## Value of Various Plate Approaches

Analysts and commentators frequently rave about a player’s ability to hit to the opposite field. Extreme pull-hitters are often knocked by many fans who consider hitting to the opposite field a key indicator of a great hitter. However, some of the best hitters in the game - Albert Pujols, Alex Rodriguez, Ben Zobrist, Carlos Beltran, Paul Konerko, Mark Teixeira, and Ken Griffey Jr. - could be considered pull-hitters: hitters who have pull rates above the 84th percentile, or one standard deviation above the mean, among all players. Thus, I wanted to understand the value of hitters with extreme split tendencies versus hitters without any extreme split tendencies, (spray hitters).

I looked at the past seven years worth of data, evaluating 310 hitters in the process. These 310 hitters had at least 300 plate appearances that resulted in balls that were pulled, hit up the middle, and hit to the opposite field, (so a total of at least 900 plate appearances per player).

I started off by studying the correlation between a player’s pull wOBA, up-the-middle wOBA, and opposite-field wOBA against his overall wOBA. Below are the scatterplots with the directional wOBA on the x-axis and the overall wOBA on the y-axis, followed by the correlation coefficient - the measure of the strength of linear dependence between two variables - of the data.*

r = .6027

r = .7042

r = .5057

It’s interesting to see that a player’s up-the-middle wOBA has the strongest relationship with a player’s overall wOBA, (r=.7042). However, this analysis doesn’t bring about many tangible results. While it’s an interesting conclusion, there is a glaring issue with this analysis: directional wOBA does not include walks or strikeouts - it only records a player’s wOBA on the balls that he puts in play to each part of the field - so these correlation tests aren’t very meaningful.

Once I realized the relatively fruitless analysis I had just performed, I tweaked my methodology in the hopes of finding something more relavent. Instead of looking at directional wOBA, I looked at the relationship between the directional frequency of their plate appearances - how frequently these 310 hitters pulled the ball, hit it up the middle, and hit it to the opposite field - and their overall wOBA. Below are the scatterplots with the directional frequency on the x-axis and the overall wOBA on the y-axis, followed by the correlation coefficient of the data.

r = .2032

r = -.1858

r = -.1730

Here, pull frequency has the strongest positive association with overall wOBA, while both up-the-middle frequency and opposite-field frequency have negative associations with wOBA. In other words, the more frequently a player pulls the ball, the higher his wOBA likely is; however, the more frequently a player hits the ball up-the-middle or to the opposite field, the lower his wOBA likely is. This makes a lot of intuitive sense - players who can pull the ball will have an easier time hitting extra base hits and home runs, resulting in higher overall wOBAs. On the flip side, players who hit up-the-middle and to the opposite field will have a harder time hitting home runs, (the centerfield fence is usually the deepest, and hitting home runs to the opposite field is significantly more difficult than pulling home runs), and extra base hits, (hitting to the opposite field with power is significantly more difficult than pulling the ball with power), resulting in lower overall wOBAs. Let’s see if this logic applies when we test it on individual players and their overall wOBAs.

To do this, I needed to test the relationship between players with extreme directional frequencies and wOBA. I began by calculating the distribution of each directional frequency. I then categorized each of the 310 hitters into four plate approaches: pull, up-the-middle, opposite-field, and spray. Those who were categorized within one of the pull, up-the-middle, and opposite-field approaches had to have a directional frequency greater than one standard deviation above the mean, (higher than the 84th percentile), in that specific frequency. So, for example, in order for a hitter to be categorized as a pull-hitter, the hitter must have a pull frequency greater than 45.5%, (the 84th percentile of pull frequency amongst the 310 hitters). Those who did not fall into any of the first three categories, fell into the spray category - these hitters did not have extreme directional tendencies and are the ones who essentially hit to all fields. Once the players were categorized, I calculated the average wOBA of each category and compared it to the weakest wOBA of the four categories. Here are the results:

Pull hitters have the highest wOBA, followed by spray hitters, opposite-field hitters, and up-the-middle hitters. When compared to the weakest category, pull hitters were worth, on average, an additional win over the course of 600 plate appearances.* As we found in the correlation study, hitters who pull the ball more frequently tend to have higher wOBAs than those who hit the ball up-the-middle and to the opposite field.

Thus, we can conclude that, on average, pull-hitters are significantly better than up-the-middle and opposite-field hitters, and only slightly better than spray hitters.

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* The higher the correlation coefficient, the stronger the relationship between the two variables.

* Assuming that 10 runs equals a win.

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