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January 24, 2017

Prospectus Feature

Introducing Pitch Tunnels

by Jeff Long, Jonathan Judge and Harry Pavlidis

One day I sat a dozen feet behind Maddux’s catcher as three Braves pitchers, all in a row, did their throwing sessions side-by-side. Lefty Steve Avery made his catcher’s glove explode with noise from his 95-mph fastball. His curve looked like it broke a foot-and-a-half. He was terrifying. Yet I could barely tell the difference between Greg’s pitches. Was that a slider, a changeup, a two-seam or four-seam fastball? Maddux certainly looked better than most college pitchers, but not much. Nothing was scary.

Afterward, I asked him how it went, how he felt, everything except “Is your arm okay?” He picked up the tone. With a cocked grin, like a Mad Dog whose table scrap doesn’t taste quite right, he said, “That’s all I got.”

Then he explained that I couldn’t tell his pitches apart because his goal was late quick break, not big impressive break. The bigger the break, the sooner the ball must start to swerve and the more milliseconds the hitter has to react; the later the break, the less reaction time. Deny the batter as much information—speed or type of last-instant deviation—until it is almost too late.

- "Greg Maddux used methodical approach to get to Cooperstown" by Thomas Boswell

Greg Maddux may have known about the concept of pitch tunnels. He may not have. Regardless, he knew how to put the concept into practice, and really that’s the important part. Maddux:

[My] main goal was to make all of my pitches look like a column of milk coming toward home plate. Every pitch should look as close to every other as possible, all part of that ‘column of milk’.

What we’ve set out to do is start quantifying pitch tunnels. In order to do that we’ve looked at how pitch tunnels intersects with things like pitch sequencing, movement and velocity, command and control, and many other things. This new pitch tunnels data should be another valuable tool in our toolbox when we set out to analyze pitcher performance.

If you’re still unsure what this looks like in the real world, Driveline Baseball provides a great look at how different two pitches can really look:

How We’re Doing It

You’re probably wondering how exactly we’ve gone about measuring something like pitch tunnels. The beauty of PITCHf/x (and Trackman) data is that it allows for a full reconstruction of the entire likely flight of the pitch. Using the Pitch Info database, we are able to calculate the probable position of each pitch at any point on its flight from the release point to home plate.

The first step in quantifying tunnels is to forget everything we think we know about pitchers. The first step is to think like a hitter.

There are three types of hitters with regard to pitch recognition. There are hitters who attempt to predict the next offering, using scouting reports and their gut and the sequence of pitches they’ve seen in the current plate appearance. There are hitters who simply read and react, going into each pitch with a clear mind looking for any and all cues that allow them to properly identify the pitch and likely location. Then, of course, there are the hitters who do a little bit of both—maybe eliminating certain pitches or looking for a particular pitch based on the available intel before reacting to the next offering.

Regardless of the approach taken by the hitter, there’s one thing they all have in common: They’re limited by their human brains.

As the diagram above shows, it takes about 400 milliseconds for a 90 mph fastball to reach home plate. One hundred seventy-five milliseconds before contact, the batter must have decided whether or not to swing and where it is they want to swing[i]. One hundred seventy-five milliseconds after the pitcher releases the ball, the hitter must start deciding whether swinging is in the cards. It all comes down to those 50 milliseconds in the middle that remain—that’s the decision point.

The point of no return, except for check swings that is, ends up being roughly 24 feet from home plate[ii]. That’s not a hard and fast number, as distance is actually variable depending on pitch speed, but 23.8 feet is the decision-making point based on 175 milliseconds and a league-average fastball.

It’s a complicated concept, but this excellent video from Business Insider helps explain it exceptionally well:

First we have to define the point during the pitch trajectory that is most important. The point we’ve identified—the one 23.8 feet from home plate where the batter must decide whether or not to swing and where they want to swing—we call that the Tunnel Point. It’s here that we capture the differential between pitches, because it is here that a pitcher’s mastery of tunneling makes all the difference. We’re then going to pair that data with readily available information from the pitcher’s Release Point and where pitches end up at the plate.

In order to capture the differential between pitches at each point we recreate the trajectory of each and every pitch in three dimensions. Once these trajectories are established, we can measure the difference between any two pitches at any point along their flight path. We of course focus only on the three key points we detailed above.

