A clutch hitter is a baseball player with a knack for coming up with the "big" hit. The big hit is typically a game-deciding hit, sometimes a home run, often coming with two outs. Being known as a clutch hitter is a position of high honor and responsibility, as the clutch hitter is recognized as the "go-to guy" for the team, and his exploits in pressure situations are celebrated by both fans and players alike.
Most studies on the matter involved comparing performance in the "clutch" category of statistics (production with runners in scoring position, performance late in close games, etc.) between seasons; if clutch hitting were an actual skill, it would follow that the same players would do well in the clutch statistics year in and year out (the correlation coefficient between players' performances over multiple seasons would be high). Cramer's study was the first of its kind, and it found that clutch hitting numbers between seasons for the same player varied wildly; in fact, the variance was the kind one would expect if the numbers had been selected randomly. Since Cramer published his results, many others have tried to find some evidence that clutch hitting is a skill, but almost every study has confirmed Cramer's initial findings: that "clutch hitting," in terms of certain players being able to "rise to the occasion" under pressure, is an illusion.
Despite the evidence, though, most people in baseball steadfastly cling to the idea of the clutch hitter. "You can take those stat guys," Derek Jeter once told Sports Illustrated after SI informed the Yankees shortstop that many analysts deny clutch hitting as a skill, "and throw them out the window." While many do not believe clutch hitting actually exists, supporters of it cite Jeter's teammate, Alex Rodriguez's (A-Rod) perceived struggles in clutch situations as proof that even great statistical hitters like A-Rod (who was the 2005 MVP) are different players in the clutch.
Jeter is perhaps a prime example of the difference between perception and reality when it comes to "clutch hitting." Widely considered a "clutch player," Jeter's career BA/OBP/SLG (through the end of the 2007 season) numbers are .317/.388/.462, while his playoff numbers are in fact marginally worse at .309/.377/.469. Jeter's home run to win Game 4 of the 2001 World Series helped earn him the nickname "Mr. November," but his offensive numbers for the series were a very poor .148/.179/.259. (It is notable that few of the Yankees were able to produce at their normal level in this series, in part due to Arizona's pitching, which included the co- World Series MVP's of Randy Johnson and Curt Schilling. The New York Yankees ultimately went on to lose the series in seven games.)
The problem with clutch hitting is that some people interpret it as always getting that big hit in a critical situation, while the reality is that it is unreasonable to think a player can get a hit each time out. To many, being "clutch" is being able to handle the pressure and getting that game tying/go ahead/ or winning hit. No one remembers a poor batting average in a series where a player hits a game winning home run.
The fact that a player shows improved statistics in "clutch" situations is also not proof that clutch hitting exists, because random statistical variations can produce such occurrences. For example, using the binomial probability distribution, one can calculate that there is about a 4.8% chance that a .300 hitter will bat .500 or better in 20 at-bats, based merely on random chance. This is analogous to the fact that there is always some nonzero probability that a fair coin will produce a surprising amount of consecutive flips, e.g. there is a chance that one will get 20 straight flips of "tails", without attributing any "clutch" characteristics to the coin. Given the great number of players who have played the game, players who have average career statistics but seemingly exceptional statistics in certain situations (e.g. the playoffs or with the bases loaded) are expected without providing proof that "clutch hitting" skills exist.
Conversely, the perceived struggles of Alex Rodriguez are easily explained as a statistical anomaly. Rodriguez is a career .306 hitter in the regular season with 41 hits in 147 post-season at bats (.279). Based on a binomial probability distribution, one can calculate that there is a 26.9% chance that a career .306 hitter like Rodriguez would have 41 or fewer hits in 147 post-season at-bats. While this does not prove that Rodriguez is exactly the same player in the post-season that he is in the regular season, the statistical arguments that say otherwise are not particularly strong.
In addition, the cause of "clutch" situations must be considered. For example, if a player hits better with the bases loaded, it may be in part because the bases are only loaded because the other team's pitcher is not pitching well at that time, thus giving the batter a better-than-average chance for a hit in the first place. Furthermore, a pitcher may pitch differently with runners on (from "the stretch" rather than a full wind-up pitching motion), resulting in a strategic advantage for a batter.
This is not to say that it is impossible for a player's mental state to have some impact, either positively or negatively, on their performance---e.g. confidence leading to "clutch hits" or a lack of confidence leading to "choking". However, there is little-to-no statistical evidence that shows this to be common, favoring the idea that any such impact is frequently overstated and most "clutch hits" are simply cases where success occurred at fortunate moments, and players perceived as "clutch" are simply players who have been lucky enough to get an above-average number of these hits.