### An explanation of its definition, function and why we care

## Introduction

This article aims to explain what vertical approach angle (VAA) is, what causes it, and how teams can utilize it for their benefit. Vertical approach angle is the angle at which a ball vertically crosses in front of home plate, measured in degrees. For instance, if a pitch entered the strike zone on a path that was perfectly perpendicular to the ground, it would have a VAA of 0°. On the other hand, a pitch dropped perpendicular onto the plate would have a VAA of -90°. Flat VAA at the top of the zone matters because it is more difficult for a batter to get their bat on-plane to square these pitches up. Pitches obviously drop as they enter the hitting zone due to gravity, so if one can make their pitch’s shape atypical as it approaches the plate, the batter is going to have a tougher time. In this regard, extreme VAA can almost act as a factor of deception.

The following table shows a summary of the vertical approach angles of college pitches in the Power 5 conferences in 2022 (with outliers removed):

Pitch |
Minimum |
1st Quartile |
Median |
Mean |
3rd Quartile |
Maximum |

Fastball | -9.16 | -6.46 | -5.62 | -5.68 |
-4.82 | -2.26 |

Sinker | -9.33 | -6.86 | -6.10 | -6.15 |
-5.36 | -3.05 |

Cutter | -10.13 | -7.60 | -6.74 | -6.77 |
-5.94 | -3.80 |

Changeup | -11.23 | -8.20 | -7.21 | -7.20 |
-6.21 | -3.20 |

Slider | -12.15 | -8.79 | -7.74 | -7.67 |
-6.57 | -3.23 |

Splitter | -11.89 | -9.05 | -8.32 | -8.09 |
-7.11 | -4.50 |

Curveball | -14.29 | -10.28 | -9.06 | -8.84 |
-7.56 | -3.47 |

Note that for the remainder of this article, the only pitches that will be discussed are fastballs, as that is where the greatest gain in effectiveness due to vertical approach angle can be found.

## Does Vertical Approach Angle Matter?

As many in the field have demonstrated, fastballs with flat vertical approach angles thrown at the top of the zone perform better than others. Using a general additive model, one can clearly see the relationship between fastball location, vertical approach angle and swinging strike rate.

It seems that there is a clear pocket of fastball pitch height and vertical approach angle that maximizes the likelihood of a swinging strike. If one can determine how to flatten the vertical approach angle of a fastball, presumably they could take advantage of the apparent swinging strike pocket shown on the visual above by attacking the top of the zone with a flat fastball.

## What Affects Vertical Approach Angle?

In order to determine if this insight is actionable, we must first discern if vertical approach angle is a product of other variables or if it is a pitch feature that can be affected independent of everything else, like pitch location or pitch velocity. The answer is somewhat complicated. As I will demonstrate, vertical approach angle is largely dependent on pitch height, but its pitcher-by-pitcher variance is partially unexplained by TrackMan metrics. By running a feature importance test from the Carat package in R, one can clearly see that pitch height is far and away the most important feature in vertical approach angle:

Using a second generalized additive model, this relationship becomes even more clear:

Note that in the model above, the vertical approach angle metrics are standardized on a scale from 0 to 1, meaning a VAA of 1 is the highest of the sample. Furthermore, the following visual further demonstrates the relationship between pitch height and vertical approach angle:

With an R value of 0.556, there is clear correlation between VAA and pitch height. However, an R^2 of 0.309 indicates that only 31 percent of the variance in pitch height is due to the end height of the pitch. What about pitch release height?

The influence pitch release height has on vertical approach angle exists, but is minimal (R = -0.147, R^2 = 0.022). The graph below exhibits the relationship between pitch release height and VAA:

It seems that lower slots contribute to flatter VAA, but there appears to be too much variance in the release height data itself to yield strong findings. However, decreasing this variance is possible by grouping release point data into four distinct arm slots based on arm angle.

However, even looking specifically within each unique arm slot group, the relationship between release height and fastball vertical approach angle on the pitch-by-pitch level is weak at best. In fact, of the four subgroups, the highest R^2 was for submarine pitchers and it was only 0.028, meaning just 3 percent of the variance in vertical approach angle was caused by release height.

Finally, I performed a linear regression test with available TrackMan metrics – pitch velocity, spin rate, release location (x and y dimensions), extension, zone location (x and y dimensions), induced vertical break and horizontal break – to see if the combination of each can explain a given pitch’s vertical approach angle. The R^2 for this regression model was just 0.445, indicating that 44.5 percent of the variance in vertical approach angle is explained by the TrackMan metrics used in the model. This reveals that while vertical approach angle is largely affected by external factors like release height, it is still somewhat unexplained. Further investigation is needed to determine what accounts for the unexplained variance in the model.

## How can teams use Vertical Approach Angle to their advantage?

Regardless of this finding, college teams should take advantage of the flatter vertical approach angle fastballs by attacking the top of the strike zone.

Updating the visual from the beginning of the article, there is a band of fastball pitch locations that yield an above average swinging strike rate. While this increase is certainly augmented by a flatter vertical approach angle, the advantage exists at seemingly all approach angles, nevertheless.

Does that mean pitchers should increase their usage of high fastballs? It depends. From 2021 to 2022, there was weak relationship (R = 0.216) between proportion of fastballs thrown into the specific zone height band by a pitcher and that pitcher’s overall fastball swinging strike rate:

If pitchers want to increase fastball swing and miss rate, they should consider attacking the top of the strike zone to take advantage of an inherently flatter vertical approach angle. However, this is not advisable for all pitchers. Depending on fastball characteristics like shape, as well as movement profiles and synergies of off-speed and breaking pitches, it might make sense for pitchers not to adopt this strategy. However, this change may be advisable without velocity considerations. In the graph above, velocity does not appear to have any influence on which pitchers succeeded as a result of their location. Furthermore that being said, it is a far more productive strategy than chasing raw spin rate, which is a trend in the industry. In fact, fastball VAA demonstrates a much stronger correlation with swinging strike rate than spin rate alone.

## Conclusion

Fastballs thrown at the top of the zone with a flat vertical approach angle perform significantly better than their counterparts, however, pitch location height is a main factor in determining a pitch’s vertical approach angle. That being said, pitch-by-pitch variation in vertical approach angle is still somewhat unexplained by TrackMan metrics. Perhaps this could be due to unmeasured variables such as weather effects. Regardless, while it is not advisable in every situation, pitchers should flatten the approach angle of their fastballs by throwing them at the top of the zone, or by taking advantage of a combination of their fastball’s inherent pitch traits. in order to increase their effectiveness.

In the 643 Charts Interface, Vertical Approach Angle data is available in the Pitch Description table located in the Pitch Highlighter and Pitcher Arsenal tabs for TrackMan SYNC clients. Pitch-by-pitch VAA info is also available in the Pitcher Arsenal tab by hovering over the individual pitches in the K-Zone.