From there we calculate and add key pieces of information including total flight time, movement between release and the Tunnel Point, movement between the Tunnel Point and home plate, and some ratios of the average movement at various points along the flight path.

The next piece that builds onto what we’ve established above is pitch sequencing. Each pitch is viewed in the context of the one thrown before it, so we’ve worked to identify all pitch pairs—for example fastball-fastball or sinker-curveball or slider-changeup—for each pitcher. Data from the full season has been aggregated for each pitch-type pairing, allowing us to create rolled-up averages for each pitcher, as well as data for each individual pitch-type pairing by pitcher[iii].

Here are some terms you’ll need to know as we work through this data:


This project started as an effort to tie pitch break areas (i.e., the amount of space in square inches that a pitch thrown at a given point could move based on a pitcher’s repertoire) together with pitch usage rates. Shortly after we set off down this path Jon Roegele released his own research on a similar topic. Roegele’s work confirmed our suspicions and spurred our search for ways to measure and calculate the relevant differentials between subsequent pitches.

Indeed, Roegele’s work was a critical pre-cursor that fundamentally changed the way we approached our own research. The conclusion he reached became the target we aimed for over the subsequent months (bolded emphasis our own):

Through this study I’ve convinced myself that there is value for pitchers in being able to throw back-to-back pitches of different types that have almost identical trajectories during the initial stage of flight up to the point where the batter must make a decision of whether to commit to a swing. In both seasons studied, consecutive pitches that were close to overlapping at the swing commit point but that crossed the plate in relatively different spots generated consistently higher rates of swings and misses. In addition, the closer consecutive pitches in a plate appearance are to overlapping at the swing commit point of the trajectory, the closer they can be as they arrive to home plate and still generate these additional swings and misses.

"The Effects of Pitch Sequencing" by Jon Roegele

Our goal quickly became clear. While Roegele had shown that there was some performance merit to the concept, we had yet to measure the space between sequential pitches. We hoped to do just that; measuring the differential between pitches at the hitter’s decision-making point (tunnels) and on back-to-back pitches (sequencing), while incorporating additional details like break/location (tunnels, again) and velocity (speed changes). Today we’re finally able to roll out our findings.

The Data

To do this, we’re introducing a few new statistics that might need a bit of explaining. There are two ways to look at this data, and each has its own pros and cons. We calculate the differential between every pair of pitches thrown, and then aggregate them into distinct pitch sequences.

This means that we have average differentials between each sequence every pitcher uses (e.g., there are 21(!) entries for Bartolo Colon. (They are: CH>CH, CH>FA, CH>SI, CH>SL, FA>CH, FA>FA, FA>FC, FA>SI, FA>SL, FC>CA, FC>FC, FC>SI, SI>CH, SI>FA, SI>FC, SI>SI, SI>SL, SL>CH, SL>FA, SL>SI, SL>SL.))

We’ve also aggregated that same data by pitcher, so that you can see how all of their various pitch pairings work together to create a singular profile for the pitcher in question.

In order to gather this data, we’ve applied a series of proprietary and open-source calculations to the raw data, allowing us to identify the location of the pitch in three dimensions at any point along its flight path. This involves leveraging trajectory insights, including drag correction, from Alan Nathan and the application of some basic equations of motion.

Below we’ve provided a brief list of the data produced, along with a description of how one might interpret the resulting data. Also, it’s worth nothing that this data can be reviewed on both a sequential level (i.e., for distinct pitch pairings) and as an overall number for each pitcher:

Tunnel Differential – This statistic tells you how far apart two pitches are at the Tunnel Point—the point during their flight when the hitter must make a decision about whether to swing or not (roughly 175 milliseconds before contact).

Example: Jon Lester’s pitches average 9.8 inches of separation 23.8 feet in front of home plate. The average in our sample (min 1,000 pairs, n = 162) is 10.0 inches.

Data: This is found in the column “diffattunnel” on our stats pages.

Plate Differential – This statistic shows how far apart back-to-back pitches end up at home plate, roughly where the batter would contact the ball. This includes differentiation generated by pitch break and trajectory of the ball (which includes factors like gravity, arm angle at release, etc.).

