A lot of questionable votes in the 80s, which saw relievers win the award on four separate occasions (three of which are listed below, with Willie Hernandez in 1984 being the exception).
1980 AL Steve Stone over Mike Norris
In one of the closer votes in Cy Young history, Stone edged out Norris even though both received the same number of first place votes (13). Stone's 25 wins and .781 winning percentage were the best in baseball, but he failed to lead the league in anything else and was a four-win pitcher despite amassing 250 innings. Norris, who threw 34 more innings with a 2.53 ERA (to Stone's 3.23), was a six-win pitcher for Oakland. The 25 year-old breakout also posted the league's lowest H/9 rate and ranked second in strikeouts, WHIP, wins, and innings pitched.
1981 AL Rollie Fingers over Steve McCatty
Fingers threw 78 near-perfect innings, with a 1.04 ERA and 0.87 WHIP as Milwaukee's closer. As far as relievers winning the award this is one of the more defensible cases, especially since '81 was a strike-shortened season. That said, I still think McCatty was more deserving. The runner-up won two legs of the pitching Triple Crown with his 2.33 ERA and ML-best 14 wins. He also topped the league in shutouts and placed second in H/9, complete games (16 of his 22 starts) and pitching WAR. McCatty wasn't quite as good as Fingers but still elite, so his large advantage in innings pitched should have been enough to put him over the top.
1982 AL Pete Vuckovich over everyone else
Pete who? My thoughts exactly. He had the AL's best record in '82, but that's where any discussion of him being the league's best pitcher ends. His 1.50 WHIP is unacceptably high and he walked nearly as many batters (102) as he struck out (105). Put it all together and he wasn't even a three-win pitcher. Second-place Jim Palmer would have been a better choice, but the most deserving candidate was fourth place Dave Stieb. His 17-14 record did him no favors, even though he completed more games (19) and innings (288 and 1/3) than any other American League hurler. As such, he was the Junior Circuit's most valuable pitcher per bWAR with 7.7,
1984 NL Rick Sutcliffe over Dwight Gooden
Sutcliffe was a monster after being traded to Chicago midway through the season, going 16-1 in his 20 starts as the Cubs made the playoffs for the first time since World War II. However, he was not as good as Gooden, the New York Mets' 19 year-old rookie. Gooden paced both leagues with 276 strikeouts which, compiled over 218 innings, translated to an ML-best 11.4 K/9 ratio. He also had baseball's best WHIP (1.07) and H/9 rate (6.6), as well as the league's lowest home run rate (0.3/9). Sutcliffe had the more compelling narrative, but on numbers alone Doc deserved the trophy.
1987 NL Steve Bedrosian over everyone else
The Phillies closer led all of baseball with 40 saves and won a tightly contested Cy Young race in which he beat out runner-up Rick Sutcliffe by two points and third place Rick Reuschel by three. Both would have been better choices, as would Orel Hersisher (fourth). NL ERA champion Nolan Ryan was most deserving in spite of his 8-16 record for a middling Astros squad. The Ryan Express ranked first among all pitchers in strikeouts (with 270 of them), H/9, K/9, and K/BB ratio. He also had the league's best ERA+ and threw more than 200 innings, all at the ripe old age of 40. Ryan never won a Cy Young award in his 27 seasons, but he definitely deserved one here.
1989 NL Mark Davis over everyone else
Davis saved 44 games--most in the majors--and had a 1.85 ERA, which is worthy of downballot consideration but doesn't merit the award. Runner-up Mike Scott and third-place Greg Maddux were more deserving, with ERAs close to three in well over 200 innings of work (Davis threw less than 100). The best choice would have been Orel Hersisher, who placed fourth after winning the year before. Though his record was an even 15-15, he led the league in ERA+ and innings, a marriage of quality and quantity that made him the league's most valuable pitcher by WAR.