He played junior hockey for the Stratford Kroehlers, Hamilton Whizzers, and Hamilton Lloyds from 1943 to 1946. In 1946 he turned pro with the Baltimore Clippers of the Eastern Hockey League. The next year he jumped up to the Providence Reds of the American Hockey League, with whom he spent the better part of five seasons.
The Reds traded Stoddard to the New York Rangers on January 1, 1952, and he played there for a season and a half, scoring 16 goals and 15 assists in 80 games. After that he moved back to the minor pros.