In 1975, Billy Sims was recruited to the University of Oklahoma by Barry Switzer. After injuries kept him out of the line-up for most of his freshman and half of his sophomore seasons (rushing for only 545 yards in two seasons plus one game of 1976), in his junior season he cut loose, picking up 1,762 yards on 231 carries for an amazing average of 7.6 yards per carry (160.1 yards and 10.9 points per-game) for the regular season. Including the post-season Sims had 1,896 yards, a total yardage school record that stood until 2004 when freshman Adrian Peterson tallied up 1,925. In 1978 Sims became the sixth junior to win the coveted Heisman Memorial Trophy Award was awarded the Heisman Trophy. He was runner up the following season in 1979. He led the nation in rushing with 1,896 yards and had 22 touchdowns. He also became the first running back in Big 8 Conference (now merged to form the Big 12 Conference) history to rush for 200-yards in three consecutive games, and had four 200-yard games in a single season.
After losing to the University of Arkansas 31-6 in 1978, Sims led the Sooners to two consecutive Orange Bowl titles in three straight appearances. In the Orange Bowl following the 1978 season, he scored two touchdowns in a 31-24 win over the University of Nebraska. In 1979 against then-unbeaten Nebraska, who had the No. 1 rushing defense in the country at the time, Sims ran for 247 yards and helped the Sooners to a 17-14 win. In his final game as a Sooner, he helped defeat Florida State University, 24-7, rushing for 164 yards. He ended his career at OU with 3,813 yards; most of those yards came in his final two seasons.
For only the second time in Heisman history, the winner had fewer first place votes than the second place finisher. Oklahoma's Billy Sims had 12 fewer first place votes than Penn State quarterback Chuck Fusina but built a big final total with a strong showing in second place ballots.