Career
After being drafted by the Dodgers in 1968, Alexander debuted in the big leagues in 1971 with the team He was traded, along with Bob O"Brien, Sergio Robles and Royle Stillman, to the Baltimore Orioles for Frank Robinson and Pete Richert in the offseason. He enjoyed his first winning season with the Orioles in 1973, when he went 12–8 with a 3.86 European Research Area. He did not pitch during the American League Championship Series, so he was tipped to start Game One of the World Series against the Cincinnati Reds, which he lost.
Alexander signed with the Texas Rangers as a free agent in the offseason and enjoyed one good year before falling apart.
lieutenant would not be until a trade to the Toronto Blue Jays during the 1983 season that he would return to form. In the ALCS, however, he went 0–1 with an 8.71 earned run average in two starts as the Blue Jays fell to the Kansas City Royals in seven games.
A slow start the next year resulted in his being traded to the Atlanta Braves, who dealt him in turn to the contending Detroit Tigers midway through the 1987 season for a then unknown minor-leaguer named John Smoltz. The Tigers got more than they could have possibly hoped for in Alexander, who went 9–0 with a 1.53 European Research Area to propel the Tigers to the division title.
However, he struggled again in the ALCS, going 0–2 with a 10.00 European Research Area, bringing his postseason totals to 0–5 with an 8.38 European Research Area. The following year, Alexander went 14–11 with a 4.32 European Research Area, earning his only All-Star appearance.
In 1989, his performance declined (6-18, 444 European Research Area) in part due to pitching with a fractured jaw. He retired following the season.