Rethinking the Origin and Preservation of Baseball's Antitrust Exemption

Why was Baseball granted an exemption from Section 1 of the Sherman Act, and why did it last in its entirety so long - until the Curt Flood Act of 1998?  On Concurring Opinions, Aaron Zelinsky (who I believe is the first U.S. Supreme Court clerk and Sports Law scholar) has a terrific two-part series (Part 1, Part 2) that addresses the question and also reviews a new book by Stuart Banner on the topic, The Baseball Trust: A History of Baseball's Antitrust Exemption.