Dotson was born in Cincinnati and drafted out of Anderson High School by the California Angels in the summer of 1977, but was traded along with Bobby Bonds and Thad Bosley to the White Sox for Brian Downing, Chris Knapp and Dave Frost on December 5, 1977.

White Sox manager Tony La Russa handed him the ball on September 4, 1979, as the starter for a game at Anaheim, but the 20-year-old Dotson retired only four Angels and left the park that day with an earned-run average of 33.75.

On the final day of the regular season, he and Dennis Lamp combined for a shutout at Seattle that put the White Sox in first place by a whopping 20 games over the nearest contender.

The Orioles' lone hit and the only run of the game was Dan Ford's one-out opposite-field solo homer over the right-field fence in the eighth inning.

[4] He was also the losing pitcher in his only postseason appearance, an 11–1 defeat to the Orioles in Game 3 of the American League Championship Series at Comiskey Park five months later on October 7.