The Physics of the Knuckleball 87
snoop.daub writes "R.A. Dickey, pitcher for the New York Mets, has been in the news this week after two dominant pitching performances in a row, holding opponents to one hit in each of the games for the first time since Dave Stieb did it in 1988. He has taken over as the league's only knuckleball pitcher after Tim Wakefield retired last season. But just what is it about the knuckleball that makes it hard to hit? Conventional wisdom has it that the lack of spin on the knuckleball causes it to move in completely unpredictable ways, even changing directions in mid-flight. In the last few years, there has been a lot of good science done to understand baseball pitch trajectories, and a few months ago Prof. Alan M. Nathan showed that knuckleballs aren't really so different from other pitches. It turns out that the same 9-parameter equation that can be used to describe other pitch trajectories applies just as well to the knuckleball. The difference appears to be that, like in a chaotic system, knuckleballs depend sensitively on the initial conditions, so that small changes can cause randomly different forces at the start of the pitch which determine the resultant trajectory. Much of this and similar work depends on the Pitchf/x tool, which has recorded the complete trajectory, spin angle and spin rate of every MLB pitch since 2007! Baseball really does have the best sports stats geeks."
Wait, what? (Score:3, Insightful)
Guy 1: We have amazing technology that allows us to know EXACTLY what happened.
Guy 2: Awesome, so we don't have to rely on humans in those really close calls.
Guy 1: Well...not really...
Guy 2: ?
Guy 1: We're only going to use it to record pitches...
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Awesome, so we don't have to rely on humans in those really close calls.
What... you mean like a "let's go to instant replay" type close call? As in "we think he struck out, but we'll have to go back and analyze each pitch to be sure"?
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no, you don't need to "go to replay", the system knows faster than the umpire if it's a ball or strike. You could simple put some lights up to show the count immediately after each pitch.
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no, you don't need to "go to replay", the system knows faster than the umpire if it's a ball or strike.
How does it know that, exactly? It says the system has recorded "the complete trajectory, spin angle and spin rate" of the pitch. How does it know where the strike zone is?
Please tell me you're not one of those who wants to turn baseball into American football, where the whole thing is an interminable, mind-numbing exercise in replays, computer graphics, satellite-based ball tracking systems, and submarine-mounted sonar? I like my sports to be about human beings. In baseball, umpires determine balls and str
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Awesome, so we don't have to rely on humans in those really close calls.
What... you mean like a "let's go to instant replay" type close call? As in "we think he struck out, but we'll have to go back and analyze each pitch to be sure"?
Baseball doesn't use instant replays.
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Actually there are a few things they do use instant replay for now in cases where the call is not clear such as determining if a hit ball is a home run or not.
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Most of the time it's not hard to figure out but occasionally the ball hits just barely above the home run line and bounces back on the field or it's difficult to tell if it was just inside the foul pole or not. That's where they use it, not for every home run, just ones that can be disputed.
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You don't watch a lot of baseball, do you?
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There's a difference between understanding what the ball is doing and playing the game as it happens. Recording what's happening is good for umpires to be able to view their mistakes after the game and correct their misinterpretations over time, but like many (most?) other baseball fans, I don't want it affecting the game as it happens.
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I favor umpires that have a tighter definition of delay of game. It's one thing to pin a runner on base, but quite another to do that five times in a row.
I know that MLB is trying to not let it get out of hand, limiting its use to post-season and only certain kinds of calls. I understand what they're trying to do, but I still don't think it's appropriate in baseball.
And yes, the sig is a reference to GPB. :)
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but like many (most?) other baseball fans, I don't want it affecting the game as it happens.
I'm exactly the opposite. For me the refs in any sport are an annoying distraction when they make wrong calls, and calling of balls and strikes is over 90% of the game in baseball. There's really no reason computers can't take over for balls and strikes except for tradition.
Re:Wait, what? (Score:5, Insightful)
Beyond the fact that many baseball fans LOVE to disagree with the ump, part of the game includes pitcher, catcher, and batsman working out where the ump is seeing the strike zone that day. Meanwhile, the pitcher tries to slowly expand the ump's strike zone, the catcher tries to frame the pitch as a strike and the batsman tries to crowd the plate and shrink the strike zone. The pitcher then tries to brush the batsman back. All of that gameplay is lost is a computer and cameras call the balls and strikes.
Beyond that, how will the computer decide if the batsman swung or not? We don't even have official rules for that.
I don't think it would really be the same game without the ump making the call.
