In 1977, the Yankees traded Hoyt with fellow pitching prospect Bob Polinsky, outfielder Oscar Gamble, and $200,000 to the Chicago White Sox for shortstop Bucky Dent.

[3] A relief pitcher when he made the White Sox to stay in 1980, Hoyt was switched to the starting rotation in 1982 and tied a club record by winning his first nine decisions.

[4] After the 1984 season, the San Diego Padres traded Ozzie Guillén, Tim Lollar, Bill Long, and Luis Salazar to the White Sox for Hoyt, Kevin Kristan, and Todd Simmons.

[9] He was targeted by Padres general manager Jack McKeon to bolster their starting rotation, which struggled in the 1984 World Series.

[4] He gave up one run in three innings of work to earn the win and the Major League Baseball All-Star Game Most Valuable Player Award.

He pitched through an injury to his rotator cuff rather than risk a surgery that could end his career, and he logged an 8–11 won-loss record with a 5.15 ERA.

[4] Barely a month after the season ended, Hoyt was arrested again for drug possession when he tried to bring 500 pills through the San Ysidro Port of Entry on the U.S.–Mexico border.

[14] He began to serve his sentence at Federal Correctional Complex, Allenwood,[15] and was transferred in July to a halfway house in Columbia, South Carolina.