Being a die-hard Red Sox fan, January is a slow time of year. It is the middle of the off-season and spring training is still over a month away. The only thing baseball has going on at this time of year is free agency.

Slow does not mean we can’t have some fun though. As players sign the big bucks with teams, it seemed suitable to me to take an economic look at a few signed-player’s new contracts to see what teams are over (or under) spending.

To do this, I will be breaking out an old paper I wrote in my labor economics class at Penn State (thanks Wootenomics). The premise of the paper was to apply some of the economic methods behind GM Billy Beane’s moneyball Oakland A’s of the early 2000’s, to look at various teams’ expected revenues, and their player’s expected salaries, through the lens a few key statistics. The point was to evaluate what businesses (the teams) are spending on their employees (the players), and whether or not the employees’ past performances warranted the pay they would be receiving.

Before diving into the methodology of the paper that I will be using here, I must give due credit to the economists who did the original research that I based my paper off of: Benjamin Morris; Tobias Moskowitz and L. Jon Wertheim; and Jahn K. Hakes and Raymond D. Sauer. I will be using these wise men’s techniques to perform my player evaluations in this post.

**A Little Moneyball Overview**

To give a little backstory, this whole “moneyball” idea started in the early 2000’s when Billy Beane was managing Oakland Athletics. The term “moneyball” itself came from Michael Lewis’s book of the same name that gave a synopsis of Beane’s tactics.

The A’s were a very low budget team at the time, and Beane needed a way to get players in a cost effective way. Since Beane could not afford to pay the players with big home run stats and RBI numbers, he began researching other performance metrics that may allow for quality players to be attained for less money.

Beane basically came to the realization that the major statistics being used to analyze hitters at the time (home runs, RBI’s, stolen bases) were not reflective of their actual contribution to the team. Taking a much more analytical approach, Beane began focusing on statistics that he believed were more reflective of a hitter’s contributions to the team (on base percentage, slugging). Many batters who had a high OBP, for instance, were cheaper than many big ticket players with high home run numbers, since this was not a highly valued statistic at the time.

The approach worked extremely well. Since 2000, the A’s have had the 6th lowest payroll and the 5th highest winning percentage. They have had comparable win totals to teams like the Red Sox, who have spent three times as much on their payroll.

**Methods**

Before evaluating any players, let me lay out my methods.

Economists Hakes and Sauer, who I mentioned above, took a purely economical approach to analyzing Beane’s methods in their moneyball hypothesis paper. Their research found that on base percentage is the most important statistic for gauging performance (like Beane found), followed by slugging percentage. Using this, they created the following index for hitter’s performance: 100*[2(OBP)+SLG].

In my original paper, I used this index for entire teams to compare overall team performance. I then used team revenues to estimate how much more revenue a team should expect to get for an increase of one point to their overall index (i.e. their marginal revenue). I found that for every increase of 1 point to a team’s performance index, their revenue is estimated to rise by $2,701,639.89.

By this logic, if a team is expected to earn $2,701,639.89 for each increase of 1 point to their index, then players should be paid $2,701,639.89 for each 1 point they add to a team’s index if this is a competitive market.

How do we know how much a player contributes to a team? We compare their performance index to that of a “Mendoza player” according to Tobias Moskowitz and L. Jon Wertheim. This is a player that a team can essentially sign no matter what at the minimum $535,000 salary. A “Mendoza player” has a 0.200 batting average, a 0.250 on base percentage, and a 0.300 slugging.

By subtracting a “Mendoza” index from a player’s index, we can determine how much that player contributes to the team (their marginal product). The marginal revenue product is then found by multiplying this contribution by $2,701,639.89, since this is the player’s expected revenue contribution. Since the price paid should equal the marginal revenue product, a player’s expected salary is equal to this number plus $535,000, since every player must be paid at least that much.

Now that the methods are laid out, let’s see if some batters’ new contracts are reflective of their performances from the 2018 season.

**2018-2019 Free Agent Hitters: Over or Under Paid?**

Since the index only applies to hitters, they are the only players I will be looking at. I will also only be examining new free agent contracts that have been signed since the end of the 2018 season. This narrows the list down to about 30 players. Free agent’s new contract details were retrieved from Spotrac.com and player’s statistics were retrieved from baseball-reference.com.

Let’s start with the highest paying contract signed so far: Josh Donaldson. His new contract has him being paid $23 million per year. This contact is a quite interesting if you only consider stats from 2018. He played only 52 games total over the course of the season, with and an OBP of 0.352 and a slugging percentage of 0.449. These are only 0.34 and 0.40 above average, respectively, yet his salary is $19 million above the $4 million league average.

As you may assume, his expected salary is far lower than his $23 million contract, at just over $10 million per year.

How about the other end of the spectrum? The smallest contract signed so far has been $550,000 by Troy Tulowitzki, nearly at the league minimum. Remember that “Mendoza player” who you can expect to get for the $536,000 minimum? The stats for a “Mendoza” are a 0.250 on-base and a 0.300 slugging. Did Troy get these numbers in 2018? He was actually well above them, with a 0.300 on-base and a 0.378 slugging.

His contract is in fact estimated to be under-valuing him. His expected pay based on his stats is just over $5.3 million.

So the highest paid player is over-paid, and the lowest paid player is under-paid. As it turns out, this is a common trend for all of the free agent batters in 2019. Table 1 below shows the difference between the players’ new salaries and their expected pays based on the performance index, sorted from the highest 2019 salary to the lowest. Positive values indicate the player is being over-paid, while negative indicates under-paid.

There is a clear trend can be seen.

One reason for this may comes from the valuation of years prior to 2018 in the contract negotiations. For instance, Josh Donaldson was an all-star 3 years in a row (from 2014-16) and won the 2015 AL MVP award. He has shown value in the past, which helps teams look past his poor numbers from 2018.

Another major contributor to this pay discrepancy may be that teams simply still are not valuing the correct stats. Yasmani Grandal did not surpass a 0.350 on-base from 2016-18, but he hit over 20 home runs for each of those years. His 2019 salary is $18.25 million, about $11 million over his expected salary. Andrew McCutchen is another player being over valued, specifically by $6.5 million. Like Grandal, he surpassed 20 home runs in 2018.

This occurs on the other end of the spectrum as well. Daniel Descalso is being paid $7.2 million below his expected salary. Part of this may be from his 0 stolen bases and 0.238 batting average in 2018. But despite these low stats, his on-base was in fact **higher** than our $23 million Donaldson’s.

Clearly, the moneyball successes have not penetrated all areas of the league.

**Final Remarks**

As with most things related to economics, this is not a perfect analysis. Many other factors about a player need to be looked at aside from these two statistics. For example, my analysis has Lonnie Chisenhall as the most under-valued player out of the whole bunch. His stats were quality, but he played less than 30 games for the whole year, which surely contributed to his low salary.

However, the big picture still stands. If teams took a purely economical approach to their “employee” spending, some budgets may shrink a considerable amount over time.

At the end of the day though, the MLB is a sports league and not a cut throat financial firm. Costs are not as much of a concern. Looking back on Beane’s strategies with the A’s, however, some lower budget teams may be surprised by how competitive they could be with a little more economic reasoning sprinkled into their payroll decision.