What I do think is good is the umps themselves reviewing footage, their call, and what the computer says during the off season.
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Beyond the fact that many baseball fans LOVE to disagree with the ump
They'll still be there to call tags and whatnot, just not there to impose themselves on every pitch.
All of that gameplay is lost is a computer and cameras call the balls and strikes.
I don't consider gaming the umpire a good part of the game. The vast majority of baseball comes down to the pitcher/hitter duel, and I'd prefer the true skill of those dynamics to constant interference by umpires. It really kills me when a good pitch is spoiled by a bad call, or vice versa when a good eye by the hitter on a ball is spoiled by the ump.
Beyond that, how will the computer decide if the batsman swung or not? We don't even have official rules for that.
Then let the umpire decide. Unlike balls and strikes, it's
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Then let the umpire decide. Unlike balls and strikes, it's a fairly rare call anyways.
Every time the ball misses the strike zone, it comes down to swing/no swing. The call happens several times every inning. Gaming the umpire is really just an extension of the pitcher gaming the batsman. The pitcher wants to catch him looking, so he has to distort his view of the zone.
You can't get the ump out of it anyway. Baseball is nearly unique in it's reliance on the ump. In many 'odd' cases that actually come up fairly often, it comes down to what the ump believes should/would have happened. That is w
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Every time the ball misses the strike zone, it comes down to swing/no swing. The call happens several times every inning.
I think you're trying to force a point that isn't relevant. It's perfectly obvious the vast majority of the time when the batter swung or not, and as a critic of the umps, it's not something that bothers me, unlike the nearly constant aggravation of balls and strikes.
Gaming the umpire is really just an extension of the pitcher gaming the batsman. The pitcher wants to catch him looking, so he has to distort his view of the zone.
The umpire is there to enforce the rules, and ideally inserts himself into the game in a 100% correct manner. I like the pitcher/hitter psychological duel. I do not like the umpire getting in the way of that.
You can't get the ump out of it anyway. Baseball is nearly unique in it's reliance on the ump.
Actually, it's just the opposite. Ba
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Ah, I see. You are not a fan of the sport and so may not have an understanding of it's more subtle elements. You don't seem to want that to change so I'll leave you in peace.
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Ah, I see. You are not a fan of the sport
Ah, the "No true Scotsman" fallacy. I followed baseball a fair amount, but gave it up because in the end it was too aggravating.
and so may not have an understanding of it's more subtle elements.
Ah, the argument by authority fallacy. You told me the subtle elements you liked, and I told you I explicitly disliked what appealed to you. It's a difference of opinion.
You don't seem to want that to change so I'll leave you in peace.
Good, because I'm tired of replying to your weak arguments.
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You said:
I almost never watch baseball, though, because the pace of the game is slow, and the major compelling factor that would make it tolerable, the pitcher/hitter duel, is ruined by the umpire's inconsistent strike zone.
Why would I think that someone who almost never watches the game, who finds the game to be too slow, and considers it intolerable because the only thing they like about it is ruined to be a fan? You don't seem to like anything about it!
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I like the pitcher/hitter duel, which I've mentioned several times and is the meat of the game. The other action is fine, too, but it only comes in spurts. While it's true I'm not a current fan, it's not because I didn't give it a try or from lack of understanding.
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Beyond the fact that many baseball fans LOVE to disagree with the ump, part of the game includes pitcher, catcher, and batsman working out where the ump is seeing the strike zone that day. Meanwhile, the pitcher tries to slowly expand the ump's strike zone, the catcher tries to frame the pitch as a strike and the batsman tries to crowd the plate and shrink the strike zone. The pitcher then tries to brush the batsman back. All of that gameplay is lost is a computer and cameras call the balls and strikes.
Where does batsman find the time to play baseball? I'm pretty sure Commissioner Gordon doesn't moonlight as a place kicker.
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What I do think is good is the umps themselves reviewing footage, their call, and what the computer says during the off season.
I agree that umps and their errors are part of the game and I agree with the umps reviewing their calls (I would say post-game, though, instead of post-season), but I would like to take it one step further and give them a per game bonus and subtract from it for every blown call they make.
I would also like to see those statistics published, just like the players', whose stats are based on those calls. Then, we would have hard numbers to yell at the umps and we could stop with the more generalized insults
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More likely I would just find the game less interesting. Or, perhaps it would just degenerate into a new ruling on the official strike zone every year and everyone would start losing interest.
