*By Father Gabe Costa*

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I still remember how the squatty catcher, who wore Number 15, would waddle while coming up to the plate…the nervous twitches…the walrus-like moustache…the re-adjusting of the batting gloves…and the feeling that I had…just knowing that Thurman Munson would get a clutch hit.

To this day, Thurman Munson is the player (of all the players I’ve seen since 1958) I would most want up at bat in the midst of a clutch situation. And I put Derek Jeter just a shade behind him.

But a question does arise: Can we really explain what “clutch” means?

I suspect we all have an intuitive idea as to what “clutch” is, and we can pretty easily come up with examples of these situations, but to quantify this concept is another story.

In this episode of By The Numbers, our guest blogger takes a shot at this very question. Mr. Samuel Ellis is a student of sabermetrics and a rabid Detroit Tigers fan. By considering clutch hitting in the context of “dependent probability”, he offers an interesting approach with respect to trying to understand this not so simple concept.

Samuel Ellis: Consider the last game you saw where you were on the edge of your seat because of a pivotal plate appearance. As you rooted for your team, the moment of suspense probably seemed to drag on with an excruciating slowness. You hoped and prayed that the batter would come up with a clutch hit. To get some insight into this situation, you checked the player’s statistics for the game and the season. Did it matter that the player had not yet had a hit in the game? How important was the player’s batting average when he stepped up to the plate? How many times had this player been in a situation similar to this one?

The answers to these questions are rooted in the difference between dependent and independent probability. Independence can be defined as two or more events occurring without any influence of one on another. This concept can be illustrated by a classic example—the coin flip. When you flip a fair coin, the probability of getting either a heads or tails is exactly the same as the probability was of getting a heads or a tails on your last flip: 0.5 or 1/2. It is a common misconception that if you flip a fair coin and get heads five times in a row, that the next flip it bound to be a tails. Unfortunately, that thought is pitfall of probability that one just has to accept.

On the other hand, dependent probability can be described as probability of an event having an effect on or being affected by some condition(s). For example, if Billy Baseball wants to purchase a box of Crackerjacks from the busy refreshment stand in his section of the ballpark, he knows that the availability of purchasing the Crackerjacks is dependent upon how early in the game he goes to the stand. Given that it is early in the game, the probability of Billy getting his Crackerjacks is much higher. Incidentally, dependent probability is much more common than independent probability when modeling real world events. Mainly due to complexity, independent probability is often times posited; baseball modeling is one of the areas where independent probability is frequently assumed.

With this being taken into consideration, I believe that each time a player steps up to the plate, the probability of his getting a hit is indeed a dependent probability. Think about the myriad of factors that go into whether or not a player gets a hit for a particular at bat: how much pressure is on him, how he matches up with the pitcher, and his mental state due to previous performances at the plate, to mention a few. Although it is easy to think that every time a player steps up to bat the probability of his getting a hit is his batting average, that is actually not the case. If you look back into a player’s hitting career in detail, you may notice certain patterns that can be very revealing.

Why it is that one starts to see patterns in certain situations for many players? Simply put, we are creatures of habit that have the tendency to, on average, act the same in recurring situations. Some players seem thrive on pressure with an uncanny consistency, while many others tend to crumble under a full count when their team needs them most. Incidentally, the homerun derby is a pretty good controlled example of how players react differently to pressure. The homerun derby takes players that are all quite similar in hitting power and consistency and gives them pitch after pitch that are very similar in speed and location. On paper, the winner of the homerun derby should be the player with the highest homerun hitting percentage. In reality, that is usually not the case. Each player in the homerun derby has different tendencies under pressure, and the players who thrive under pressure tend to do the best. Clearly, there are many more factors and conditions in regular season and post-season games.

We all feel that there are some players who perform better than others during pressure situations, but how can we model these performances? Perhaps the answer lies in the assumption that players perform similarly in recurrent situations. For the majority of situations, one can develop a dependent probability for what will happen for a certain player during a given at-bat. This probability is derived by looking back at each at bat the player has had and considering the “relative frequency” of the current situation as compared to all other situations. For example, let’s say a player has been to bat twice and was unsuccessful both times. In order to determine the probability of getting a hit during his third at bat, one would look back at every time the player had two previous at bats without getting a hit. Once this was known, one can compare all the times the player hit successfully to the total number of times he came up in that precise situation; this will determine the “dependent” probability of the player getting a hit.

Granted, this method only takes one factor (previous hits) into consideration, but it provides more insight than the player’s batting average. With more robust analysis with regard to the use of dependent probability, one can ponder how this approach can be extremely helpful in measuring a player’s performance under pressure, also known as clutch.

**Who’s the best clutch hitter in your book? Let us know in the comments below…**