Written by: Ethan Moore (@Moore_Stats)

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Understanding pitching is hard. The interaction between the batter and the incoming pitch is incredibly complex and the public has barely scratched the surface of understanding what goes through a batter’s mind while the pitch is in the air. Will he swing? Will he be on time? Will he make good contact? We literally don’t know.

We currently understand pitching as a combination of control (where the pitch ends up in the strike zone) and “stuff” (the pitch’s flight characteristics like velocity and movement). However, there are a few other things that can influence a pitch’s impact as well, like a pitcher’s release point. We think, anecdotally, that it is harder to hit pitches that come out of funky release points than normal ones with all else being equal. But of course, all else isn’t equal because we also understand that changing release point can alter a pitcher’s pitch characteristics. Everything is connected in pitching.

In this article, I want to dive into a pair of existing metrics tracked by TrackMan and now Hawkeye for every pitch of every MLB game to see if they hold new information that can change how we think about pitching. They are called Vertical Approach Angle (VAA) and Horizontal Approach Angle (HAA).

**Definitions**

Vertical Approach Angle tells us how “steep” or “flat” the pitch was when it crossed home plate. Almost every pitch has a negative VAA because almost every pitch crosses the plate *lower* than where it was released (because pitchers are standing on a hill and throwing down towards the strike zone).

For example, this pitch has a VAA of about -3 degrees, which is relatively flat because it is a fastball up in the zone.

Aroldis Chapman, 102mph Fastball (side view w/ Tail).

Good luck. pic.twitter.com/JXIbFCyFb0

— Rob Friedman (@PitchingNinja) August 17, 2019

But this pitch has a much lower, steeper VAA of about -15 degrees, because it is a curveball low in the zone.

Clayton Kershaw, Beautiful 73 mph Curveball (release/path). 👑 pic.twitter.com/XGTnrgl4Fq

— Rob Friedman (@PitchingNinja) April 21, 2018

Horizontal Approach Angle tells us about how the ball came into the zone horizontally. A fastball thrown arm-side to a righty has a positive HAA because it entered the zone moving towards a right handed batter

Gerrit Cole, Inside 97 mph Fastball. 😬#WatchYourLips pic.twitter.com/rAKikOlmJw

— Rob Friedman (@PitchingNinja) May 23, 2018

Whereas this curveball away is going to have a negative HAA because it is moving away from a righty as it crosses the plate

Aaron Nola, Dirty 80mph Curveball (home plate view). 🤭 pic.twitter.com/XK4VQ8x22l

— Rob Friedman (@PitchingNinja) August 5, 2020

Typical HAA values range between -3 degrees (a very sharp angle into the plate) and +0.5 degrees (a fairly straight trajectory into the zone) for Right Handed Pitchers (flip the signs of those numbers for Lefties), but vary based on the pitch type which I will get into later. Most pitches enter the zone moving away from a Right Handed Hitter.

*Note: These metrics have nothing to do with a pitch’s “movement” (in the way that we normally calculate it) and everything to do with the direction the ball is moving as it crosses the plate.*

**Question**

Now that we know what VAA and HAA are, we can begin to answer our question: “Does a pitch’s VAA and HAA typically affect its results?”

**Try 1: Individual Pitches**

I started at the individual pitch level. Does knowing the VAA and HAA of a single pitch give us enough information to determine whether that pitch will be swung on and missed?

I made a model to predict whether each pitch in 2019 was a whiff or not based on only its VAA and HAA. The model was significant (meaning VAA and HAA did give some useful information), but the R-squared of the model was 0.01 (meaning VAA and HAA gave verrrrrrrry little useful information).

if this table scares you, just move on. it’s not that important!

This model was statistically significant but not practically significant, something that can happen when your sample size is too big. (I used 700k pitches, so this makes sense). This model does not help us answer our question.

**Try 2: Pitcher Averages**

Next, I looked at whether a relationship existed between pitchers’ average VAA and HAA and the pitcher’s whiff rate in 2019. I did this for each of the four main pitch types to make sure I am only comparing apples to apples. Also, I only looked at pitches against Right Handed Hitters to control for batter handedness.

*Four Seam Fastball*

This model was significant with an R-squared of 0.24. Not bad in this context! 24% of the variation in a pitcher’s fastball whiff rate in 2019 could be explained by its average VAA and HAA alone (with no information about its velocity, movement, or typical location). The table tells us that fastball whiff rates tend to increase when average VAA increases (flatter FBs = better) and when average HAA decreases (moving away from righties = better), in general.

*Changeup*

Average VAA and HAA had no influence on the whiff rates for pitchers’ changeups in 2019.

*Slider*

Pitchers with lower (steeper) VAAs on their Slider tended to have significantly higher whiff rates using that pitch. Interestingly, average HAA did not significantly influence whiff rate despite sliders typically being a more lateral moving pitch.

*Curveball*

The average VAA and HAA of pitchers’ curveballs did not have a significant effect on their whiff rates with that pitch in 2019.

**Initial Takeaways**

That was a lot of information. Here’s what you need to remember. Looking at the average Vertical Approach Angle and Horizontal Approach Angle of a pitcher’s pitches is most helpful when predicting a pitcher’s whiff rate **for fastballs**. These measures alone are not very informative for the other main pitch types.

Therefore, the rest of this piece will only be in regards to four seam fastballs.

**A More Comprehensive Model**

In the last section we looked at the isolated effects of average VAA and HAA on pitcher whiff rate for the four main pitch types. But remember what I said earlier?

