I'm not a huge believer tagging someone as clutch and others as non-clutch, especially in baseball. Coming from a research background, it's troubling that you are nearly always working with a small sample size. You also have to take into account that baseball is the most random of sports, and that trying harder doesn't necessarily produce better results (see: A-Rod).
But I think there is a fundamental difference between clutch pitching and clutch hitting. The pitcher is the proactive while the batter is reactive. For the first part of the pitcher/hitter interaction, the batter is actually on the defensive; he is trying to protect the plate. Only after the ball is put in play does the burden of defense shift back to the fielding team. So, pitchers have more control of the situation, and more control means more responsibility for the outcome. And as the old baseball cliche goes, "good pitching beats good hitting".
That said, watching Sabathia in the postseason has been less than awe inspiring. In the 2007 ALDS against the Yankees, Sabathia walked 6 guys in 5 innings, after walking just 37 in 241 innings during the regular season. But CC was let off the hook by Chein Ming Wang who pitched even worse, allowing the Indians to win that game. Against the Sawx in the ALCS, he walked 7 guys in 10.1 innings, and rounded out his postseason line by giving up 15 runs, walking 13, and giving up 21 hits in 15.1 innings for a WHIP of 2.21. Yikes.
It wasn't just 2007. In his postseason career (only 25 innings) he has given up 33 hits, 22 runs, and walked 22 for a WHIP of 2.20. He's got a postseason WPA of -0.74. I know, I know, small sample size, but that is a pretty alarming trend developing.
You may want to offer up what he did with the Brewers this year, taking the ball on short rest and carrying them into the playoffs. In September, he had three awesome starts (25 IP/3ER), and two okay ones (14IP/7ER), and one that was pretty bad (5.2IP/4ER). In his only postseason start, he gave up 5 runs and walked 4 in 3.2IP.
Why would a guy who walks about a guy every three innings throughout his regular season career, nearly triple that rate in the postseason? If a top quality control pitcher were to fold under pressure, the first thing I would expect to go would be that control. You get nervous, lose your rhythm and can't find the strike zone. I'm not a world class golfer, but I've played in Club Championships, State Am's, and DII College tournaments that I felt were pretty important. I have not only felt some nerves, but had them negatively affect my performance. The golf swing, probably like the pitching motion, has little room for error and is best performed under relaxed conditions and a calm mind.
I'm not labeling CC a "choker" or anything like that, I just think it's worth pointing out that so far, he hasn't been able to perform in the postseason. Bad sportswriters like to brand guys with the tag of "clutch" or "anti-clutch" like its some indelible part of their character. David Ortiz, Reggie Jackson, Mariano Rivera, and Curt Schilling are forever enshrined in the Hall of Clutch, just as A-Rod, Bill Buckner, and Mitch Williams are portrayed as choking dogs.
For A-Rod and CC, there is still time to turn it around. A great season leading up to the playoffs could calm some nerves. A few small breaks from the get-go could inspire some confidence, which could snowball into success. A few big moments in October can swing the perception from goat to hero.