He played in the National Basketball Association (NBA) for the Phoenix Suns, Buffalo Braves, Detroit Pistons, Houston Rockets, San Antonio Spurs, and Seattle SuperSonics from 1975 to 1981.

[2][1][3] Shumate received a scholarship to attend the University of Notre Dame, graduating in 1974 with a Bachelors of Arts degree in sociology.

He was twice the Fighting Irish team captain, a two-time All-American, including a consensus All-American as a senior selected to both the Associated Press (AP) and United Press International (UPI) All-America teams.

[7] The Fighting Irish ended the year with at 26–3 record, ranked 5th in the nation, and went to the NCAA tournament.

[9] A 6 ft 9 in forward/center, Shumate played five seasons (1975–1978; 1979–1981) in the National Basketball Association (NBA) as a member of the Phoenix Suns, Buffalo Braves, Detroit Pistons, Houston Rockets, San Antonio Spurs and Seattle SuperSonics.

[14] Shumate was fifth in rookie of the year voting, with the Suns' center Alvan Adams winning the award.

[15] In the 1976-77 season for the Buffalo Braves, Shumate had his best year, averaging 15.1 points and 9.5 rebounds per game.

[10] Barnes had been a first team All-American selection in 1974 with Shumate (along with Bill Walton, David Thompson, and Jamaal Wilkes).

[10] Shumate also appeared as a member of the Detroit team in the cult classic basketball film The Fish That Saved Pittsburgh in 1979, alongside Pistons teammates Bob Lanier, Eric Money, Chris Ford, Kevin Porter, and Leon Douglas.

His best season was 1992-93, when the Mustangs went 20–8, won the Southwest Conference title, and went to the NCAA tournament (losing in the first round).