Example: On average, Jon Lester’s pitches end up roughly 19.1 inches apart at the plate. The average in our sample is 18.7 inches.

Data: This is found in the column “diffatplate” on our stats pages.

Break Differential – This stat tells us how much each spin-induced movement is generated on each pitch between the tunnel point and home plate. Think of this like PITCHf/x pitch movement, except that it is only tracking the time between the Tunnel Point and home plate.

Example: Jon Lester’s pitches move, on average, an additional 2.8 inches in the final 23.8 feet to home plate, roughly the diameter of a baseball (baseballs range from 2.88 to 2.94 inches in diameter). The average in our sample is 2.6 inches.

Data: This is found in the column “posttunnelbreak” on our stats pages.

Speed Changes – This is the average difference, in seconds, between back-to-back pitches.

Example: Jon Lester’s pitches have an average flight time difference of 0.028 seconds, or 28 precious milliseconds if you’re a hitter. The average in our sample is 0.026 seconds or 26 milliseconds.

Data: This is found in the column “flighttimediff” on our stats pages.

Release Differential – When analyzing pitchers, we often talk about consistency in their release point, pointing to scatter plots to see if things look effectively bunched or not. This stat measures the average variation between back-to-back pitches at release.

Example: Jon Lester’s average release point varies by just 1.2 inches, best in our sample. The league average in our sample is 2.4 inches.

Data: This is found in the column “diffatrelease” on our stats pages.

Break:Tunnel Ratio – This stat shows us the ratio of post-tunnel break to the differential of pitches at the Tunnel Point. The idea here is that having a large ratio between pitches means that the pitches are either tightly clustered at the hitter’s decision-making point or the pitches are separating a lot after the hitter has selected a location to swing at. Either way a pitcher’s ratio can be large.

Example: Jon Lester’s Break:Tunnel Ratio is 28.3 percent. The average in our sample is 27.6 percent.

Data: This is found in the column “breaktotunnelratio” on our stats pages.

Release:Tunnel Ratio – This stat shows us the ratio of a pitcher’s release differential to their tunnel differential. Pitchers with smaller Release:Tunnel Ratios have smaller differentiation between pitches through the tunnel point, making it more difficult for opposing hitters to distinguish them in theory.

Example: Jon Lester’s Release:Tunnel Ratio is 13.6 percent, the best mark in our sample. The average ratio in sample is 23.7 percent.

Data: This is found in the column “releasetotunnelratio” on our stats pages.

The Potential

The value in creating these new statistics is largely rooted in their ability to inform us on opportunities for improvement and other such practical applications. In that spirit, we’ve started by listing some of the ways that we envision teams leveraging this pitch tunnels data to improve their pitchers.

We’re not leaving it there of course; over the next few days we’ll be publishing additional articles that highlight some applications and examples of analysis to show how tunnels can be applied, what it tells us about teams or players, and how it plays nicely with some of our other pitching data. For now though, here are the high-level ways to think about applying this new data:

Adding a Pitch

Let’s assume a pitcher is working on a new experimental pitch in spring training. By pulling the relevant data about average tunnel areas for pitchers with that same pitch and the pitcher in question’s other pitches we can quickly get an idea of how adding said pitch might impact their tunnel and break differentials. It could also help identify the optimal sequence(s) for the new pitch that would maximize its likelihood of success, diversifying the pitcher’s repertoire and enabling him to be more successful.

Better yet, any team could replicate this methodology and apply actual data from any given pitcher during bullpen sessions, making the hypothetical adding of a pitch more concrete. In this way the pitcher in question isn’t looking at the league-wide average for a new pitch, but rather specific data for their own arsenal. All it takes is relevant data from the new pitch to be added, which can then be compared/contrasted with their existing repertoire and data. One way to show that a pitch may be ready for “prime time” is when it generates a favorable tunneling profile.

Changing Sequences

Here’s a solution that’s even simpler than our first hypothetical above. Simply mixing pitches differently can produce different results. For example, using a slider and curveball back-to-back could produce better results for a pitcher than his typical fastball > curveball sequence. Looking through the data can help identify underutilized pitch combinations, allowing a pitcher to enhance the effects of their existing offerings.

