John Tudor, as has been noted by many of us (especially those of us old enough to remember events from 20 years ago), had a marvelous 1985 season and might well have taken the award if not for Dwight Gooden. Tudor, who finished 21-8 that season after starting out 1-7 (he won 20 of his last 21 decisions and pitched ten shutouts to boot!) finished in second place and 65 points on the 3-man ballot; Joaquin Andujar (who also won 21 games that year) finished fourth. Tudor's season was a great one - but what are you gonna do when Gooden had that "season for the ages" – try (24-4, 1.53, and 268 sstrikeouts) and unlike that fellow Roger, had the complete games (16, two more than Tudor, although he only had 8 shutouts to Tudor's 10) to go with everything else.
As an aside, pity poor Jim Kaat - Kaat won 25 games in 1966, and would have been an easy CYA winner that season except for the fact that there was only one CYA in those days, and Sandy Koufax won 27 for the Dodgers. That's probably why they split the award in 1967 to give one for each league - and since Gibson broke his leg in 1967, some guy named Mike McCormick won the first NL Cy Young Award (a useful trivia question for those so inclined; if you ask that question – "Who won the very first National League Cy Young Award?" you aren't likely to get too many people who would correctly guess McCormick!).
But is John Tudor really the Guy Who Came Closest? Well, here is how Cardinal pitchers have done in Cy Young voting over the years, since the award was instituted in 1956, so let's see:
1956-59 - no votes
1960 - Ernie Broglio and Lindy McDaniel each received one vote and finished tied for third, behind Vernon Law and Warren Spahn.
1961-67 - no votes
1968 - Bob Gibson was a unanimous choice with all 20 votes.
1969 - no votes
Commencing in 1970, the Cy Young balloting went to the MVP-style voting, the "weighted ballot", because of the tie vote in the AL in 1969 (McLain and Cuellar each got 10 votes). Instead of just voting for one guy, as was the case from 1956-69, the writers had to vote 1st, 2nd, and 3rd place (MVP is a ten-man weighted ballot). So, to resume the listing:
1970 - Bob Gibson got 23 of 24 first-place votes (Gaylord Perry got the other) and 118 of a possible 120 points to win the award.
1971 - Gibson finished 5th with 3 points.
1972 - Gibson finished tied for 9th with 2 points.
1973 - no votes
1974 - Al Hrabosky finished 5th with 9 points; Lynn McGlothen tied for 9th with 1 point.
1975 - Al Hrabosky finished 3rd with 33 points.
1976-80 no votes
1981 - Bruce Sutter finished 5th with 1 point.
1982 - Bruce Sutter finished tied for 3rd with 25 points; Joaquin Andujar finished tied for 7th with 1 point.
1983 - no votes
1984 - Bruce Sutter finished 3rd with 33 points; Joaquin Andujar finished 4th with 12 points.
1985 - John Tudor finished 2nd with 65 points; Joaquin Andujar finished 4th with 6 points.
1986-88 no votes
1989 - Joe Magrane finished tied for 4th with 7 points.
1990 - no votes
1991 - Lee Smith finished 2nd with 4 first-place votes and 66 points.
1992 - Bob Tewksbury finished 3rd with 22 points; Lee Smith finished 4th with 3 points.
1993-95 - no votes
1996 - Andy Benes finished 3rd with 9 points.
1997-99 - no votes
2000 - Darryl Kile finished 5th with 1 first-place vote and 8 points.
2001 - Matt Morris finished 3rd with 31 points.
2002-2004 - no votes
As we can see, Bob Gibson received votes in the most years – 4 (1968, 1970, 1971, 1972). Bruce Sutter received votes in 3 different years (1981, 1982, 1984), as did Joaquin Andujar (1982, 1984, 1985). Lee Smith and Al Hrabosky got votes in two years each (Smith in 1991 and 1992, Hrabosky in 1974 and 1975). The other Cardinal pitchers who've gotten votes only did it in one season – Broglio and McDaniel in 1960, McGlothen in 1974, Magrane in 1989, Tewksbury in 1992, Benes in 1996, Kile in 2000 and Morris in 2001.
(By the way, which among the list would be your most-unlikely Cardinal to get votes in the Cy Young balloting? Ernie Broglio in 1960, or Lynn McGlothen in 1974?)
Anyway... it actually turns out that Lee Smith, not John Tudor, came closest to joining Bob Gibson on the list of Cardinal Cy Young winners, as he got one more point in 1991 (66) than Tudor did in 1985 (65), and got four first-place votes to boot - joining Gibson and Kile as the only Cardinal pitchers ever to get a first-place vote in Cy Young balloting. (It seems a sure bet that even if he's somehow unjustly denied the Cy Young Award this season, Chris Carpenter will at the very least surpass Lee Smith in terms of total points as well as first-place votes! At least, he'd better!)
Finally, one wonders what "might have been" in 1989 - Joe Magrane had 18 wins by the end of August that year, and the Cards were, in early September just a half-game behind the Cubs and leading Chicago going into the bottom of the 9th with Ken Dayley on the mound, Todd Worrell having blown out his elbow earlier that week. But Ryne Sandberg homered to tie the game, the Cubs won in extra innings, the Cards proceeded to lose 7 in a row to fall out of the race, and Joe Magrane went 0-5 in September and blew his chance for a possible Cy Young Award - the award went, that year, to reliever Mark Davis. Surely, had Magrane even split his six starts, going 3-3 instead of 0-5 with a no-decision, he would have won 21games and beaten out Davis in the balloting!