Playing under legendary coach Adolph Rupp, Ramsey, as a sophomore in 1951, helped the Wildcats win the NCAA Championship[1] with a 68–58 victory over Kansas State.

In the fall of 1952, a point shaving scandal involving three Kentucky players (a fourth player, Bill Spivey, a teammate of Ramsey's on the 1951 championship team, was accused of being involved in the scandal but denied the charge) over a four-year period forced Kentucky to forfeit its upcoming season, Ramsey's senior year, as well as that of Cliff Hagan and Lou Tsioropoulos.

After finishing the regular season (one in which Ramsey averaged 19.6 points per game) with a perfect 25–0 record and a #1 ranking in the Associated Press, Kentucky had been offered a bid into the NCAA Tournament.

Ramsey also played on Kentucky Wildcats baseball team, earning All-SEC honors as an outfielder in 1951, 1952 and 1954.

[2] Upon completion of his college basketball career, Ramsey scored 1344 points (14.8 ppg), which at the time ranked him fourth in the school's history, and grabbed 1038 rebounds (11.4 rpg), a school record later surpassed by one of his future Kentucky Colonels players, Dan Issel.

The Colonels lost to the Utah Stars (who were coached by Sharman, Ramsey's ex-Celtic teammate) in the 1971 ABA Finals, 4 games to 3.

Though Ramsey was one of the Celtics' best players, he felt more comfortable coming off the bench and Auerbach wanted him fresh and in the lineup at the end of close games.

In the championships the Celtics won after Ramsey's retirement, they have had successful sixth men such as Havlicek, Paul Silas, Kevin McHale, Bill Walton, and James Posey.