He was named First-Team All-Southeastern Conference in all three of his college seasons and All-American in his junior and senior years.

Upon completion of his collegiate career, Grevey scored 1,801 points, which at the time ranked him second in University of Kentucky history behind only Dan Issel's 2,138.

[2] Grevey signed with the Bullets and played mostly as a backup small forward and shooting guard his first two seasons.

When Phil Chenier suffered a season-ending back injury early in the 1977–78 season, Grevey became the starting off guard and averaged 15.5 points per game.

The Bullets won their only NBA championship that season, led by Grevey, newly acquired Bob Dandridge and the future Hall-of-Fame duo of Elvin Hayes and Wes Unseld.