A Visible Primer on Horizontal Method Angle (HAA)

It’s been nearly two years since I authored a visible primer on vertical method angle (VAA) and nearly three years since I first mentioned VAA right here at FanGraphs. The subject instantly adjoining to VAA — horizontal method angle (HAA) — has been marinating in my thoughts (and in my drafts) ever since.

In an auspicious flip of destiny, whereas revisiting this draft, our beloved Eno Sarris reached out to ask if I had ever revealed something about HAA. He had questions on Brandon Pfaadt — particularly, Pfaadt’s sweeper. A lot was made about Pfaadt’s success this postseason, which could be attributed, in no small half, to his sweeper and the way he weaponized it. (Extra on that later.) I used to be spurred into motion. Thanks, Eno!

HAA: Like VAA, however Not as Cool

Simply as VAA captures the angle at which a pitch crosses house plate vertically, HAA captures the identical horizontally. The pitcher’s launch level (the start of the pitch’s trajectory), the pitch’s last location (its finish), and the pitch’s velocity and acceleration vectors in all three dimensions in the end decide the pitch’s motion by means of house. This motion by means of house consists of the angles at which the pitch breaches the entrance airplane of house plate. As a result of HAA is a perform of those different bodily descriptors, it correlates with them to various levels — and, due to this, can also be type of obscured by them.

For VAA, I prompt adjusting it for vertical pitch location. VAA correlates so strongly with pitch top, it appeared nearly meaningless to me to quote uncooked VAA numbers. A -4.0 diploma VAA? Okay, however did the pitcher throw it on the high of the zone the place VAAs of -4.0 levels are commonplace, or did he throw it on the backside of the zone the place they nearly all the time aren’t? Like all issues baseball and sabermetric evaluation, context is essential.

Location is basically the total extent of the changes wanted for VAA (that, and pitch sort, as a result of method angles range so broadly throughout pitch varieties). HAA is extra sophisticated. Like VAA, we’ll modify HAA for location, besides it’ll be horizontal pitch location, not vertical. It’s additionally crucial to normalize for:

• Pitcher handedness: Horizontal motion patterns are distinctive to pitcher handedness, whereas vertical motion patterns are largely immune.
• Horizontal launch level: A pitcher can range his horizontal launch level just by shifting his beginning place on the mound. If a pitcher throws two “similar” pitches to the very same goal from totally different ends of the rubber, they may naturally exhibit totally different HAAs. (Owen McGrattan mentioned this when he researched HAA two years in the past.) Until a pitcher stands on a crate or digs a gap within the mound, he can not alter his vertical launch level in the identical manner with out dramatically affecting his arm slot and mechanics (and all of the pitch traits that outcome from them).

In Chris Gilligan’s deep dive on Pfaadt, Postseason Hero, he famous that after Pfaadt was optioned and recalled, pitching coach Brent Strom and pitching guide Perry Husband labored with him to regulate his place on the rubber, shifting from the third-base aspect to the first-base aspect. Husband (accurately) asserted that Pfaadt might change the looks — and, thus, the efficiency — of his pitches with out essentially altering their shapes. Husband preached tunneling and efficient velocity. HAA doesn’t handle these subjects, at the least in a roundabout way, nevertheless it rests adjoining to them: by shifting towards the first-base aspect of the rubber, Pfaadt augmented his HAAs and his efficiency.

Horizontal Method Angle Above Common (HAAAA)

Simply as I adjusted VAA for location to create VAAAA, I’ve adjusted HAA for location, handedness, and launch level inside every Statcast pitch sort classification to create Horizontal Method Angle Above Common, or “HAAAA.” Would “Adjusted HAA” have been higher? Perhaps. Is HAAAA spectacularly uglier? Positive. Is it enjoyable to scream on the high of your lungs? Completely.

Each pitch sort may have a unique league-average HAA worth (sliders and cutters have a lot sharper angles on common than sinkers or changeups), however they’ll all have HAAAAs that heart on zero, with “plus” or “minus” values to point above or beneath common for that pitch sort. To wit: listed beneath are 5 pitchers whose common HAAs are almost similar, each with each other and to the 2023 league common (1.3 levels, per my Pitch Leaderboard). HAA alone, one may misconstrue their four-seamers’ HAAs as similar to at least one one other and/or as “common” on advantage.

As you possibly can see, in adjusting for the distinctive combos of launch factors and areas (not on common however for all of the four-seamers they threw in 2023), HAAAA depicts these 5 choices as having considerably totally different method angle profiles.

Let’s Take a look at 4-Seamers First

Earlier than we proceed, please acquaint your self with these legends. These illustrations are offered from the catcher’s perspective.

As a result of we’re working with two laterally-oriented metrics — horizontal location and HAA — we’re burdened with forcing one in all them to adapt to the vertical Y-axis. HAA drew the quick straw. The farther up the Y-axis, the sharper the HAA towards left-handed hitters; the farther down, the sharper towards righties.

The third legend beneath synthesizes the primary two. Actually, I can’t inform you what number of instances I’ve needed to refer again to this. It’s turning my mind to mush. I ought to have it tattooed on my forearm, or possibly on the insides of my eyelids.

