The 6’7″ Stoddard started at forward for North Carolina State’s 1974 NCAA basketball champions. He was originally signed by the White Sox in 1975, but was released after two minor league seasons. Stoddard reached the ML for good in 1979, posting a 1.71 ERA in 29 appearances for the AL champion Orioles. He had an RBI single in the World Series against the Pirates, the first player ever to drive in a WS run in his very first ML at-bat. In 1980 he led the Orioles with 26 saves. Stoddard shared the Orioles closer role with lefthander Tippy Martinez from 1981 to 1983, but in 1983 his ERA was 6.09, and he was traded twice before the 1984 season, first to Oakland and then to the Cubs. Stoddard won 10 games and saved 7 in his one season with the Cubs, then signed with the Padres in 1985, and was traded to the Yankees for Ed Whitson in July 1986. In New York, Stoddard was mostly a set-up man for Dave Righetti, and was released in August 1988 with a 6.38 ERA. Stoddard never started a game in 12 ML seasons.
