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Tommy Bennett tried to determine how teams and players come up with the arbitration figures they exchange in the piece reprinted below, which was originally published as an "Expanded Horizons" column on February 2, 2010.

Arbitration avoidance is in full swing as we enter the month of February. Forty-four players have exchanged salary figures with their clubs. Of those, all but 18 have reached deals avoiding arbitration, which begins in approximately two weeks. Most of the remaining 18 will also reach deals. Perhaps a handful will proceed to arbitration. This year's most interesting case is Tim Lincecum, a Super Two player who is set to go to his arbitration hearing armed with two Cy Young awards. The gap between the salary Lincecum is seeking ($13 million) and what the Giants have submitted ($8 million) is the largest for any player this year. It's worth wondering, as a sharp reader did during my first BP chat, how teams and players come up with the numbers they exchange.

Tug of War or Rubber Band?
There are two forces that shape both parties' decisions in the arbitration process. First, teams and players recognize that most cases settle before reaching arbitration, and that most cases settle at or near the midpoint between the player figure and the team figure. However, the two sides also must grapple with the small but real possibility that they do not reach a deal and the case goes before a three-person arbitration panel. Although the percentage of cases that proceed to a hearing is small (just three of the 45 non-free-agent cases in 2009), the structure of the arbitration process looms large. It is unclear whether there are any general trends that dictate which cases go all the way to arbitration (for example, whether such cases adhere to the Priest-Klein selection hypothesis), although this remains a question of interest for me.

The vast majority of arbitration-eligible players agree to deals that avoid hearings. Often, hearings create bad feelings that carry over into the season. Furthermore, the process is expensive and time-consuming. For both sides involved in the process, it is usually easiest to agree to a deal that is exactly at the midpoint. For example, in 2009, the (unweighted) average settlement was 46 percent of the difference between the two numbers. In other words, the average settlement was very close to the midpoint, and it slightly favored teams. So far this year, the corresponding figure has been 44 percent, perhaps reflecting weaker overall demand. Nevertheless, by far the most common single settlement percentage is 50 percent. Here is a simple table showing the settlement percentages for 2009. Zero represents the team figure and 100-percent represents the player figure:

 Percentage       Cases
of Difference    Settled
    0-25            2
   26-35            3
   36-45            6
   46-55           16
   56-65            3
   66-75            0
   76-100           1

Here is a similar table for this year:

 Percentage       Cases
of Difference    Settled
    0-25            0
   26-35            1
   36-45            9
   46-55            6
   56-65            0
   66-75            0
   76-100           0

Note again here that the distribution appears to favor teams ever so slightly. This is a somewhat odd result that we shall return to later. However, suffice it to say that most of the cases cluster near the midpoint of the two figures.

Incentives to Cheat
This phenomenon gives teams and players a peculiar set of incentives. If, by striking deals at the easy focal point of 50 percent, parties hope to save time and money, they had better hope that the practice doesn't distort incentives. But the possibility exists for it to do just that. For every dollar a team reduces its figure by, the anticipated settlement price declines by fifty cents. Similarly, for each dollar a player increases his figure, his anticipated salary increases by fifty cents.

This set of incentives, if teams and players always settled at the midpoint, would be unstable. Teams would simply offer zero dollars and players would submit exorbitant figures. Of course, this doesn't happen in reality because the parties to the dispute are conscious of the possibility that they will go all the way to the hearing, which is binding. Because of the unique nature of baseball's arbitration rules, the arbitrators may not select any salary figure they like, but rather they must choose either the player figure or the team figure. That is to say, it's an all-or-nothing affair.

What incentives does this create? In fact, it creates exactly the opposite set of incentives from the ones created by the midpoint settlement norm. Each dollar that a club reduces its offer by increases the likelihood that an arbitrator will select its figure. Because the outcome at arbitration is binary, that likelihood is crucial. If one party can appear ever so slightly more reasonable than the other, it wins the whole pie. Of course, the other party seeks to appear yet more reasonable. In essence, the fact that the parties bargain in the shadow of the law means that they are forced toward the middle of the settlement range.

These two forces work against each other. The first, the fact that parties tend to settle at or near the midpoint of the settlement range, pushes their salary figures apart. The second, the structure of baseball's arbitration hearings, pushes the parties back together. However, in individual cases, the parties may miscalculate. If one party is willing to submit a figure very close to the expected salary for the player and the other does not, the party close to expected value may insist on proceeding all the way to a hearing. In that case, the party far from the midpoint may end up holding the bag. I suspect this is what happened with Lincecum. Although his $13-million filing was a record for a player in his first year of eligibility, it is perhaps closer to what he could expect to earn than the number submitted by the Giants. If that is the case, Lincecum may insist on proceeding all the way to a hearing, where his case centered on the two Cy Youngs might carry the day.

Question of the Day
Which of these forces do you think is stronger: the norm of midpoint settlement, or the incentives created by the structure of baseball arbitration? Am I right about Lincecum's salary figure, or are the Giants in fact closer? How likely is a deal at the midpoint ($10.5 million)?

Thank you for reading

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