 While pitching for the Padres, on June 18, 1986, Stoddard hit his only career Home Run in what turned out to be his final Major League at bat.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.