Ain’t No Athlete Worth $400 Million

John B. Moore

What do you think about the high salaries being paid to elite athletes in all major sports? Major League Baseball (MLB) recently announced that Mike Trout, centerfielder for the Los Angeles Angels has signed a contract extension that will pay him $436 million over the next 12 years. Numerous National Football League players will have 2019 salaries over $20 million. Several National Basketball League players’ salaries will exceed $30 million in the 2019–2020 season. The Argentinian soccer player Lionel Messi took home $84 million in salary and winnings last year.

Are These Athletes Paid Too Much?

The debate centers around three different perspectives — the moral issue, the free-market issue and the logical issue.

The Moral Argument

Moral issues focus on whether paying an individual a large salary for playing a game is justified in a world where there is much good that could be achieved by using that amount of money to reduce poverty, improve health or fight climate change.

An example. A Major League pitcher with a $30 million salary is paid approximately $10,000 every time he throws the ball to the plate (assuming 100 pitches in each of 30 games). This means 2 pitches could lift a family out of poverty for a year. Or, this annual salary could feed 329,000 children in Africa for a year (25 cents per child per day). The salary could also build 3,500 schools in a third world country ($8,500 per school).

Many persons believe that benefits to society such as these are far more important than the benefit to one individual. The moral high-ground is defended by those who strongly believe the tenet “I am my brother’s keeper”. On the other hand, what is the value of the enjoyment of fans who participate vicariously in the performance of elite athletes?

Persons who believe in the brother’s keeper argument to a lesser extent argue that each person has the right to choose his or her degree of altruism. They believe that making donations to charitable activities is for others and not for them. Many highly-paid athletes do distribute large amounts of money and time to charitable organizations and are frequently recognized for their community service and philanthropy.

The Free-Market Argument

High salaries can be justified using one of the foundations of economic theory, namely, the law of supply and demand. This “law” simply says that in a free, uncontrolled and open market that the price of a product or service will adjust to balance supply and demand. Consider the case of salary contracts:

1. The contract between an athlete and an organization is like all other contracts in a market-based economy. It is simply a legally-binding agreement between a buyer and a seller to exchange perceived values. Either party is free to walk away without an agreement.

2. The terms of the contract should not violate any laws that are applicable.

3. No public funds or commitments are required to fulfill the contract.

Player unions would argue that employment in professional sports leagues is not a true free market. They would argue that there is collusion among franchise owners to keep salaries low; that there are limits on the time a player must play at the league minimum salary and time before a player can become a “free agent” and able to negotiate the best deal possible.

The counter argument is of course “If you don’t like it, don’t play”. Nonetheless, when it comes to signing a salary contract — free agent or not — either party is free to walk away.

The Logical Argument

What is the business case for paying an athlete tens of millions of dollars per year? In the diagram below, what is in the Black Box?

There are two inputs — demonstrated performance and intangibles. The intangibles include experience, star power, injuries, trends, attitude, and other subjective factors. On the other hand, quantitative factors are numerous. The field of sports analytics has exploded in recent years. For instance, Statcast captures a terabyte (1,000 gigabytes) of data about each Major League Baseball game. Much of that information helps to improve player skills. Other data about game situations is used to improve game strategies and in-game decision making.

How do you convert a player’s performance data to a fair salary? Performance measures differ from sport-to-sport. Baseball will be used as an example. There are two major strategies — Wins Against Replacement (WAR) and RunPlusMinus. A detailed comparison can be found in the Medium article here.

Neither approach uses a menu of prices such as “A strikeout is worth $X; a Home Run is worth $Y, etc. Because the object in every game is to score more runs than the opponent, both methods start by measuring a player’s contribution in terms of how many runs — real and potential — his team is better off by his participation in a play. The difference between this run contribution value and an average player’s run contribution in the same situation is the basis for ranking players and calculating fair salaries. However, there are some major differences in the two approaches. Specifically:

Wins Above Replacement (WAR): different implementations exist but have similar approaches.
The formulas used for offensive and defensive players are different.

• A runs-above-average (RAA) value is calculated for each player using historical data and standard statistical methods; formula inputs are aggregate values and not at the play-by-play level
• The RAA value is modified by incorporating the RAA value of a minor league player that could replace the given player
• Assuming an average of 10 runs produce a win, a player’s WAR value = RAA / 10
• The WAR value is converted to a salary assuming 1 win is worth $10 million

RunPlusMinus: (a more detailed explanation can be found here)

• Calculates the better-off-than-average run contribution for every player involved in every play in every game
• These tiny run contributions are added to get a player’s total run contribution
• A player’s fair salary is the fraction of the total salary pool justified by his run contribution

Example using Mike Trout: Los Angeles Angels Centerfielder

Using WAR methodology. Baseball Prospect forecasts that Mike Trout’ total WAR value over the 12 seasons covered by his contract extension will be 44.5 wins which would justify a salary of $430 million or an average annual salary of $36 million.

Using RunPlusMinus Methodology. Unlike WAR, RunPlusMinus calculates the justified salary based on the total of a player’s batting, running, pitching and fielding run-contributions in a given season. In 2018, Trout, a non-pitcher, ranked 1st in batting and running and 3rd in fielding on his team. Combined, this justified a team salary of $23 million. His actual salary was $34 million. In spite of his outstanding performance the Angels ranked 17th in wins in 2018 primarily because the team’s average player rating was 15th out of 30 teams. These results suggest that winning depends more on the average ability of team players than on the existence of a super star. This is not surprising since in MLB baseball, the super star is only one player out of 25.

Note. Many MLB players with fewer than 3 year’s experience justify salaries above the league minimum based on their performance. However, league rules limit their salaries to the league minimum of $545 thousand. This gives team owners wiggle room to overpay top players who are free agents or about-to-become free agents without jeopardizing a team’s profitability.

Summary

• Salaries paid to professional athletes are often viewed as excessive.
• Arguments whether the high salaries are justified fall into three groups: moral arguments, free-enterprise principles and performance analyses.
• RunPlusMinus and Wins Above Replacement take different approaches to calculating salaries that are justified by historical player performances.
• As with every freely-negotiated contract, the result may be a good deal for only one party or a win-win for both.
• Justified salaries for players on a team are team-dependent because they depend on the business goals of the team owner and the team’s payroll budget. Justified league-wide salaries are smaller for elite players and have a narrower distribution.

Author Note

John B. Moore has been a Professor of Management Sciences at the University of Waterloo and is a co-founder of RunPlusMinus Inc. His email is jbmsavvy@gmail.com