Does Clutch Hitting Exist?

Yes.
Here is David Ortiz‘s career line for the information below:

Manny Ramirez has had a better career than David Ortiz, and a better 2003 and 2004 than Ortiz. And yet, it is Ortiz we want up there in the “clutch”.
A lot of people think that clutch hitting means someone who gets better in the clutch. As ‘HillysLastWalk’ (excellent username) states in the protected forum of SOSH:

I would imagine that the definition is closer than this: someone who can maintain their skills during the ultimate pressure situation. There are those that just shrink in that situation.
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Listen, these ballplayers are human beings. As a human being there is just no doubting that 0-2, bottom of the 9th, down by 1 run, runners on base is a whole lot different … mentally … then Up 8 runs, in the 5th inning. It just is. And this isn’t something that you can just fake. You can’t go up there in the 5th inning, up by 8 runs, and “psyche yourself” into believing that you’re now in a “clutch” situation.
Obviously he is trying when it’s not a “clutch” situation. But when a clutch situation does occur, it’s hard not to have your heart racing a little more or your mind focused a little more – because this is human nature. You’ve got the crowd screaming at you, and your adreniline is going crazy, you can’t control it. The situation dictates this. You can’t just turn on something like this.
When the situation does present itself, there are some people that are going to be more successful than others. There just is. And the ones that are successful .. yes … as you say … tend to hit better in those situations. This may be because those situations are rare. Think about it: If every time you took an at-bat the clutch situaion presented itself, the novelty would wear off after the 200th straight at bat. And you’d probably see numbers close to their career levels. But obviously you can’t have that every at bat. You can’t falsely create this. Just like hitters hitting differently vs. lefty or righty, there are people that hit differently clutch vs. non-clutch.

You should check this link out but here are some important facets of that article.

The results were surprising. The probability that data less consistent than the actual data would be created with no clutch difference was a mere 0.9%, which means that the “zero clutch” model matched the data extrmely poorly. A perhaps more useful number is the ratio of the probabilities that the data were generated with and without a clutch difference, often times referred to as bookmakers’ odds. Odds of 1:1 indicate no indication of a difference between clutch and non-clutch hitting; I measured odds of 14:1 in favor of a difference.
To ensure that this was not a result of my definition of clutch situations, I ran the same calculations using a few other definitions of ‘clutch’ hitting. One is from the Great American Baseball Stat Book (7th inning or later with a 1-run lead, tie, or tying run on base, at bat, or on deck). Using this definition, the probability becomes 4% that comparable or worse data were produced with no inherent clutch/non-clutch difference, with bookmakers’ odds of 4.2:1 that there is a difference. (Interestingly, if I remove plate appearances with 1-run leads from the GABSB definition, the clutch/non-clutch discrepancy increases, as one might expect since a 1-run lead is not a situation in which there is unusually high pressure to score.) Finally, I defined “clutch situations” as those with runners in scoring position (in any inning); this produced a probability of 0.02% and bookmakers’ odds of over 400:1.
Regardless of how one chooses to define “clutch” situations, it is clear that there is indeed a statistically significant difference between how players perform in clutch and non-clutch situations.

The fact that clutch hitting is indeed a real skill in baseball does not necessarily mean it is an important one. If it accounts for a maximum change of 0.0005 points of OBP, for example, it makes a difference at most once in 2000 clutch at-bats, which means a player with a 13-year career would likely get one additional clutch hit. So the second important question is: how large a factor is clutch hitting?
To answer this, I took the same calculations made above, but introduced a small amount of randomness in the Monte Carlo tests when calculating simulated player clutch batting stats. Assuming a Gaussian distribution of clutch hitting skills, a standard deviation of 0.0071 (OBP) was sufficient to model the acutal data adequately. (Note that the standard deviation is the typical difference of a player from average, not the maximum difference.) While an OBP variation of 0.0071 does not sound like a whole lot, it is significant. Making a similar calculation for overall skills, the standard deviation of players’ overall OBP rates is only 0.0258, meaning that the difference between a good and bad clutch performer is 28% the difference between a good and bad hitter — a fraction much larger than has generally been thought. Is clutch everything? No. Is it important? Absolutely.

The argument about clutch hitting has been going on and on and on and I don’t think there will ever be a solution, but I firmly believe, both in all the articles I have read, players I have seen, and more importantly, from playing the game myself, that there is indeed clutch hitting. What do you think?