here is a paragraph from the baseball rules arbitration.
They do not have the latitude to split the difference.
How does salary arbitration work?
The process is what is known as "Final Offer Arbitration" (though in the world of alternative dispute resolution it is now becoming known simply as "Baseball Arbitration"). In mid-January, each side to the dispute submits a salary figure to a panel of independent arbitrators. After a few hours of hearings, held in early February, the arbitrators pick one figure or the other. The arbitrator cannot "split the baby" and settle on a salary in the middle of the spread between the club's figure and the player's. One side leaves the arbitration a winner and the other a loser, heightening risk and encouraging negotiation and settlement.
This is the critical element of baseball arbitration: it is designed to produce a settlement, not a verdict