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With the release of BP’s new data on pitcher tunnels, the idea is that one way a pitcher can fool the hitter is to make sure that his pitches all look the same as they fly through the air toward the batter, until they get to the point where the batter has to make his decision of whether he will swing, and if so, where he will aim his bat. If a pitcher can keep all the pitches going through the same “tunnel” and have the break (or lack thereof) be a surprise that reveals itself only after the batter has started his swing, then he’s going to get more swings and misses and weakly hit balls.

With a little bit of math and physics, we can reverse engineer the flight path of every pitch thrown in the major leagues over the past nine years. And by doing that we can see some interesting things about pitchers. But before we freak out about these numbers, we need to ask some more basic questions about them, starting with “what do they really tell us about a pitcher?”

We need to establish them as a reasonably reliable reflection of a pitcher and his talent, and not just some numbers that end up being as random as ice cream bones. In other words, we need to do some #GoryMath.

Warning! Gory Mathematical Details Ahead!

The first thing that we need to do is establish reliability, which is the idea that a measure of something is stable over time. For example, we are comfortable labeling certain hitters as “power hitters” because hitters tend to hit home runs at roughly the same rate in one year as the next. It’s not exact, of course, but the leaderboards from one year to the next tend to have the same names on them. So, we assume that a player’s home run total is actually a reflection of some talent that he has, and not simply the result of randomness.

There are two types of numbers that we have released so far. One looks at all pitches that a pitcher threw during a given year and another looks at specific pitch sequences (i.e., fastball, then changeup) for a pitcher. We have calculated several indicators from this data, which are explained elsewhere, but to recap:

Tunnel Differential: How far apart two pitches are at the tunnel point. If this number is low, then in general a pitcher’s pitches are all in the same basic space (relative to what the batter sees) as they come in. If this number is big, then the pitches tend to be far apart. That might mean a lot of movement (we’ll talk about that in a minute) or it might mean that he’s a poor tunnel-er.

Plate Differential: Same basic idea, except now we’re talking about how far apart pitches end up as they cross home plate. This is probably one where the pitcher doesn’t want things to be too low, because that means that all of his pitches go to the exact same spot time after time. Every once in a while, it pays to change things up a bit. But if it’s too high, it might mean that the pitcher doesn’t really know where the ball is going.

Break Differential: This is the amount of break that a pitch has (spin-related) after the decision point. In theory, the more of this the better, but that’s not always going to be the case. One way to get a lot of break after the tunnel point is to have a pitch that is very obviously already breaking before the tunnel point, so that the batter can pick up what’s going on. So, this is going to be an ingredient in success, but not the entire recipe.

Speed Change: The average difference between the flight time of two pitches. This is largely a function of pitch velocity, but not entirely. In a game where milliseconds might be the difference between hitting the ball square or being out in front, sometimes it helps to catch a batter off-balance.

Release Differential: The distance between the release point of two pitches in a row. Some pitchers tip their pitches by having one release point for one pitch and another for the second. If a batter picks up on that, it can be a disaster.

Break-to-Tunnel Ratio: This is the ratio between how much post-tunnel movement a pitch has (break differential) to how closely packed together the pitches are at the tunnel point (tunnel differential). In theory, the perfect break-to-tunnel is one where the pitches all look the same at the tunnel point and then break in all sorts of crazy directions leaving the batter utterly powerless to figure out where the ball is going. However, it could be a sign that the pitcher just gets a lot of post-tunnel movement, which may or may not be fooling anyone.

Release-to-Tunnel Ratio: This is the ratio between the spread in the pitcher’s release point (release differential) to the variance at the tunnel point.

To figure out whether these measures are reliable, I started with the overall aggregated numbers and the numbers for all pairs of pitches for all pitchers, with the assumption that a pitcher had 500 pairs in the year under consideration. (This is a relatively low bar, with even most relievers being included.) I separated the data into one data set for 2009-2012 and another for 2013-2016. This was so that I could run the analyses twice.

I used a technique known as the AR(1) rho intra-class correlation. One way that we establish that a stat is reliable is to check a simple year-to-year correlation. This technique allows us to incorporate more than one year of data, but the eventual readout is on the same scale as a correlation. The higher, the more consistent the metric is across years.

Here are the results, minimum 500 pitch pairs for each measure:

Measure

2009-2012 data

2013-2016 data

Tunnel Differential

.753

.738

Plate Differential

.643

.617

Break Differential

.894

.905

Speed Change

.870

.881

Release Differential

.858

.925

Break-to-Tunnel Ratio

.888

.898

Release-to-Tunnel Ratio

.858

.912

Looks pretty reliable to me.

Now, a note of caution. In the past, I’ve done estimates of reliability for various stats that try to pinpoint at what sample size (i.e., 50 PAs, 100 PAs, etc.) a stat becomes reliable. The analysis that I’m doing here is slightly different. In the previous work I’ve done, what I do is artificially limit a sample of 100 PAs for each pitcher/hitter so that everyone in the sample has 100 PAs to work with. In this case, I’m taking everyone as they are, with the only restriction being that they need at least 500 pitch pairs. Some might have 500, some might have 2,000.

