 After pitching for the Padres for a year and a half, Stoddard was traded to the New York Yankees on July 9, 1986 for Ed Whitson who had famously fought with Yankees Manager Billy Martin.Stoddard served mainly as a Yankee setup man for closer Dave Righetti.While pitching against the then-California Angels (today the Los Angeles Angels of Anaheim) on September 5, 1987, Stoddard gave up the first-ever "broken bat" home run to Jack Howell.