What Would You be Paid Without Antitrust Law?

The U.S. Supreme Court exempted Major League Baseball from the Sherman Antitrust Act. As a result, debuting players are still precluded from switching teams, rendering owners de facto monopsonies. By how much does this lower wages? Using a quasi-random discontinuity in the rule determining eligibility for Arbitration, by which a third party determines the player's wage to a level commensurate with his market value, this exemption is found to have lowered wages by at least 32% compared to its market rate.