even though owners operate their teams, they only own shares of the league and not the individual team. This format has stripped players of bargaining power because they aren’t selling their labor to the highest paying team, but instead whatever the league deems appropriate. This is especially true for American players that lack international potential. Since owners have limited costs and limited motivation to win games, teams will just sign one or two big-named South American or European stars to high value contracts and then field the rest of the team with lower tier South American and American players. This obviously drives income inequality. In fact, Jozy Altidore is the only American player that ranks in the top 30 highest paid players for 2020. Out of 730 players, only 20 players made over $2 million in 2020 and 360 players, or 50% of the league, made less than $200k.
- Since the EPL competes in an international market, they don’t have a salary cap structure. Instead they follow global “financial fair play” rules but they aren’t very strict. They essentially only affect teams that continuously spend significantly more money on player salaries than they make in revenue. I believe the reason for the EPL’s smaller Gini index is similar to the reason why the NFL’s Gini index is larger. This has to do with MRP. MRP is defined as the product of marginal product and marginal revenue (MRP = MP × MR). MP is a measure of how productive a worker is in terms of output, and MR is a measure of the additional revenue generated by each new unit of output. The highest paid players in the EPL tend to be the attacking players that score goals but the premium put on these players is nothing compared to the premium put on a QB or DT in the NFL. This is because it’s much harder to increase your MRP as a forward in soccer than it is as a QB in football or as a PG in basketball where there’s only five on the court. Another reason for the smaller Gini index could be a result of how the league is divided. For decades the EPL has consisted of a “big six” clubs who compete for titles, and then everyone else who just fights relegation. There is a positive correlation between points won and the Gini index (inequality) of team payrolls, but majority of the correlation is driven by these “big six” clubs. So while six teams a year may experience high wage inequality, the rest of the teams find little incentive to sign players to massive contracts. This is a crucial reason for why the variance in salaries of Premier League players is more comparable to those of the NHL.
- If the sports leagues were countries, the MLB would be ranked #1 in the world in terms of income inequality ahead of South Africa. The NFL, MLS, and NBA would be ranked number 3, 5, and 6 ahead of countries like Brazil, Botswana, and Honduras. The NHL and EPL would be just outside the top 20.

Each league has the same goals of maximizing output and profits but they all have different ideas on how to pursue that goal. These decisions that are constantly altered by leagues and player unions have a direct impact on how player salaries get distributed and its clear that inequality has prevailed. Despite the excessive levels of income inequality in sports, one thing is for certain: Play sports if you want to get paid.

Check out the link below to see my interactive PowerBi report where I created all my tables and visuals.