So far as color-coding is anxious, pink means sizzling and blue means chilly, for those who can consider it. The metrics that underpin these warmth maps account for ball-strike rely. Swing charges on 0-0 are vastly totally different from swing charges with two strikes, for instance. Pitchers inadvertently create choice bias by utilizing totally different pitches (with various levels of high quality) in numerous conditions. It’s essential to make sure we examine apples to apples. The depth of the warmth represents the magnitude of every metric above or beneath common, impartial of rely.

OK!

For pitchers throwing four-seamers towards hitters of the identical handedness (i.e., righties versus righties), sharper method angles towards the hitter correspond with increased swing charges on the within edge and decrease swing charges on the surface edge. Because the method angle shifts away from the hitter, swing charges drop inside and enhance exterior.

I see two traits:

1. Particularly on the edges of the zone, sharper HAAAAs beget extra exaggerated plate self-discipline outcomes; and
2. Sharper HAAAAs afford themselves wider locational targets. For instance, a four-seamer with -0.6 diploma of HAAAA that’s situated a complete ball’s width off the within fringe of the plate will induce swings at a price roughly commensurate with a median (+0.0 levels) four-seamer instantly on the black. That’s extra swings on would-be balls (and fewer swings on would-be strikes) for pitchers with sharper method angles.

Per MLB’s Mike Petriello, Strom mentioned this of Pfaadt throughout his instances of turbulence:

“Earlier than, he was throwing balls out of his hand which turned strikes,” Strom mentioned in July. “Now now we have pitches which can be strikes that may turn into balls, which is what I used to be attempting to attain.”

That is good teaching! No matter tunneling, efficient velocity, and Strom’s/Husband’s different factors of focus, Strom leverages HAA in a significant manner. He understands the worth of location and (once more, accurately) implies that, by merely altering his launch level vis-à-vis his place on the rubber, Pfaadt can increase his sweeper’s efficiency with out altering his mechanics or the form of his pitch(es).

Within the absence of swings, now we have non-swings that, relying on location, end in referred to as striks. The combos of method angle and site that see fewer swings — sharper HAAAAs towards the hitter on the periphery — naturally produce extra referred to as strikes. Presumably these sharper method angles in these areas create the phantasm of a pitch that’s on a trajectory exterior the zone however cuts again in on the final second. Certainly, generally they really are, and it’s the umpire who has been fooled:

(I’ve lengthy thought this phenomenon, along with excessive VAAAAs on the high and backside of the zone, has implications for catcher framing — a dialogue for an additional day or a better thoughts than mine.)

When it comes to contact on swings, the farther inside, the more serious the hitter’s contact price (higher for the pitcher, in pink), exhibiting a delicate development in favor of sharp angles towards, inside over sharp angles away, exterior:

Flattening swings and call into one determine, we see normal favoritism for sharp method angles away from the hitter, even in weak areas like the middle of the zone:

Additional flattening all the things into referred to as strikes plus whiffs (CSW), in the end the most effective method is to seize referred to as strikes on the periphery with pitches breaking sharply towards from the hitter. This can be a handy and considerably intuitive final result: VAA(AA) is a swinging-strike weapon, HAA(AA) is a called-strike weapon.

This, in fact, focuses solely on plate self-discipline and neglects hitter contact high quality, which is an important part. When incorporating hitter contact high quality, we see just a few fascinating traits: the locational margin of error on the periphery is dramatically smaller, whereas it’s a lot wider inside. In actual fact, sharp method angles towards the hitter which can be situated healthily inside are particularly efficient:

In different phrases, there’s a time and place for chasing strikes, particularly referred to as strikes, which come far more simply than swinging strikes — however hitter batted ball outcomes are markedly inferior away from the areas the place these referred to as strikes come best. Not less than for four-seamers, largely we see that extra intense HAAAAs don’t precisely translate to superior efficiency. There are obvious plate self-discipline positive aspects with sharper HAAAAs, however they’re type of rendered inert by the volatility of batted ball occasions.

What About Non-Fastballs?

Slightly than taking a look at different pitch varieties individually, I merged all of them into one warmth map. We lose the granularity of every pitch sort’s quirks and nuances however obtain a broad understanding of method angles locationally — which, in the end, are usually not distinctly totally different from four-seamers anyway. Right here’s righties versus righties for all pitches:

As with four-seamers, the interior edge is king, particularly for pitches with ample arm-side. There are exaggerated results for ample glove-side reduce off the periphery, too, extra so from this all-pitch perspective than for four-seamers alone. Having the ability to generate above-average outcomes on pitches exterior the zone? That’s useful! That margin of error for sweepy pitches off the periphery, nonetheless, is visibly smaller.

The warmth map towards left-handed hitters is successfully the identical, simply rotated 180 levels:

As a bonus, to carry it again to Pfaadt one final time, right here’s efficiency from righties towards all hitters for sweepers and sliders. There could also be some light bolstering results from sharper HAAAAs, however location prevails at first.