To be on the safe side to make sure that the starters with all those pitch pairs aren’t unnecessarily inflating the reliability estimates, I limited the sample to those pitchers who had between 500 and 1,000 pitch pairs. Here are the result from the 2013-2016 data (I ran the 2009-2012 data and it came out similarly.)

Measure

2013-2016 data

Tunnel Differential

.909

Plate Differential

.611

Break Differential

.693

Speed Change

.876

Release Differential

.925

Break-to-Tunnel Ratio

.904

Release-to-Tunnel Ratio

.900

So, even at reasonably small (reliever sized) sampling frames, we can be fairly certain that these new tunnel stats represent something stable about a pitcher. If he has a lot of release point variation one year, it will probably be there next year. It means that we can do the types of analyses that will hopefully yield some interesting findings, and (at least for the tunnel part) feel confident in the credibility of our findings.

Next, I dug into the data on pairs of specific pitch types, (e.g., fastball-then-curve), to see whether these metrics were reliable for these specific pitch-type sequences. For example, if we see that a pitcher has a differential in his release point between his fastball and his curve, is that likely to continue?

I used data from 2013-2016 again, and used all possible combinations of the five following pitches: fastball (four-seam), curve, change, sinker, and slider. That means I looked at fastball-then-fastball, fastball-then-curve, fastball-then-change, etc., but also curve-then-fastball, change-then-fastball. At first, I asked the computer to only consider cases where there were 250 pitch pairs for the pitcher in question during the season under study, but there were some combinations where very few (or no one) met the threshold. So, I dropped the inclusion criteria to 100 pitch pairs.

For the most part, I still got reliability measures in the .70s and .80s for just about everything except plate differential, which sometimes (but not always) drifted into the .40s and .50s. Reliability in this range is not awful, but it leaves something to be desired. (Home run rate is considered a “true” outcome for pitchers, despite consistently hitting a year-to-year reliability in the .30s and .40s). It’s probably a reflection of the fact that plate differential looks at how far apart pitches were as they arrive at the plate, and for some hitters it makes sense to always pound them in the same place and others it makes sense to move it around. Perhaps this is more of a reflection of who the pitcher faced than anything. Still, it probably gives us some useful information.

So, now that we know that we have fairly reliable metrics, let’s take them out for a quick spin. I used the 2013-2016 data set for all pitch pairs, and threw all seven variables into a factor analysis (for the initiated, simple Varimax rotation, nothing fancy). A three-factor solution emerged, and since factor loading charts are sexy:

Variable

Factor 1 Loading

Factor 2 Loading

Factor 3 Loading

Tunnel Differential

.284

.860

Plate Differential

.910

Break Differential

.952

.239

Speed Change

.844

.202

Release Differential

.990

Break-to-Tunnel Ratio

.967

Release-to-Tunnel Ratio

.990

Minimal cross-loading here, so we have three pretty clean factors. (And since someone will ask, I ran it on the 2009-2012 data, and it came out with the same loading structure.

Factor 2 seems to be all about release point. It’s interesting that break differential, which is how much the pitch moves after the tunnel point, and speed change, which is how much a pitcher’s back to back pitches differ in their flight time to the plate, line up so nicely on Factor 1. This suggests that late movement and changing timing tend to go together like peas and carrots. The third factor seems to be about how much movement a pitcher has prior to the tunnel point, and how big a canvas he tends to paint on at the plate. The commonality there is pitchers who are going to have a lot of movement.

The important thing to know about the three factors is that the type of procedure I used (Varimax rotation) specifically constructs factors that are not correlated and are therefore independent from one another (for the initiated: orthogonal). That means that a pitcher can have a lot of variation in his release point (or a little) and this tells us very little about his ability to use tunnels to his advantage.

We’re left with three question then to answer about a pitcher. 1) How consistent is his release point? 2) How well does he use tunnels? 3) How much do his pitches move in general?

A Whole New World …

This is going to be fun. For a long time, we’ve been able to look at a pitcher’s pure stuff (velocity, movement) and to some extent his location abilities, but now we have another piece. There have always been pitchers who seemed to thrive despite having “stuff” that was pedestrian, and this might be the key that unlocks that mystery.

There are several ways to get a hitter out. Some pitchers do it through just throwing it fast and throwing it past. Some get the hitter to chase stuff that moves like crazy. Some do it with sequencing. But some do it by having stuff that doesn’t give the hitter a lot of information to go on. Maybe it’s some combination of all three. There are a lot of questions out there worth answering and now we can feel fairly sure that we have good reliable tools with which to answer them. And once we’re done looking at pitchers, I think that there are questions with hitters that would be fun to answer. Are there hitters who seem immune to this tunneling technique. While a pitcher might keep his pitches tightly packed before the tunnel point, perhaps some hitters can discern some of those finer movements?

Have fun, everyone.