Alfredo began his career as a member of the Cleveland Indians, who signed him as an amateur free agent in 1973. On December 5, 1978, before having played a season in the majors, he was traded along with Phil Lansford (minors) to the Toronto Blue Jays for Victor Cruz. Alfredo made an immediate impact, co-winning the American League Rookie of the Year Award in 1979 with John Castino.
Alfredo won the AL Gold Glove Award for a shortstop in 1985.
Teams include: Cleveland Indians (1976-1978), Toronto Blue Jays (1979-1984, 1992-1993), Oakland Athletics (1985-1987), and Los Angeles Dodgers (1988-1991).