Born in Hattiesburg, Mississippi, Purvis is the younger brother of Gene Short, who played one season in the league with the New York Knicks.

[4] Purvis attended Blair Center Hattiesburg High School, where he led his team to the state championship title in 1974.

[6] He was the NCAA's second leading scorer in 1978, averaged 8.9 rebounds per game, and was named SWAC Player of the Year in 1977 and 1978.

The Warriors traded for Bernard King prior to the 1980–81 season, moving Short to a reserve role.

[10] Short finished the 1984–85 season with an average of 28.0 points per game, and was the NBA's fourth leading scorer.

[13] Golden State reached the playoffs, an achievement Short later recalled as "the best time" in his Warriors career.

He was traded to the Houston Rockets for Dave Feitl and a future first-round pick prior to the 1987–88 campaign.

[14] At the time of the trade, Short averaged 19.4 points per game in nine seasons with the Warriors and was sixth on the all-time scoring list while second in steals.

Short led the team to a successful season that ended in a 3–2 loss to archrivals Maccabi Tel Aviv during the playoffs.