Moses batted and threw left-handed, stood 5 feet 10 inches (1.78 m) tall and weighed 160 pounds (73 kg).

He is the only player in Major League Baseball history to accomplish a "walk off steal of home" more than once, which he did twice.

Prior to the 1940 season, he missed the opportunity to play for a World Series team, when his trade to the Detroit Tigers for Benny McCoy was nullified by Baseball Commissioner Kenesaw Mountain Landis.

But in 1943, with the Chicago White Sox, he posted a career-high 56 stolen bases and co-led the American League in triples (12).

Immediately following his playing career, Moses became a coach for the Athletics from 1952 to 1954, the A's final three seasons in Philadelphia.

He then moved to the Philadelphia Phillies (1955–58), Cincinnati Reds (1959–60), New York Yankees (1961–62; 1966) and Detroit Tigers (1967–70), serving as both a first base coach and hitting instructor.