[2] Walker batted left-handed and threw right-handed; he stood 6 feet 2 inches (1.88 m) tall and weighed 175 pounds (79 kg).

[3] "Harry the Hat" got his nickname from his habit during at-bats of continually adjusting his cap between pitches[2]—there were no batting helmets in his day.

In the decisive seventh game against the Boston Red Sox, with Enos Slaughter on first base, Walker doubled to left center and Slaughter, running on the pitch and taking advantage of a slow relay from the Red Sox' Johnny Pesky, scored from first base in a "mad dash" with the winning run.

After piloting the Jacksonville Suns to the 1964 International League pennant, Walker was hired[7] by the Pittsburgh Pirates as manager, replacing Danny Murtaugh, who stepped down for health reasons.

The Pirates battled for the pennant until the closing days of the 1965 and 1966 seasons—each year finishing third behind the champion Los Angeles Dodgers and the runner-up San Francisco Giants.

But when the 1967 Pirates—further strengthened by an off-season trade for standout shortstop Maury Wills—stumbled to a disappointing .500 mark in mid-season, Walker was let go on July 18 in favor of his predecessor, Murtaugh.

The last-place 1968 Astros were only 23–38 under Hatton, but, featuring players like Joe Morgan, Jimmy Wynn, and Don Wilson, their record under Walker improved to 49–52.

"[13] Walker's uniform number 32 has been retired by the UAB baseball program, and he was inducted to the Alabama Sports Hall of Fame in 1978.