Certainly it would make sandlot games less interesting since they could never be the same. It could even go so far that eventually a sandlot league where an umpire is used would become more popular than the 'professional' league or where people such as me actually WOULD indeed suggest doing away with the machine and le
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RE: Renex ... tradition and COST are the main reason for umpires. It's why Baseball and Soccer (football or fóótbaal or whatever) are two of the most popular sports in the world: Low barrier of entry.
What exactly do you need to play soccer? One ball among 20-or-so players ... and maybe some rocks or backpacks or whatever to use as goals. Likewise baseball (or stickball for the N.Yarkers) can be played with 1 stick/bat and 1 ball between dozens of kids, and whatever random junk to use as bases
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Pitch count doesn't matter as much to a knuckleballer because they don't throw nearly as hard as a fast ball pitcher. They couldn't hold on to the ball reliably if they tried.
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can be played with 1 stick/bat and 1 ball between dozens of kids
Let's not forget the bad ass milk container glove.
batters don't just take walks or run up your pitch coun
Pitch count? They're knuckleballers. They can throw 18 innings if they wanted. Hell, I'm going to be 34 this year, and I still hold out hope that I might be able to develop a knuckleball and make the bigs.
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can be played with 1 stick/bat and 1 ball between dozens of kids Let's not forget the bad ass milk container glove.
And ghost-man-on-second if you don't have enough kids.
Naming the followers (Score:5, Funny)
Back in the late 80's/early 90's the Mets had a very successful pitcher named David Cone, and his fans were known as Coneheads... and sometimes dressed the part.
Now for R.A. Dickey.... hm.... I think we'd better focus on his pitching style instead of his name. Let's go with Knuckleheads.
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Sorry, already taken for fans of Chuck Knoblauch. I'm sure Mets fans don't want to go with dickheads so how about penismouths?
Some great quotes on the knuckleball:
Bob Uecker on how to catch it: Wait till it stops rolling then go pick it up.
Jimmy Cannon on what a knuckleball is: A curve ball that doesn't give a damn.
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They're Raddies or radishes.
Hockey goalies (Score:4, Insightful)
I'm a hockey fan and it's not unusual to see goalies get beat by what seem like simple shots. Someone skates over the blue line into the offensive zone and shoots an average wrist shot towards the goal. It's a routine save for the goalie under normal conditions... a really low percentage shot. But if the shot gets tipped, even ever so slightly and even a long ways away from the goalie, the goalie can have trouble with it.
It's because the goalie reads the shot not by plotting the course of the puck but by seeing so many shots that by the motion of the shooter's stick and body language, he already knows where the shot is going and reacts accordingly. A tip, even a foot away from the shooter's release, turning a 20 foot shot into a 19 foot one, throws it all to the wind. You'd think it would give the goalie enough time to make the save but he's already moving to the top right corner before he realizes is going bottom left.
I'm sure it's the same in baseball. Batters don't have time to judge the ball's trajectory itself so they rely on the pitcher's delivery to tell them where the pitch is going. When a knuckleball comes their way, there's nothing to read because even the pitcher doesn't know where it's going.
Re:Hockey goalies (Score:4, Interesting)
Also the reason why a good change-up can be effective; looks like a fastball, moves 10-20 MPH slower.
Re:Hockey goalies (Score:5, Interesting)
I'm sure it's the same in baseball. Batters don't have time to judge the ball's trajectory itself so they rely on the pitcher's delivery to tell them where the pitch is going. When a knuckleball comes their way, there's nothing to read because even the pitcher doesn't know where it's going.
You're close, but not quite right. Batters can pick up some aspects of the pitch from the delivery, especially at lower levels of play, but pitchers try very hard to avoid "tipping their pitches" in such a manner. So in the majors, what batters really look for is the spin of the pitch, judged by looking at the conveniently bright red seamsw. Since major league pitchers throw balls with 2000+ RPM of spin on them, the seams will mostly be a blur, except for key exceptions. For example a 2-seam fastball will appear to have two pinkish vertical stripes on it. On a sinker, those stripes will be tilted. Breaking balls look like they have dots (as the axis of rotation passes through or near the seam), with the dots in different places depending on the type of pitch. Of course, you only have about 200 ms to pick up the seams. On a 3" diameter circle. From fifty feet away. That sharp vision and quick thinking is probably the number one element in setting apart top hitters.
On knuckleballs, there's nothing to read. Which means that major league hitters need to forget about their standard approach. All their skills and practice count for nothing, and they're forced to just hack away at it the way you or I would (albeit with a swing that won't draw laughter from the crowd).
