A gifted all-around athlete, Allison attended the University of Kansas for two years and was a star outfielder on the baseball team and fullback on the football team. In his Major League career, he hit 30 or more home runs three times and 20 or more in eight different seasons. Although he struck out often like many sluggers, reaching the century mark in strikeouts in five seasons, he received more than his share of walks and despite a mediocre career .255 batting average, Allison finished with a lifetime on-base percentage (OBP) of .358 and he finished in the top 10 in OBP in four seasons. Allison wasn't an especially fast player, but he was among the most feared base-runners of his time in hustling out numerous doubles and triples – leading the league in triples in 1959 (with 9) and finishing in the top 10 twice in doubles (1960 & 1964) and four times in triples (1959, 1962, 1967, and 1968).