After twice playing in the Indiana high school final four at Central High School, the 6-foot-1 Schaefer continued his career at Indiana University where he lettered from 1939 to 1941. During the 1939-1940 season, Schaefer helped IU win its first national championship, beating Kansas 60-42. Schaefer was IU’s leading scorer in the tournament, including scoring nine points in the title game. He was an all-American selection as a senior in 1941, and later helped the Minneapolis Lakers win the first NBA title in 1949, becoming the first player to win both an NCAA and NBA championship.