In 1989, he won a career-high 19 games for the A's during a season which the A's won 99 games, more than any other team in Major League Baseball. After Davis (and reliever Rick Honeycutt) pitched in the only AL Championship Series game that the A's lost that year, Davis was originally scheduled to be the A's starting pitcher for Game Four of the 1989 World Series. When the Loma Prieta earthquake caused Game 3 to be delayed by ten days, Tony La Russa decided to re-use the winners of Games 1 and 2, Dave Stewart and Mike Moore, as the starting pitchers of Games 3 and 4; La Russa also penciled in Davis as the starting pitcher for Game 6, if necessary. La Russa's strategy worked: both Stewart and Moore won their games, and Davis, publicly angry at La Russa for the change, became a free agent at the end of the season.
Years later, Dave Stewart described Davis as the "best fifth starter [Stewart] had ever [seen]....[Davis] pitched 165-170 innings (actually 169), won 19 games (19-7) and spent some time doing a pretty good job out of the bullpen, too. Storm was the perfect fifth starter." Stewart's high opinion of Davis' 1989 season is not shared by sabermetricianBill James, who cites Davis' 19-7 winning record as a canonical example of how a pitcher's won-lost record can be misleading.
After the 1989 season, the Kansas City Royals signed Davis to a three-year, $6 million contract; this has been called one of the worst blunders in baseball history. Davis had an ERA that was worse than the league average in 1989, but Royals pitching coach Frank Funk said, "We don't want pitchers with good ERA's. We want pitchers with wins." In his two seasons in Kansas City, Davis had a win–loss record of 10-19. He pitched mostly in relief in 1991 before being traded to the Baltimore Orioles.
According to his 1987 Topps baseball card, Davis' nickname derived from a character in a book his mother read while pregnant. Another story traces his nickname to similarities with Jim Palmer, the Orioles' Cy Young Award-winning pitcher; he was a "cyclone" or "storm."
Storm Davis' parents are the adoptive parents of Glenn Davis, also a former major league player.
Davis worked as head baseball coach at The Bolles School for the 2008 and 2009 seasons after spending the previous two seasons as an assistant on the Bolles baseball staff. He resigned to become pitching coach at Low-A Hickory team in the Texas Rangers organization.