 In his sophomore year Bradley scored 40 points in an 82 – 81 loss to St. Joseph's and was named to The Sporting News All-American first team in early 1963. The coach of the St. Louis Hawks believed he was ready to play professional basketball. The AP and United Press International polls both put Bradley on the second team, establishing him as the top sophomore player in the country; Bradley also hit .316 as a first baseman for the baseball team. The following year The Sporting News again named him to its All-American team as its only junior, and as its player of the year. At the Olympic basketball trials in April 1964, Bradley played guard instead of his usual forward position but was still a top performer. He was one of three chosen unanimously for the Olympic team, the youngest chosen, and the only undergraduate. The Olympic team won its sixth consecutive gold medal.