TL;DR

Crucial HAAAA results are proven for method angles breaking sharply towards the hitter on the surface edge (by way of CSW and referred to as strikes) and likewise on the within edge (by way of weak contact high quality). These positive aspects can’t be realized with out pretty well-executed location, though, like VAAAA, excessive HAAAAs make command much less essential. That, I feel, would help the argument for capital-‘s’ Stuff over command. However location is essential for HAAAA, arguably far more so than for VAAAA.

Reminder

By design, that is a very simplistic train. Binning and averaging, whereas loads illuminating in its personal proper, is wildly primitive in comparison with regression evaluation or machine studying. There are results proven right here that in a broader, extra rigorous evaluation could be proven to be over- or understated.

I have to additionally reiterate that this evaluation critically lacks the contextualizing advantages of many different pitch traits (Though HAA/AA does inherently account for velocity, acceleration, launch level, and site. In its protection, that’s truly plenty of issues.) Like all analysis effort in baseball, a person variable — on this case, HAAAA — ought to most likely by no means function a sole metric for evaluating a pitch. Let it complement or be supplemented.

Making the Changes to HAA

HAAAA reveals a lot smaller location-adjusted variations than VAAAA does. Whereas the the flattest (steepest) pitches could be as much as 1.5 levels and even 2.0 levels flatter (steeper) than the common pitch of their class, the runniest/sweepiest pitches hardly ever surpass 0.5 levels of extra HAA. It’s doable that if we modify HAA by one thing extra broadly outlined, like pitch class (“fastballs”) as a substitute of pitch sort (“four-seamers,” “sinkers”), then our magnitudes of HAAAA would really like enhance. I’m unsure how far more readability it might present us.

VAAAA is basically a weapon for fastballs however has use circumstances for different pitch varieties. HAAAA could have extra utility for breaking (and off-speed) pitches given their motion profiles. Once I modify HAAAA for horizontal location (along with pitcher handedness and horizontal launch level), I achieve this by pitch sort. I need to know the way sharp a fastball’s method angle is in comparison with different fastballs. That’s probably not as useful for breaking pitches, not simply because breaking pitches range so broadly of their motion profiles but in addition as a result of breaking pitches now undertake so many various names and terminologies. And albeit, that’s nice. I help that effort fully. Name a pitch no matter you need to name it to greatest describe its motion traits. However that makes it tough to check, for instance, sliders to sliders. A few of these sliders are referred to as sweepers now. A few of these sliders are referred to as sliders however are literally sweepers. A few of these sweepers are literally sliders. Some are slurves! And a few are tiny hamburgers. Who even is aware of anymore. Taxonomy is an actual problem, although, and it might constrain this evaluation (along with affecting the “changes” made on the premise of the aforementioned pitch sort classifications).

The Stuff-Versus-Command Wars

Accentuated HAAAAs can typically fail in unhealthy areas the place VAAAAs may thrive. Why?

To me, the reason is pretty intuitive. A hitter’s swing has a a lot wider margin of error laterally than it does vertically. Horizontally, an inch off the barrel most likely nonetheless leads to contact, simply inferior contact. In actual fact, with a miss of a number of inches, a hitter can nonetheless foul one off and even luck right into a base hit. Then again, a one-inch miss vertically is, at greatest, a foul tip; at worse, it’s a straight-up whiff. And a whiff, on common, is unequivocally worse than inferior contact. This helps clarify not solely why elite VAAAAs (greater than elite HAAAAs) play up in unhealthy areas, however why elite VAAAAs play up higher than elite HAAAAs usually.

Certainly, HAAAA stays depending on location. There’s a chicken-and-egg scenario right here. Stuff is a greater predictor of success, a lot to the chagrin of old-school varieties and innumerates. For HAAAA, although, stuff can’t exist with out command to some extent. It’s solely with some semblance of fine location — the strike zone’s edges, particularly — that HAAAA can play up. Even then, location shoulders most of that load. However good HAAAA-related stuff broadens the pitch goal, reduces the locational dependency, buys extra wiggle room. That’s, good HAAAA-related stuff elevates a command-oriented profile.

Pitch Modeling

Earlier than being employed to the Rockies’ R&D division, Ethan Moore wrote a seminal article on method angles. He present in modeling pitch traits that HAA demonstrated exorbitant run prevention results, though he admits “now we have to take this with a grain of salt.” It’s doable that making use of changes to HAA (past together with location, launch level, and so on. as unbiased variables within the mannequin) may yield a extra cheap (i.e., smaller) coefficient for HAA, particularly as HAAAA yields a a lot narrower distribution of doable values.

Lastly…

I apologize if I missed (and subsequently didn’t cite) your analysis on HAA. A cursory Google search of “horizontal method angle” turns up possibly half a web page price of posts earlier than devolving again into posts about vertical method angle. I’ve seen people from Driveline and Tread evoke VAA and HAA on Twitter, however no analysis got here up. If I’ve missed something, please be at liberty to drop it within the feedback.

Editor’s notice: Subsequent to publication, the graphics on this piece had been up to date to appropriate an earlier error.