This solution could quickly and easily be implemented by every pitcher in baseball without the pesky need to tinker with new pitches, grips, etc.

Tweaking Pitches

Let’s suppose that a hypothetical pitcher, we’ll call him Pitcher A, throws a curveball. Through analysis of Pitcher A’s tunnel and break differentials his team discovers that his favorite sequence of fourseam > curveball produces a relatively small tunnel window, but also a small break differential. Through tweaking of this pitch in accordance with spin axis and spin rate data, the team could help Pitcher A to adjust his grip and change the shape of the curve. This new curveball shape could then produce a more optimal ratio of tunnel differential to break differential, thus enhancing that sequence.

This same process could be replicated by any team and any pitcher for any pitch. Perhaps it’s a fastball that needs to be adjusted. Maybe it’s a slider or a changeup. Each pitcher will be able to identify which of their offerings could be easily tweaked to produce a better ratio, enhancing their ability to keep hitters guessing

So many people were a huge help in pulling this project together, but we’d be remiss if we didn’t mention Dan Brooks, Sam Miller, Alan Nathan, Bret Sayre, R.J. Anderson, Craig Goldstein, and the entire BP Stats team specifically

Relevant Previous Research

We’ve worked on this project for over two years, and have gone through many iterations of the data you now see on our stats pages. Along the way, we’ve found inspiration, assistance, and insight in a variety of places. Many of those works are listed below. If you really enjoyed this introduction to Pitch Tunnels, we recommend you explore the many pieces of research below that got us here:

  1. http://www.sbnation.com/longform/2014/6/18/5818380/effective-velocity-pitching-theory-profile-perry-husband
  2. http://www.hardballtimes.com/the-effects-of-pitch-sequencing/
  3. http://www.baseballprospectus.com/article.php?articleid=24862
  4. http://www.beyondtheboxscore.com/2013/7/26/4558940/strikeout-pitch-sequences-pitchfx-sabermetrics
  5. http://www.beyondtheboxscore.com/2013/8/9/4599550/strikeout-pitch-sequences-by-location-pitchfx-sabermetrics
  6. http://www.beyondtheboxscore.com/2011/3/31/2068855/pitch-fx-primer
  7. http://grantland.com/the-triangle/2015-mlb-actual-versus-perceived-velocity-statcast-pitcher-data-carter-capps/
  8. http://www.beyondtheboxscore.com/2016/4/12/11401508/statcast-data-perceived-velocity-vs-actual-velocity
  9. https://www.drivelinebaseball.com/2014/03/protect-curveball/
  10. http://www.hardballtimes.com/tht-live/trevor-bauers-pitch-design/
  11. http://www.fangraphs.com/blogs/qa-trevor-bauer-pitching-genius/
  12. https://www.oatesspecialties.com/wordpress/trevor-bauer-and-pitch-trajectory-drills/
  13. http://www.espn.com/mlb/insider/news/story?id=6630630
  14. http://www.fangraphs.com/community/babipfx-a-predictive-pitch-based-model/
  15. http://www.baseballprospectus.com/article.php?articleid=10803
  16. http://ericcressey.com/troubleshooting-baseball-hitting-timing-is-not-always-the-problem
  17. https://vimeo.com/39177797
  18. http://www.baseballprospectus.com/article.php?articleid=28193
  19. http://www.baseballprospectus.com/article.php?articleid=26195
  20. https://www.drivelinebaseball.com/2012/05/choosing-the-correct-pitch-sequences-data-driven-decisions/
  21. http://www.sloansportsconference.com/wp-content/uploads/2016/02/1479-Testing_Pitch-Recognition-to-Improve-Ta
  22. http://www.sloansportsconference.com/wp-content/uploads/2016/02/1482-Baseball.pdf
  23. http://www.baseballprospectus.com/article.php?articleid=14572
  24. http://sonsofsamhorn.com/baseball/hitting/hitting-visual-analysis/how-do-hitters-perform-with-their-eyes-wide-shut/
  25. http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0148498
  26. http://ftw.usatoday.com/2016/03/houston-astros-spin-rates-statcast-mccullers-mchugh-keuchel-mlb
  27. https://tartansportsanalytics.com/2016/03/02/a-new-method-for-clustering-pitchers/
  28. https://www.amazon.com/Downright-Filthy-Pitching-Book-Effective-ebook/dp/B00EDP3GN
  29. https://www.amazon.com/Art-Science-Pitching-Tom-House/dp/158518960X/ref=sr_1_1?s=books&ie=UTF8&qid=1481574514&sr=1-1&keywords=the+art+science+of+pitching
  30. https://www.amazon.com/Picture-Perfect-Pitcher-Tom-House/dp/1585186023/ref=asap_bc?ie=UTF8
  31. http://www.hardballtimes.com/recasting-pitchfx-data-in-two-dimensions/
  32. http://www.fangraphs.com/blogs/what-can-hitters-actually-see-out-of-a-pitchers-hand/
  33. http://www.sfgate.com/sports/article/The-art-and-science-of-Barry-Ball-Reflexes-2781677.php#photo-2202106
  34. https://mglbaseball.com/2013/10/08/do-ex-pitchers-understand-how-to-pitch/
  35. http://makenolittleplans.net/a-new-view-on-pitch-sequencing/
  36. http://lokeshdhakar.com/baseball-pitches-illustrated/
  37. http://baseball.physics.illinois.edu/trajectory-calculator-new.html
  38. http://baseball.physics.illinois.edu/spindown.pdf
  39. http://www.hardballtimes.com/dissecting-a-mystery-pitch/
  40. http://www.baseballprospectus.com/a/23864
  41. http://baseball.physics.illinois.edu/trackman/SpinParametersSportsBallPatent.pdf
  42. http://baseball.physics.illinois.edu/trackman/SportsBallTrajectoryPatent.pdf
  43. http://baseball.physics.illinois.edu/FastPFXGuide.pdf
  44. http://baseball.physics.illinois.edu/Movement.pdf
  45. http://www.fangraphs.com/community/estimating-pitcher-release-point-distance-from-pitchfx-data/
  46. http://www.baseballprospectus.com/article.php?articleid=13109
  47. http://www.baseballprospectus.com/article.php?articleid=12965
  48. http://www.baseballprospectus.com/article.php?articleid=14098
  49. http://www.hardballtimes.com/yes-we-actually-classified-every-pitch/
  50. https://www.washingtonpost.com/sports/nationals/greg-maddux-a-hall-of-fame-approach-that-carried-an-average-arm-to-cooperstown/2014/01/07/fdd7ae82-77d3-11e3-af7f-13bf0e9965f6_story.html?utm_term=.640c0c1b41dd
  51. http://spiff.rit.edu/richmond/baseball/traj/traj.html
  52. http://baseball.physics.illinois.edu/Magnus.pdf
  53. https://www.nytimes.com/video/sports/1247468158551/how-mariano-rivera-dominates-hitters.html
  54. http://www.baseballprospectus.com/article.php?articleid=19994
  55. http://baseball.physics.illinois.edu/KaganPitchfx.pdf
  56. http://baseball.physics.illinois.edu/AJPFeb08.pdf
  57. http://baseball.physics.illinois.edu/Template-for-drag-and-spin.xls
  58. http://catfishstew.baseballtoaster.com/archives/576977.html

[i] Based on a 90 mph pitch.

[ii] 23.8 feet or 23 feet, 9.6 inches to be exact.

[iii] Bartolo Colon, for example, threw 21 pitch type pairings in 2015. They were: CH>CH, CH>FA, CH>SI, CH>SL, FA>CH, FA>FA, FA>FC, FA>SI, FA>SL, FC>CA, FC>FC, FC>SI, SI>CH, SI>FA, SI>FC, SI>SI, SI>SL, SL>CH, SL>FA, SL>SI, SL>SL.

Jeff Long is an author of Baseball Prospectus. 
Click here to see Jeff's other articles. You can contact Jeff by clicking here
Jonathan Judge is an author of Baseball Prospectus. 
Click here to see Jonathan's other articles. You can contact Jonathan by clicking here
Harry Pavlidis is an author of Baseball Prospectus. 
Click here to see Harry's other articles. You can contact Harry by clicking here

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