He played in Major League Baseball (MLB) for the Boston Red Sox and Oakland Athletics in parts of six seasons spanning 1978–1984, primarily as a reserve outfielder.

He was drafted again in the secondary phases of 1973, 1974 and 1975 by the Cleveland Indians, Rangers and California Angels, respectively, but did not signed and remained in school.

He finally was signed when the Indians made him the number seventeen overall selection of the 1976 MLB Draft's January secondary phase.

Hancock then batted .294 with a career-high 21 home runs at Pawtucket in 1982, and was called up to the majors again late in September.

That winter, he was traded by Boston along with third baseman Carney Lansford and a minor leaguer to Oakland for outfielder Tony Armas and catcher Jeff Newman.