Legend has it that University of Texas football coach Clyde Littlefield first heard of Stafford when assistant Shorty Alderson announced "Clyde, I found you the darndest football player you ever saw. He tore up a couple of dummies and hurt a couple of men. He says his name is Harrison Stafford." Stafford, a native of Wharton, would soon acquaint himself with the rest of the SWC in 1930: the first of three consecutive All-SWC seasons for the 6'0,185 pound halfback. Former Texas Longhorn teammate Wilson "Bull" Elkins recalled, "Harrison was the only person I ever saw who hurt himself blocking. He blocked with his head a great deal, but he had absolutely perfect timing. He was the best blocker I've ever seen." Stafford, along with "Bull" Elkins, Ernie Koy and Dexter Shelley, led the Longhorns to an 8-1 record and the 1930 SWC Championship. In 1969 Stafford was elected to the All-Time Southwest Conference Team. He is a member of the College Football Hall of Fame (1975) and was inducted into the Texas Sports Hall of Fame in 1976.