A center fielder, and good all-around athlete, Moseby's nickname, "Shaker", was said to stem from his ability to get away from or "shake" players who attempted to defend him on the basketball court.

Despite some growing pains early in his career, Moseby developed into a well-polished batter, fielder, and base-runner, driving in nearly 100 runs in three seasons (1984, 1986, and 1987) and regularly stealing 30-plus bases.

[2] In the mid-1980s, he was part of the powerful "Killer B's" outfield trio for the Jays, playing center field between George Bell and Jesse Barfield.

On April 19, 1983, he hit a walk-off two-run home run against Dan Spillner to give the Blue Jays a 9-7 victory over the Cleveland Indians.

As of 2018, Moseby ranks in the top 10 for Toronto Blue Jays career leaders in WAR, games played, at-bats, runs, hits, doubles, triples, home runs, RBI, walks, stolen bases (franchise leader), and extra-base hits.