 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.Stoddard was released by the Yankees on August 14, 1988 after posting a 6.38 ERA.Stoddard pitched his final season () with the Cleveland Indians, pitching in 14 games with a 2.95 ERA before being released on July 12, 1989.