An Arbitration Compensation Update

Yesterday, I released a study of the average compensation that players who qualify for Super Two arbitration receive in their pre-free-agency years. Today, I’m replicating the same study for players who reached standard arbitration. This should help add numerical context to the negotiations between the league and the MLBPA around pre-free-agency compensation – though those negotiations aren’t going well at the moment.

As a reminder, I’m looking at the production and subsequent-year salaries of every player since 2013 to establish a rule of thumb for what players can expect to receive in arbitration given their production in the preceding year. The methodology will follow, but first, here’s the high-level summary of what players have received based on their service time, position, and production:

This table displays the amount of money a given player should make above the minimum salary based on who they are and what they did. Just as with the Super Two numbers, this broadly makes sense – players receive less per unit of production than they would in free agency, but their compensation gets close and closer to free agency levels (roughly $6.5 million above minimum salary per WAR) as they go further into arbitration.

The sample for this study is every player who reached arbitration eligibility starting in the 2013 season, the first year of the current arbitration system. To compile this database, I took each player’s cumulative service time and days of time accrued in each year, which gave me a list of first-time-eligible players in each year. I manually removed international free agents who bypassed the arbitration process. I then compiled each player’s WAR and position in each of their three years of arbitration, as well as their salary in the following year. If you’ll permit me a quick moment to vent, wow was this a lot of data to clean and collate, and I’m not planning on doing another project like this anytime soon.

As an example of how these calculations work, consider Lorenzo Cain. He reached arbitration eligibility in the 2014-15 offseason. His previous season, 2014, had been solid, to the tune of 4.4 WAR. He and the Royals agreed on a salary of $2.725 million, avoiding an arbitration hearing. The next season, he broke out with a 6.1 WAR performance and settled with the Royals again, this time for a salary of $6.425 million. After reaching that deal, however, he signed a two-year extension with the team that replaced that salary with $6.5 million in 2016 and $11 million in 2017.

Whether a player went through arbitration each time, settled to avoid it, signed a multi-year extension, or was non-tendered and signed with another team, I recorded the salary they received in their first, second, and third years of arbitration eligibility. Contracts signed outside the arbitration process nonetheless give us information about how players who enter the process are compensated. Cain’s extension was available to him because he was a star performer who stood to receive a handsome arbitration award.

In the same fashion, players who were non-tendered and signed deals for less than they likely would have made in arbitration are part of the set of players who reach arbitration eligibility. Both of these groups – as well as the core group of players who proceed year-to-year through arbitration – are part of the full accounting of what a player can expect to receive based on his previous production.

For each group of players (batters, starters, and relievers), this approach gave me three years of paired seasonal WAR and subsequent seasonal salary. From there, I engaged in two transformations. First, I considered all WAR totals below zero as being zero-WAR seasons. Teams can’t pay negative dollars for negative contributions, so if we’re considering a dollars-per-WAR framework, we need to deal in non-negative numbers.

Next, I subtracted the league minimum from each salary. If a player accrues 0.5 WAR and receives the league minimum ($507,500 in the first season of this study and increasing thereafter), it would be incorrect to say that a team was willing to pay roughly $1 million per accrued WAR. They were willing to pay the minimum – the same thing they’d have to pay for a player who accrued 0 WAR, or -2 WAR, or so on. Thus, each player’s season and subsequent salary can be turned into a ratio: dollars above the minimum salary per positive WAR accrued.

By summing across an entire cohort, I also produced that ratio for the position as a whole. In the charts above, for example, position players going through their third year of arbitration were paid, on average, $3.59 million per positive WAR they accrued in the previous year.

I considered using a player’s total career WAR and previous compensation as an additional input, but decided against it. It’s a useful component for individual awards, and if I were projecting each individual payout like MLB Trade Rumors does, I’d include those details. I think it’s less useful, however, when looking at the aggregate population. We simply want to know the total amount of positive WAR a class accrues, and what teams pay for it. For broad averages, I prefer a more straightforward approach. Heck, for individual players, WAR is the wrong statistic to use – arbitration payouts depend heavily on traditional statistics. If we’re considering the league as a whole, however, I find it important to know how much WAR the group we’re looking at accrued, and how much teams paid for it in arbitration.

Some other methodological details: all of these salaries were paid in the past. To account for this, I assumed a steady 2% inflation rate. I considered varying the rate by CPI or PCE, using overall major league revenues, or using overall league salaries. None of these meaningfully changed the conclusion, and a static rate comes closest to matching actual arbitration awards, so I stuck with that.

For players who haven’t yet completed all three years of arbitration, I used data up until the 2020 season (and 2020-21 offseason). For players who accrued WAR in 2020, I scaled up their performance to a 162-game season. For players who stopped playing in the major leagues before reaching their final year of arbitration, I used every year where they signed a major league contract. I removed pitchers who went through arbitration in a season where they didn’t appear in the majors, mostly those recovering from elbow surgery.

Conclusions
Position players and starting pitchers were compensated roughly equally. Relievers earned a higher salary per accrued WAR. That’s consistent with free agency and Super Two arbitration. For every player type, more years in arbitration meant a higher salary the next year, even for the same accrued WAR – consistent with the aims of the arbitration process and also previous estimations of arbitration payouts.

In each case, players who were eligible for Super Two arbitration did better than their regular-arb counterparts in every year of team control (there’s one exception — relievers hitting arbitration for the second time — but I believe that’s a sample size artifact). Here’s that data in one chart, with Year One as the final pre-arb year for players in the regular system and the first year of arbitration for Super Two players:

When considering the economic impact of changing arbitration eligibility, understanding this data is crucial. For example, we calculated yesterday that an expanded Super Two class would result in $110 million in arbitration awards in 2021 for players with two or more years of service time. In addition, it would increase payouts for the players who in reality hit their first year of arbitration this year but would be in their second time through the process if the new rules applied to them. That would result in roughly $60 million more in aggregate salary if the payout multipliers held. Similarly, players going through their second year of arbitration (which would be their third in an expanded system) would receive roughly $45 million more in total. Players going through their third year would receive roughly $15 million more. That’s an aggregate $120 million in expanded arbitration salaries if every player qualified for Super Two – though the union’s proposals haven’t been quite so sweeping.

The upshot of all of this? The salary arbitration process pays players less than they would receive on the open market, but it converges on that value as players get closer to free agency. Position players and starting pitchers get paid roughly equally for their WAR contributions, while reliever are paid at a higher rate but accrue less WAR on average. There’s no guarantee that arbitration will look the same in the future, but if you’re wondering what a player should expect to receive in arbitration, or what a team should expect to pay its young, productive players, this is a good starting point.