Predicting Arbitration Hearings; Was Mookie an Outlier?

Mookie Betts went to an arbitration hearing. Marcus Stroman went to an arbitration hearing. George Springer and Jonathan Schoop did not. Other than the obvious differences between these players, there are others— related to the arbitration process itself— that may have affected these outcomes. Particularly, the differences and qualities of their filings.

To those unfamiliar with the arbitration process, eligible players and teams who are unable to come to a settlement ahead of the given deadline, submit salary filings which reflect either party’s evaluation of the player’s worth. Even after filing, teams and players are able to negotiate a one-year contract, but in some cases, a panel of arbitrators will decide a salary: either the player’s bid or the team’s bid, but not any number in between. This “final-offer arbitration” system is designed to create compromise and negotiation between bargaining parties as the threat of losing a large amount of money increases the incentive to settle early while a midpoint is still available. By extension, teams and players are encouraged to moderate their bids as an outlandish one is surely to be challenged and lost.

But, two different theories exist as to how the difference in bids itself affects the likelihood of hearing. Some argue that higher differences between teams and players in valuation would increase the likelihood of an arbitration hearing as the difference in bids reflects differences in valuation. However, others— namely Carell and Manchise in Negotiator Magazine (2013)— argue that differences in bids increase the risk of heading to a hearing and incentivize teams and players to hammer out a settlement.

Using two separate probability models and data on all players that filed for arbitration between 2011 and 2017, I examined the likelihood that a player goes to an arbitration hearing based on the differences in bids between the player and the team. The models both control for the player performance— by incorporating the effect of WAR— and utilize a dummy-variable for Super-Two status— controlling for the effect of players granted a “bonus year” of arbitration eligibility. The only difference between the two models is the variable of interest. The first uses the ratio of the absolute bid differences to the midpoint between the two salaries in order to measure the effect of a growing gap between filings relative to the actual size of the filings. The latter model separates the two effects to understand whether absolute gaps and absolute filing size have an effect on arbitration hearings. The model specifications and regression results are shown below. The table below essentially shows the marginal effect on likelihood to go to hearing due to a 1 unit change in the corresponding variable.

Model 1:

Model 2:

Results:

 

Both models demonstrate highly significant coefficients indicating that players with large gaps in salary filings are less likely to enter hearings. In fact, in the aggregate sample of players an increase of $100,000 in bid differences reduces the likelihood of a hearing by 2.7% and a 1% increase in Bid Difference to Midpoint Ratio decreases the likelihood of a hearing by 1.1%. This stands as an incredibly significant effect considering only 16.73% of players in the sample even made it to a hearing. Quite evidently, teams and players are incredibly risk-averse and fear losing the arbitration hearing and being forced to agree to a suboptimal salary. Thereby, the incentive to settle is driven up by higher bid differences.

Another interesting result shows that in all samples, an increase in filing midpoint by $100,000 increases hearing likelihood by 0.56%. As such, all else equal, players with higher filing midpoints are more likely to head to a hearing. The intuition behind this is best explained considering this with the negative coefficient on WAR, as both WAR as Midpoint are highly related but have opposite and significant signs. While WAR indicates that better players are less likely to head to a hearing, the positive coefficient on Midpoint states that “better” players are more likely to head to a hearing.

Though these indicate opposite effects, considering the effect of a high midpoint with WAR constant and vice-versa, the theory provides explanatory qualities. A more aggressive salary bid— given an exogenous and fixed level of production— is easier to dispute for a low-value player than a high-value player. Thus, independent of the player’s production level, a higher Midpoint leads to a higher likelihood to enter an arbitration hearing. As such, the positive coefficient on Midpoint likely reflects bad players bargaining for extra money rather than good players— whose effects on hearing likelihood are captured by the WAR coefficient. Considering the WAR coefficient independent of the filing midpoint as well, teams are more likely to focus their negotiation efforts on their better players, thereby reducing the likelihood high WAR players end up in hearing.

The final variable of interest in these regressions is the dummy-control for Super-Two status. As mentioned earlier, Super-Twos represent young players with substantial playing times who are rewarded with an extra year of arbitration eligibility. The models predict that Super-Two status increases the likelihood of hearings by 14.3%-16.9% depending on the model. As such, these young players seem more likely to challenge their teams in salary evaluations. This too comes as no surprise since challenging a team in your first (and bonus) year of arbitration eligibility can lead to significant level effects in subsequent arbitration hearings. A salary increase from the league minimum to $545,000 to even $1M can snowball into much larger raises in the following years with an arbitration victory. As such, these players may have a higher incentive to enter hearings and capture these multiplicative effects.

Now, revisiting the four cases above— Betts, Stroman, Springer, and Schoop— some interesting cases do pop out. Betts may not have been the most likely candidate to head to an arbitration hearing, the $3M difference between Betts and the Red Sox was incredibly high and reflected an enormous risk for either party entering a hearing. The predicted path for Betts was likely closer to George Springer’s contract extension or Jonathan Schoop’s 1-year deal. By contract, Stroman may represent the classic arbitration case, a low-risk hearing for either party, bargaining over a small fraction of their bids. And while Stroman expressed his frustration— or lack thereof— following the hearing, history shows that the Stromans of the world will likely end up there again. Ultimately, the final offer arbitration system does its job: those who disagree significantly tend to work toward compromise, while those who disagree a little take a change and roll the dice.