On November 27, 1962, Baker won the Heisman Trophy for his achievements during the 1962 season. He was the first player from a school west of Texas to win the award. In addition to winning the Heisman, he also won the Maxwell Award and the W. J. Voit Memorial Trophy in 1962, was a consensus first team All-American, was named as the "Sports Illustrated" Sportsman of the Year, was a Helms Foundation Award recipient and won 14 player of the year awards, including from AP, UPI and "The Sporting News". He also played in the College All-Star Game in Chicago on August 2, 1963, the last time the collegiate stars defeated the reigning NFL champion.