Tunnels: An Introduction


In literature, tunnels are often associated with a dark journey. I know more about baseball and math than literature, though, so I’m not going to add anything else to that. I just wanted to make sure I checked off “introduction using vague analogy to subject matter” when writing this post. Anyways. Recently, SB Nation posted an article titled The Essence of Velocity. It’s fairly long but well worth the read. The subject of the article is what Perry Husband calls “Effective Velocity.” Essentially, effective velocity says that the actual speed of a pitch is not as important as the perceived speed of the pitch by the batter. Pitches up and in look faster than they actually are, and pitches low and away look slower than they actually are. One of the concepts introduced in the article is that of “pitch tunneling,” which is making pitches appear the same during the first 20 feet of their trajectories. The article suggests that pitches that are “tunneled” are more effective than those that are not. This makes intuitive sense, as anyone who’s ever played baseball at a competitive level can tell you that breaking balls that look like fastballs are some of the most difficult pitches to hit. I was intrigued by the concept and decided to see if I could take the first steps in quantifying and studying this phenomenon.

By the way, where I was going with the dark journey bit was that batters are going to face a dark journey if they’re seeing pitches that are tunneled. It was a bit of a stretch, but don’t expect much from a kid who learned English in small town GA. I’m still working on this whole writing thing. On to the data.

As Russel Carleton of Baseball Prospectus would say: WARNING! Gory Math Ahead

As stated above, the article suggests that it is in the first 20 feet of a pitch’s trajectory that a batter decides whether or not to swing. Therefore, if after 20 feet a curve ball looks like a fastball, the batter should likely swing and miss at the pitch. To test the validity of this, I first needed a way to categorize a pitch as being tunneled or not. Using PITCHf/x data of 50,000 pitches thrown in 2014 from Baseball Savant, I created a formula to determine the predicted location of a pitch after 20 feet using the location of the pitch at the plate, the movement of the pitch, and the amount of drop due to gravity. After a quick refresher of college dynamics, two pieces of scratch paper, a few expletives, and a glass of bourbon, I had a formula I was comfortable with using as a proxy for the 20 foot location. I then was able to create a more precise definition of a tunneled pitch as follows: a breaking ball following a fastball thrown within 6 inches of the 20 foot location where the fastball was thrown. I chose 6 inches, because that is roughly twice the diameter of a baseball. This gave me a sample of 1122 tunneled pitches out of 23911 total breaking balls in my data set.

Now that I had the data I needed, I could start analyzing it. The first thing I looked at was Swinging Strike percentage for both the tunneled and the non-tunneled breaking balls. For non-tunneled breaking balls I found a Swinging Strike percentage of 11.6%. For the tunneled breaking balls, the Swinging Strike percentage was 14.4%, an increase of 24 percent. This supports our null hypothesis that tunneled pitches induce swing and misses at a higher rate than ones that are not tunneled. The next step was to determine the usefulness of this data.

From the original data set I found a sample of 14 pitchers who threw at least 1000 pitches. There are actually 120+ pitchers who have thrown at least 1000 pitches this season, but because Baseball Savant caps their CSV files at 50,000 rows and I was too lazy to download and compile the CSV files for all 120+ pitchers, I was stuck with this limited sample. However, as you are about to see, this still was a large enough sample to start making some useful observations. For the 14 pitchers in my new data set I set up a linear regression comparing their percentage of total pitches that were tunneled to their FIP.

Tunnel Perc Chart

Here we find a negative relationship between Tunnel Percentage and FIP, meaning that pitchers who throw more tunneled pitches are more effective. The regression produced an R value of 0.47 with a p-value of 0.09 indicating statistical significance at the 95% confidence level.


This is pretty obvious: pitchers who throw breaking balls that look like fastballs get more swinging strikes and are more effective than pitchers who throw less breaking falls that look like fastballs. Everyone who knows baseball already knew this, so we really don’t have any new information. However, we’ve started down the path of quantifying this information, which is a lot of what sabermetric research is about.

Should I Trust this Data?

I make a living getting car engines to run well, not analyzing statistical data, so in that sense you probably shouldn’t trust the data. However, because of the high correlation we found between Tunnel Percentage and FIP and the p-value that was greater than 0.05, you should trust the data with a slight hint of skepticism. At some point I’m going to make all of my data and models for this public in order to open them up for scrutiny and improvement, but I want to take a few next steps with the data before I do that.

What’s Next

The point of this wasn’t to be a definitive piece on tunneling, but rather to introduce the concept and determine if it is worth following up on. With what I’ve seen so far, I think a good first step has been made. Once I have more free time I will gather data for the 100+ other pitchers and see if we continue to see this relationship between Tunnel Percentage and FIP. I will also continue to refine the working definition of a tunneled pitch. At this point we still will only know what we already know, which is that tunneled pitches and the pitchers who throw them are effective. The real next steps will be in determining if this is a repeatable skill, determining how quickly it stabilizes, whether or not it can/should be used in projecting pitcher performance, and if it is attributable to the pitcher or the catcher (since the catcher is generally the one calling the game). We also will be able to produce some Tunnel Percentage leaderboards, if you’re into that sort of thing (I am). So until I do all or any of those things, enjoy having a piece of baseball wisdom confirmed.

Stephen came up with the idea for this blog shortly after graduating from Tech. Realizing that life is ephemeral, he decided to put (metaphorical) pen to paper and catalogue his thoughts. His thoughts are series of numbers and spreadsheets, casually categorized as “research,” and said research is usually conducted on the margins of what is both relevant and socially acceptable.

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One comment on “Tunnels: An Introduction
  1. Bobby Cocks says:

    Very peculiar findings you have here…..

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