In 1984, his rookie season, Roger Clemens debuted in mid-May and finished with nine wins and a 4.32 ERA (slightly higher than the American League as a whole). In his second season, an elbow injury limited him to 15 starts. But in 1986, Clemens turned in his first great season, easily leading the American League in ERA (2.48) and wins (24) and finishing just seven strikeouts behind AL leader Mark Langston.
Clemens was obviously the best pitcher in the American League from 1986 through 1992 and then again in 1997 and 1998. He was brilliant in 1994 and 1996, too. So it's not easy to pick Clemens' greatest season; after all, he's won seven Cy Young Awards, and while he didn't deserve all seven of them, there were a couple of times he didn't win but probably should have.
The competition, I think, comes down to two seasons: 1990 and 1997. In 1990, Clemens went 21-6 with a 1.93 ERA (league average: 4.07). In 1997, he went 21-7 with a 2.05 ERA (league average: 4.62). These are the only two seasons in Clemens' career in which his ERA was less than half the league average. His next best season in that regard was 1994, when the players' strike limited him to 24 starts (and his ERA was 56 percent of the league average).