*Everything is connected in pitching.*

Looking at the isolated trends can give us context, but it’s not enough. We need to understand how VAA and HAA fit into the bigger picture. To do that, we need to account for other important factors like command, stuff, and release point in order to get a more complete understanding of the role of VAA and HAA for fastballs.

To do this, I ran a linear regression using the speed and movement of each pitch, the location of each pitch, the 3D release point, and the approach angles to predict the run value of each pitch (by linear weight). Here’s the full model.

What’s important is in yellow. This term tells us that with all other terms being held constant, each additional degree of VAA (more flatness) on fastballs is associated with a decrease of 0.05 runs per pitch. For a pitcher, decreased run values are good!

Also, with all else being equal, each additional degree of HAA (more side-to-side) on fastballs is associated with a decrease of 0.83 runs per pitch. That’s a ton! However, we have to take this with a grain of salt. If a pitcher throws 100 fastballs in a game, does that mean that increasing his HAA by 1 degree will lead to his team preventing 83 runs that game? Clearly not.

This model helps us understand that generally, a flatter VAA and more side-to-side HAA on fastballs is preferable when holding everything else constant. But even after accounting for a bunch of other important variables, we are still lacking important context!

**Understanding the Intricacy**

So far, we’ve learned that less negative VAA and more negative HAA are great in a vacuum, but there are two big things I haven’t told you about yet.

- VAA is highly related to the pitch’s vertical location (R-squared = 0.76) meaning higher VAA fastballs are almost always up in the zone, and lower VAA fastballs are almost always low in the zone.
- HAA is somewhat related to the pitch’s horizontal location (R-squared = 0.28) meaning more negative HAA fastballs typically end up being outside to righties.

To visualize these points, here is the typical RHP fastball VAA by strike zone location in 2019:

Now it’s all starting to come together. Our model earlier showed that flatter VAA fastballs are better for getting whiffs. Where do fastballs get whiffs in 2019? Up in the zone, right where we see the flattest VAAs on the graph above.

Here’s the typical RHP fastball HAA by strike zone location in 2019:

*(Similar graphs with the other pitch types are in my Twitter thread* *here**)*

Again, our model earlier suggested that fastballs with slightly negative (blue-white in the graph above) HAAs got more whiffs which again should make sense given where fastball whiffs typically occur. Here’s that graph for reference.

A theory I have heard regarding fastballs and VAAs is that pitchers should avoid having the average VAA on their fastball, which is about -5 degrees. This is because a) pitches with average characteristics are easiest for hitters to hit and this is no different b) hitters typically swing upwards at an angle of about 5 degrees, so a -5 degree fastball would meet their bats perfectly leading to hard contact. This tweet describes this theory:

There’s more evidence for this in the upcoming PLUS video, but if you can’t get your vertical approach angle on your four-seamer to be above -5 degrees in the zone, you’re likely better off going with a sinker or two-seamer pic.twitter.com/Thgb5cmOhp

— Dan Aucoin (@dan_aucoin13) December 12, 2018

FBs at VAA = -5 do poorly. But because we know the relationship between VAA and strike zone location, we know that fastballs with a VAA within half a degree of -5 (which I am calling ‘Danger’ pitches) usually occur in the middle of the zone anyways!

We already know not to throw fastballs here, so I don’t find the “avoid fastballs with a VAA of -5” theory to be particularly useful in the aggregate.

When we apply everything we’ve learned regarding VAA and HAA so far, we conclude that we should… throw our fastballs up in the zone. Which we already knew we should do.

*sad trumpet noises*

**Unfortunate Conclusion**

So it turns out that VAA and HAA are helpful to our understanding of what makes a good fastball. But they are also highly correlated with pitch location, which we already knew was important for a good fastball. So in the end, there really is not much new information here. Though VAA and HAA are interesting to think about at the micro level, they really do not seem to contribute much to our understanding of pitching at the macro level that we didn’t know before.

Sometimes, learning that something isn’t important is good. It can allow you not to fixate too much on that thing and move on to the next thing that may actually be what you are looking for!

**BONUS: Fun Outliers**

Although we discovered that VAA and HAA are not that important, all things considered, in determining fastball success, I wanted to reward the readers with a few fun leaderboards.

**Flattest Pitches in 2020 (Highest VAA)**

As you can see, release point becomes very important at the extremes. Also, Tyler Rogers is in his own universe here!

**Steepest Pitches in 2020 (Lowest VAA)**

Biggest Bendiest Bois.

**Sharpest Pitches in 2020 (Greatest HAA Magnitude)**

These are usually the pitches that make you say WOW. Rogers on this list too? Nasty.

**Straightest Pitches in 2020 (Least HAA Magnitude)**

And these are the pitches that make you say… nothing, because they aren’t very visually interesting.

The fact that these lists don’t contain the most star power or line up very well with our mental list of Best Pitchers further supports my finding that VAA and HAA aren’t very important on their own.

Thanks for reading! If you have any questions or comments, you can reach me on Twitter @Moore_Stats.

*Note on Calculating VAA and HAA*

I’m sure some readers are wondering how I was able to use these two metrics on public Statcast data when Baseball Savant does not provide these columns to the user. I have access to college TrackMan data from working for the Cal Poly baseball team, and this data has VAA and HAA. I created a model to predict VAA and HAA with plate location, speed, movement, and release point for the college data set. This model had an R-squared of 0.9999, as approach angles are just a function of these other metrics. I then applied this model to the entirety of the MLB data for 2019.

*Follow P365 Data Analyst Ethan Moore on Twitter! @Moore_Stats*

Follow us on Twitter! @Prospects365

Featured image courtesy of photographer K.C. Alfred and the San Diego Union-Tribune