In the first knuckleball game thrown at Coors Field in 16 years, Matt Waldron hit home plate umpire Bill Miller right between the nuts.
No one — not Waldron, not his reliever Kyle Higashioka, not Miller — just knows where the ball is going. Despite Higashioka often (and understandably) struggling to track the ball’s movement throughout the night, Waldron pitched a career-best performance, allowing just one run over six innings.
Perhaps the most striking part of his performance was the setting. Since 2008, knuckleballers have fled Coors Field, which sits 5,200 feet above sea level. Conventional wisdom dictates that high-pitched knuckleballs are a bad idea, as Cy Young-winning knuckleballer RA Dickey told Dave Krieger back in 2012.
“It’s hard to throw at high altitudes because there isn’t much moisture that the ball can withstand,” said Dickey. “At sea level, let’s say in New York, for example, if I throw an average knuckleball, it’s still going to move, it may not move much or much. If I throw a mediocre knuckleball in Colorado, it’s going to be a BP fastball up the middle that I’m going to have to block, or I’m going to just put my glove up so the umpire throws me another ball. because that one just went 450 meters.”
After Waldron’s performance, I couldn’t help but question the conventional wisdom. Maybe, if you throw it right, the knuckleball works better at Coors than anywhere else. But is it possible to identify pitchers who can avoid throwing average knuckleballs? And if so, will the Rockies, who are notorious for their inability to put together a quality pitching staff, simply build a rotation full of these knuckleballers?
The most likely answer to both questions is “no.” But during my investigation, I discovered something unusual: We know a lot less about the knuckleball than we thought.
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At Coors Field, every pitch is slow. Part of this is because there is less drag, or air resistance, on the ball; part of it is due to Magnus’s diminished power at altitude. Utah State mechanical and aerospace engineering professor Barton Smith, famous for his work on wake dynamics, describes the Magnus effect as “the tendency of the ball to spin in the direction the ball is going.” A topspin curveball drops more than it would if only gravity were acting on the ball, while a four-seam backspin drops slightly.
Because the Magnus effect is proportional to air density and the air density at altitude is low, bad pitches lose a bit of their bite at Coors Field. So, one theory is that the ideal Rockies pitcher wants to limit the motion caused by spin in their pitches.
Pitching analyst Lance Brozdowski discussed this in a recent post about Ryan Feltner, whose name hovers around zero inches of horizontal and vertical movement. As Lance wrote, “This is the type of pitcher the Rockies need to get out of every corner of their rotation. Velo, minor situations, moderate command.”
I had another idea: The Rockies should put knuckleballers all over the rotation. My first thought was that although knuckleballs may have more total movement than any other pitch, they have very little. perfect spin. A good knuckleball makes about one rotation during the flight of the ball. So, I reasoned, knuckleballs would be less vulnerable to Magnus effects for any given pitch type, and the motion profile would change at least in height relative to “spinnier” pitch types.
Sadly, I was wrong. I emailed baseball expert Alan Nathan, who explained to me that no matter what type of pitch, it will travel at 82% of its pitch profile.
“All aerodynamic effects (drag, motion, etc.) are directly proportional to air density,” Nathan wrote to me. “In comparable atmospheric conditions, the air density at Coors is about 82% of that at sea level. That means only 82% of the movement on any pitch is due to aerodynamic effects, whether it’s due to spin or seams (the latter is responsible for knuckleball movement).”
Our limited data proves this. In the chart below, it appears that knuckleballs thrown at Coors moved about 80% as well as balls from Waldron at sea level:
But I wasn’t completely satisfied. Even if knuckleballs are equally affected by wind resistance factors, there will still be more completely movement than any other type of pitch in pitch – assuming the pitch is thrown with low rotation. Waldron himself told the media after this start that of the five pitches in his asernal, he felt that the knuckleball was the most affected in the walk.
“I feel like it hasn’t changed,” Waldron said.
If pitched well – and here “throw well” is defined as maintaining a spin rate of about 100 rpm, or one change during the ball’s flight – perhaps Waldron’s performance could be the model for the next great Rockies starter. Reduced movement due to the effects of altitude may even help dictate pitch; as Adam Ottavino said in a recent episode of Rates and Barrels, he felt more confident throwing his big bendy sweeper at Coors because the motion profile was so predictable.
“It was easy for me at Coors to get involved,” Ottavino said.
But how can the Rockies identify knuckleballers who are good at generating low spin rates? This is where things start to get confusing. I tried to test this with Waldron, and the spin levels didn’t make much sense.
