Hoyt grew up in South Carolina and was originally drafted by the Yankees in 1973. Four years later they traded him to the White Sox in the Bucky Dent deal, and Hoyt made his MLB debut two years later. After spending 1980 and 1981 in the bullpen, Hoyt moved into the rotation in 1982 and enjoyed a breakout season, going 19-15 with a 3.53 ERA in 239 2/3 innings.
In 1983, Hoyt led Chicago to 99 wins and the AL West title. He went 24-10 with a 3.66 ERA in 260 2/3 innings while walking only 31 batters. It was the first of three consecutive seasons in which he led the league in walk rate. Hoyt beat out Dan Quisenberry for the Cy Young that year, and he threw a complete game in Chicago's Game 1 win over the Orioles in the ALCS.
Hoyt went from leading baseball with 24 wins in 1983 to leading baseball with 18 losses in 1984. After the 1984 season, the White Sox traded Hoyt the Padres in a seven-player trade that sent Ozzie Guillén to Chicago. Hoyt went 24-19 with a 4.19 ERA in two seasons with San Diego while battling legal problems and substance abuse.
From 1985-87, Hoyt was arrested four times on drug possession charges and he was suspended for the entire 1987 season by commissioner Pete Ueberroth. An arbitrator reduced the suspension to 60 days, after which the Padres released him. Hoyt attempted a comeback with the White Sox soon thereafter, though another arrest followed.
In parts of eight big league seasons Hoyt went 98-68 with a 3.99 ERA in just over 1,311 innings. He was an All-Star in 1985 with the Padres in addition to winning the AL Cy Young with the White Sox in 1983.