Craft attended Mississippi College, threw and batted right-handed, stood 6 feet 1 inch (1.85 m) tall and weighed 185 pounds (84 kg).

Earlier, he managed the Kansas City Athletics (August 6, 1957–1959) and he was the "head coach" of the Chicago Cubs (April 26–May 10 and June 2–4, 1961).

On June 15 of that year, Craft caught the ninth-inning pop fly (batted by Leo Durocher) to make the final out in the historic game that gave Johnny Vander Meer his second consecutive no-hitter.

That same season, Craft batted a solid .270 as the Reds' everyday center fielder with 15 home runs and 83 RBIs in 151 games.

In six seasons, Craft had an all-time .253 batting average with 533 hits, 85 doubles, 25 triples, 44 home runs and 267 RBIs.

[1] Eventually, Craft progressed to the Triple-A level with the Kansas City Blues of the American Association in 1953–1954.

[1] Craft would also manage Roger Maris at the Major League level in 1958–1959 with the Kansas City Athletics, just before the young right fielder was traded to the Yankees.

During 1961, Craft briefly returned to managing in the minors for the Triple-A Houston Buffs of the American Association.

[4] His first team, the 1962 Colt .45s, finished eighth in the ten-team league, but six full games ahead of the ninth-place Cubs, then in their 87th year in the NL.

He remained in the game, however, as a scout and farm system official for the Baltimore Orioles, San Francisco Giants and the Yankees, retiring in 1991.