Are Players Affected Negatively by Arbitration?

There is a hypothesis out there that players perform worse in the season following their arbitration hearing. I wanted to see if there was any truth to this, because there are huge financial and performance implications, if true.

Overview

Arbitration is a strange process and I would say that it is likely to change more in the next few years than it has in the past decade due to the new CBA coming in 2021. From an organization’s standpoint, they are constantly trying to maximize their wins per dollars spent. From a player’s standpoint, they obviously want to be paid as much as possible. Some would argue that the entire system is flawed because it prevents players from being paid their market value, in addition to being evaluated on outdated metrics. Teams (and the firms they outsource the cases to) essentially try to paint a picture as to why a player is worth the least amount as possible. For some players, this can be a psychological battle and that is where the hypothesis comes into play: do the players who go through arbitration hearings play worse the following season as a result of the bashing?

Process to Find Out

This is a difficult question to answer because there is no way to truly know if a player performed worse than he otherwise would have have, much less solely due to the arbitration process. I decided to base how the players are expected to perform using the Steamer Projection system.

Steamer unfortunately has its limitations. For one, they only have preseason projections dating back to the 2010 season. The most complete dataset on arbitration numbers dates back to 2011. While my dataset is somewhat small, I will present what I found from the 2011-2019 seasons.

For position players, I based their season performance on wRAA. Initially I was planning on using WAR, but Steamer does not provide all of the needed components. For pitchers, I based their performance on FIP.

In order to prevent a consistent bias if, for example, Steamer wRAA projections were higher than actual performance 100% of the time, I averaged out the error for each season and added that back to the initial projections for each player. This was done for both wRAA and FIP. I only calculated the average error among players who met FanGraphs criteria for “Qualified” because I felt that the players below that threshold would create too much variance for not being expected to play on a regular basis. Additionally, I normalized the data so that players would not be negatively affected by less plate appearances or innings pitched compared to their peers. I set a floor of 50 IP’s and 200 PA’s to qualify for comparison.

Results

From 2011-2019, there were 78 arbitration hearings. Of those 78, I removed 9 players who did not meet criteria to be further analyzed (injury, lack of PA’s or IP’s, or no projections made by Steamer). Removing these players could induce some selection bias, as it's possible that they were performing so poorly that they did not get the chance to reach the minimum PA's or IP's to be included. Below are the percentages in which players performed worse than expected.

*I view a 50/50 split among better/worse performance as a strong projection system that is not heavily skewed in one direction or another. This would make the 2012 pitcher projections inaccurate. All other years performed pretty well.

Comparatively speaking, this chart shows that the hypothesis of players performing worse in years following arbitration hearings is potentially a fallacy. The dotted line at the bottom (44%) represents the constant average percentage of players who performed worse during the time frame of 2011-2019. While it would make more sense to use an average annual basis, there was not enough of a sample to make it meaningful from year-to-year. What this data shows is that players actually performed better in years following arbitration hearings as opposed to worse.

Of the 78 hearings, teams won 35 times (45%). Of those 35 times, players performed worse than expected 15 times (43%). This is not supportive of players performing worse following the loss of an arbitration case.

However, I would still not say this is a completely solved question which leads me to limitations of this research.

Limitations

The lazy interpretation of this could be that players are not affected negatively by arbitration. But, there are some additional factors that need to be considered.

With a larger and more accurate dataset, the answer could change. Arbitration hearings first began in 1975, so with a projection system and salary figures dating back to then, we could theoretically get a “better” answer.

One of the other issues with my process is that there are no defensive factors accounted for. This could be problematic for certain positions that hold more defensive value, such as catchers. Is it possible that a catcher could put forth less effort receiving because he feels like the team gipped him in the offseason?

Lastly, even if players do perform worse, it’s hard to imagine it is solely due to arbitration and not other factors. If anything, it would seem to me that they should be more motivated to play well and get paid the next offseason.

Implications if True

For sake of argument, say that the expanded dataset with more years and accuracy tells us that players actually do perform worse in the season following arbitration hearings. If that’s the case, we need to determine when it is worth avoiding arbitration to receive higher performance from that player.

The majority of differences in salary presentations between teams and players are within a million dollars. Dollars per WAR are constantly changing and is not exactly linear, but it hovers around $9 million. Depending on exactly how much worse we expect a player to perform, there needs to be consideration for whether or not there is a higher cost of avoiding arbitration or lack of WAR production on a cost basis. Teams should compare their projected wins per dollars spent between avoiding arbitration or settling, and the associated expected performance for each. The current state of the team should play a role, as well. If a team expects to win the following season, it may be worth the extra scratch. Those “wins” left on the table are not worth as much to a rebuilding team.

Future Research

Some ideas for further research:

-Compare performance to players who avoid arbitration.

-Do prospects who get held in minors to avoid service time play worse?

-Team by team comparisons. Maybe some teams are harsher psychologically than others. Do players from the harsh teams perform worse than less-harsh teams?.