Thinking About Horizontal Approach Angle

At the end of October, I wrote about the alterations José Urquidy made to his arsenal during the postseason, trying to estimate how much better or worse his pitches might have been given their velocity and movement changes. In that piece, I briefly touched on raw movement changes but mostly relied upon the vertical and horizontal approach angles (along with location and release point changes) of Urquidy’s pitches to try to fully encapsulate their movement. While the concept and value of vertical approach angle is rather intuitive, I figured it would be useful to go into horizontal approach angle here today and have fun with a little exercise.

This post is inspired in part by all that we have been able to grasp in the public sphere when it comes to vertical approach angle. Measuring the up-down angle of a pitch as it enters the zone is largely derived from the vertical movement measures we’re so accustomed to. Steep vertical movement on breaking pitches and “rising” four-seam fastballs in the upper parts of the zone have been coveted for a while now because we know those pitches are associated with whiffs and therefore success. Much less can be intuited by simply looking at the pitches with above average horizontal movement.

Horizontal approach angle takes into account release point, pitch location, and pitch movement to measure left-to-right (or right-to-left) angle as the pitch enters the zone. You can roughly imagine it as drawing one line directly straight ahead from the pitcher’s release and another from the pitcher’s release to the pitch location and measuring the angle between. For example, the line on a zero degree HAA pitch would look completely level from an overhead view, like the fastball here closest to the left-handed batter’s box:

Negative values represent pitches that moved from right-to-left towards left-handed batters, while positive values represent pitches that move from left-to-right towards right-handed batters. While every pitch type has its own examples of extreme horizontal approach, you can picture a sweeping breaking ball coming from the far side of the rubber as a pitch that would register a high HAA value. For example:

This extreme breaker from Aaron Loup came in with an HAA of 7.3, the largest absolute value for a pitch that crossed the plate in the 2021 season. Loup gets a lot of horizontal movement on his pitches, but its useful to see how HAA relates to pitch location, in particular sliders from lefties:

There are sliders with all kinds of movements, velocities, and release points in here, but I hope you can see how HAA for a given pitch type is largely driven by pitch location.

It isn’t hard to see why that Loup pitch works so well, but I can also imagine how it could blow up on him if it were thrown to a righty. We’re all aware of platoon splits but sometimes it’s useful to see them in terms of pitch characteristics. Sticking to the left-handed slider, here’s a look at accumulated run values by VAA and HAA, split by batter handedness:

I’ll get to the two dots in a second but some of the same pitch movements that work so well in left-on-left matchups start to fall apart against righties. I know I’m not showing you exact pitch locations, but the distinctions become clear enough in the approach angles.

This kind of view can be repeated for all manner of different pitch types and platoon splits but I want to stick to this particular case. The effectiveness of the cluster around HAAs of 2.5 and VAAs of -7.5 in particular seems to vanish for left-handed pitchers against right-handed hitters despite being so effective against lefties. In order for a left-handed pitcher with those movements to beat the platoon, they would need to be able to increase their slider’s horizontal approach angle. The differences in this instance can be subtle and visually difficult to track. The two dots above represent two sliders from Alex Wood, one with an HAA and VAA combination that’s effective against lefties and another that’s effective against righties:

It’s hard to see and quite honestly, the differences could be due to variance. Sometimes a pitch just comes off a little sharper or hangs compared to all the others.

There’s a fine line for pitchers to walk when chasing successful profiles. Location certainly plays a part in approach angle, and pitch design has become mainstream across player development, helping pitchers alter pitch movements themselves. But there’s another quick hack to altering approach angles: moving around on the rubber. Not having to come up with a new pitch, or deploy a new arm path, just moving your starting position on the rubber. By and large, no one does this because of how difficult it can be to throw strikes and hit spots while making changes to something that requires as much precision as a release point. But for the purposes of this post, let’s run with it. J.P. Feyereisen, Ralph Garza Jr., and Yusmeiro Petit all shift their release point by over a foot depending on the batter’s handedness (Ben Clemens highlighted Petit in September of 2020).

It’s maybe too much today to try and put a number on the potential value added by changing HAA via release point, but we can at least play around with the potential HAA ranges. I’ve taken the max horizontal release point to either side of the rubber that was thrown by a pitcher of that handedness, shaving off a foot from both to be conservative for pitchers of all sizes. For lefties, one extreme will be a horizontal release point off to the left of the rubber while another extreme is somewhere over the middle of the rubber. Holding everything else about the pitch constant, I’ve recalculated the HAA for both of these new extremes to generate a pseudo-range of possible HAAs by altering one’s position on the rubber.

Altering HAAs like this for big breakers makes a little less sense because without some extra work, it’d be implying that pitch movements are constant to all parts of the zone. That’s not something I am confident saying for all pitch types but I figure it’s safe enough to look at fastballs. Let’s take Robbie Ray’s four-seamer for example:

While Ray already stands to the left side of the rubber (from the pitcher’s perspective), there may be an advantage to him shifting a tad to the right against both righties and lefties given his general pitch location and movement profile. Not that a reigning Cy Young winner necessarily even needs to make this kind of shift, but you can get a sense of the different angles a pitcher can create by moving around the rubber.

We are rightfully obsessed with pitch shapes because they’re so deterministic when it comes to success. Comparing vertical and horizontal pitch movements to league average can tell us a lot and it’s easy enough to do by just looking at Baseball Savant, but our ultimate end is to measure the pitch angles as they enter the zone. VAA is common enough in public analysis, and anyone can see how highly pitchers with “rising” fastballs and sharp breaking balls are valued. At the very least, I hope HAA can catch on in the mainstream as a means of synthesizing release, location, and horizontal movement in a relatively clean fashion.

Owen is a contributor at FanGraphs. He got his start blogging about baseball when he was in college and you can find him maybe talking about something on Twitter @O_dotco.

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Drew Haugen
2 years ago

How are VAA and HAA calculated?

2 years ago
Reply to  Owen McGrattan

My physics is rusty but I think you can get a decent approximation using the velocity and acceleration vectors (at 50 feet) that are available via Statcast search.

First calculate an approximate time to reach home plate, then the velocities in x and and y directions at said time, and from those calculate the horizontal approach angle.

Drew Haugen
2 years ago
Reply to  Owen McGrattan

Thank you!