A step in the right direction

“The key step for an infielder is the first one, to the left or right, but before the ball is hit.”
—Earl Weaver

In one of the most read posts on my blog—the last one I wrote before being drafted by Hardball Times—I analyzed the correlation between the location of pitches and the trajectory of the resulting batted balls. I won’t go into details, as you can read them in that post, but I will summarize a couple of things that will be useful in this article.

The correlation between pitch location and hit direction varied, in 2008, between the values 0.00 (obtained by Brad Hawpe) and 0.42 (recorded by Doug Mientkiewicz).

Like any other correlation, this metric is bounded between minus one and one. In this case, a value approaching one means the direction of batted balls is strongly related to the location of the pitch (i.e., inside pitches are pulled, outside pitches are hit to the opposite field). A value close to zero means hit direction and pitch location are completely unrelated. A value close to minus one means the batter hits “inside-out” and “outside-in.”

As I wrote before, nobody in the majors has a negative value; players who hit inside pitches to the opposite field while pulling outside pitches, if they exist at all, don’t make to the bigs.

In my blog I went on to quantify the value of hitting the ball according to the pitch location. Here I will take a different path to see if this kind of analysis can produce useful information for players on the field.

Little digression.
When I play second base for my amateur team, I cheat on my positioning: I look at where the catcher puts the target and – when the pitcher starts his motion and the hitter can’t look anywhere else than at the ball I move slightly to one side or the other. I feel that on days when my pitchers are hitting their spots I cover more ground.

Back on MLB players.
Justin Morneau has one of the highest values in my hit-em-where-they’re-pitched ranking (0.41). That means he places balls on the inside corner more toward right field than balls on the outside corner.

Suppose I’m playing second base and Morneau is at the plate. I’m positioned according to the spray charts my manager has on him. What do I do when I see the catcher calling for an inside pitch? (Except making sure that I’m wearing all my hockey equipment.)

Here’s the distribution of ground balls on the right side of the infield produced by Morneau. (To identify inside pitches and outside pitches I simply took away from my data set every pitch that crossed the plate in the middle 8.5 inches. I believe I don’t have to explain how I divided the remaing pitches after that.)

(Note: I will use this kind of chart for the rest of the article; you can read a brief explanation in the References and Resources section.)

You can see how the trajectory for inside pitches has a slightly different distribution than the trajectory for outside pitches.
While it might not be a big deal, I think that, having this information on Morneau, I would take half a step to my left (toward the right field line) after my catcher has called for an inside pitch.

In the next chart I will look at air balls (fly balls and liners). I will stay on the right side again and present the positioning options for the right fielder.


Again, leaning to one side or the other (depending on the expected pitch) won’t hurt.
(Note that I use a different scale for this chart, so the effect for balls in the air is smaller than for balls on the ground.)

Let’s take another very good hitter who has a low correlation in my metric (0.06) instead. Alex Rodriguez is our man.
Since I looked at the right side for a left-handed batter, I’ll look at the left side for this right-handed batter.

Here are the trajectories of A-Rod ground balls between the second and the third base bags.

A Hardball Times Update
Goodbye for now.

The lines for inside and outside pitches overlap a lot, so there’s no need for a shortstop to lean to either side depending on his battery’s pitch selection. And, finally, A-Rod’s air balls to left field.


Here there is some difference, similar to what we have seen for Morneau. This can be an indication that not all the glove men on the field should behave the same way when the catcher puts down his signs.
(Note. Again, I used different scales for ground balls and air balls; you can safely compare between them Morneau’s and Rodriguez’s charts, because they are on the same scales.)

After a couple of articles, some eaders might be thinking that in my previous life I was Edwin A. Abbott.
I promise that, sooner or later, I’ll start exploring the other dimensions of the pitch locations.

References & Resources
All data from 2008 MLBAM Gameday.

Charts explanation.

On the x axis you see the hit trajectory angle: it goes from -45° (ball hit down the left field line) to 45° (ball hit down the right field line); a ball up the middle will have an angle of 0°.

On the y axis you see the density of batted balls. You can look at it this way: split the hits into ten bins according to the trajectory angle and plot a histogram with the pecentages for each bin on the y axis; repeat the procedure, but split in twenty bins instead; then suppose you can split the hits in an infinite number of bins – you have the density line you see in the charts I showed.

Below you can see an example on every groundball hit by Morneau on inside pitches.

OK, this was really quick and dirty. Here you can find a brief introduction to density estimation – something the casual reader can easily grasp, and real statisticians won’t be horriefied at.

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