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For more than a century, the knuckleball has been described as dancing, fluttering, spinning, or wobbly on its way to the plate, deviating slightly before landing in the catcher’s glove. This effect was first attributed to airflow over an uneven baseball surface in the 1975 Watts and Brown paper “Aerodynamics of a knuckleball.” In 2016, researchers in France identified other aerodynamic effects that contribute to the fragility of a slow-spinning ball. (The details are off the top of my head, but the important note is that they are not just seams; other sports balls also have knee effects.)
In 2011, Alan Nathan obtained raw tracking data from four different games started by Dickey and Tim Wakefield. Using data that captured the coordinates of the knuckleball at about 20 different points in space, he calculated that the amount of deviation from the knuckleball’s flight path is minimal; The maximum deviation, he found, is equal to 1.3 centimeters, or about one-sixth the diameter of the ball.
The knuckleball moves the most – and therefore is the most unpredictable – when it spins as little as possible. As Aguirre-Lopez et al. wrote in their 2017 paper “A phenomenological model of knuckleball aerodynamics,” “If the ball spins at a low enough frequency (<50 rpm) to remain stationary, the lift force will be changing over time and a more erratic trajectory will be created." .”
If low frequency spin leads to “mysterious tracking,” that would suggest the Rockies want to identify pitchers who can repeatedly throw slow-spinning knuckleballs. But there’s a big obstacle to doing this analysis: The unpredictable trajectory makes it difficult to reliably capture how much knuckleball spin.
The first clue that our understanding of knuckleball spin may be askew comes from a paper published earlier this year titled “Discrepancies between reported rates of knuckleball spin and force” from Aaron Hoskins, a mechanical engineering professor at Fresno State. Hoskins analyzed the “accuracy of recorded pitches on knuckleballs” for the first time in the Statcast era and found that recorded turnover rates “were not consistent with knuckleball movement statistics.” Hoskins had some ideas about the discrepancy, but no concrete answers. So I went straight to the well.
I emailed Tom Tango, Senior Data Architect for Major League Baseball, asking for any help he could provide. He copied Clay Nunnally, a data scientist at MLB, who provided some very useful information.
“Hawk-Eye takes a bunch of different images of the seams on the ball, then tries to find the spin solution that best matches the seam set,” Nunnally wrote. “However, theoretically, a ball with zero spin looks like a ball with 3000 rpm spin when the ball spins back to its original (apparent) position between shots. There are ways to break the spin ambiguity, but they don’t always work.”
This “spin ambiguity” is created from the number of different images that Hawk-Eye uses to match the stitch set. The exact number of images is unclear. In a presentation at the 2020 SABR Analytics Conference, Nunnally said Hawk-Eye uses “about 20” frames; in a follow-up email, he told me it was now “more than 30” but declined to elaborate further.
Regardless of the exact number of frames, “spin ambiguity” exists. Let’s assume that Hawk-Eye is currently training its algorithm on 40 different frames, or an image every 13.5 milliseconds during the flight of an average Matt Waldron knuckleball. In knuckleball time, 13.5 milliseconds could be an eternity. If we don’t have a true sense of the full flight of the knuckleball, then how much do we really know about the motion properties of the pitch? Could the tone be moving more than Nathan’s research suggests?
“More data on any problem helps,” said Hoskins, the Fresno State professor. “There is a chance that we will not hold all the disciplines. We definitely have problems with spin.”
Ironically, Hawk-Eye may have the answers. Their advanced cameras are capable of taking pictures at 300 frames per second, or a picture about every three milliseconds. With the average Waldron knuckleball traveling at 77 mph, that would mean the hawk-eye cameras could take about 150 different images of the ball in flight. With almost five times more images, we will certainly have more clarity.
When I asked Nunnally why Hawk-Eye uses fewer frames of spin resolution, he told me that “in general, there are some reasons to use less data compared to the larger amount possible, in some applications.” Left to guess at those reasons, one would think the explanation is straightforward: Most pitches maintain a constant spin axis and therefore do not require hundreds of frames to find a spin solution. Before Waldron’s debut last season, there were only 57 knuckleballs thrown by actual knuckleballers (ie not position players) since the start of Hawk-Eye’s partnership with Statcast. The concern for knuckleball spin rate – so far as it really is a problem – is a relatively new phenomenon.
For now, the knuckleball is still an enigma, an unknown at the heart of a game that can basically measure everything. Given all that, who’s to say if the Rockies should only throw knuckleballs?
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