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Despite all the first post nonsense, dupes, fanboyism, and a few other such annoyances that seem to be endemic to slashdot in recent years, I will continue to come here specifically for this kind of post. I think it represents the best of slashdot and the best of what the internet can be. Thanks for taking the time to post it artor3 and I hope you check back and read this.
I'm a baseball fan but even if I wasn't I'm pretty sure I'd find your post great reading.
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I remember hearing once that the reason why Ted Williams had such an unbelievable hitting ability was that he could see lace rotation on incoming pitches with better fidelity than other batters. It had something to do with his eyes' "refresh rate", which was also fast enough that he had trouble watching movies because he could see the individual frames flashing by. Not sure if it's true, but makes for a great story.
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After reading the technical paper [illinois.edu] that the author will be presenting next month I learned that the direction and magnitude of the break on a knuckleball is in fact randomly distributed within a range depending on the pitcher. The pitcher literally doesn't know what the direction or size of the break will be when pitched at a certain speed inside of a larger range than a non-knuckleball pitch.
Mod down; wrong (Score:5, Informative)
Batters don't have time to judge the ball's trajectory itself so they rely on the pitcher's delivery to tell them where the pitch is going.
Yeesh. You're just plain wrong. At least you were nice about it. But you're just wrong.
Hitters watch the pitcher's release point and try to "pick up" the ball as soon as it leaves his hand. If a hitter doesn't visually lock onto the ball as soon as it leaves the pitcher's hand, he probably won't hit it--at best, he'll foul it off.
Pitchers generally try to maintain a consistent release point; it makes it easier to develop fine control and helps prevent injury. The release point can be the same, yet the pitch location can be all over the place.
I haven't even mentioned spin yet. A four-seam fastball and a two-seam fastball behave very differently, yet they begin the same, coming straight out of the pitcher's hand with backspin. If the hitter doesn't read the spin, he probably won't hit it well. A changeup or a splitter are even more different than those pitches, yet they also come straight out of the pitcher's hand with backspin. The hitter must see the seams of the ball as it's in flight in order to recognize the pitch type and be able to estimate its trajectory. And I haven't even mentioned curveballs and sliders yet.
I'll never forget the first time I recognized a slider while hitting. I remember seeing the dot right after the ball left the pitcher's hand. I had seen enough of them on TV replays while watching games that my mind recognized it quickly, and I knew the pitch would be a ball, low and away. If I hadn't seen the dot, it would have looked like a fastball down the middle, and I would have swung and missed. And all of that visual and mental recognition and processing has to happen in a fraction of a second. It was exciting! (If only I had had my vision corrected years earlier! I didn't realize I was capable of seeing the spin on the ball.)
As for knuckleballs, it's an exaggeration to say, "even the pitcher doesn't know where it's going." Not that a pitcher has fine control over it, but if it were as wild as you suggest, it would be useless. If you can throw a baseball already with decent accuracy, you can try a knuckleball for yourself and see. It's not that hard to get it in the strike zone if you're a decent pitcher.
Yes, I used to play baseball, both pitching and hitting.
(As an aside, while you might know a lot about hockey, please don't speculate so authoritatively about something you don't actually know about. It's a shame to see a post that's just plain wrong modded +5 Insightful.)
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As for knuckleballs, it's an exaggeration to say, "even the pitcher doesn't know where it's going." Not that a pitcher has fine control over it, but if it were as wild as you suggest, it would be useless. If you can throw a baseball already with decent accuracy, you can try a knuckleball for yourself and see. It's not that hard to get it in the strike zone if you're a decent pitcher.
Yes, I used to play baseball, both pitching and hitting.
I used to play too, but I was the catcher on my high school team. I don't disagree with anything said about reading pitches: when a prima donna pitcher throws whatever he feels like instead of what you call, it's damn hard to get a glove on the ball, let alone a bat. So we learn to watch the wind up, the release, and the seams to know where the ball is headed. Once you know a pitcher well enough you can even guess where and how far a pitch will break almost before it leaves his hand. Knuckle balls are a com
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In fairness to SoupGuru, he wasn't just plain wrong about how it is not the trajectory that is being processed by the batter but indicators as to what the trajectory will be. SoupGuru simply guessed the wrong indicators. From the hitter's perspective, the lack of an identifiable spin on a knuckleball certainly changes the heuristic that they depend on to hit successfully..
After reading the technical paper [illinois.edu] that the author will be presenting next month I learned that the direction and magnitude of the break o
stats geeks (Score:3, Informative)
Baseball really does have the best sports stats geeks.
Meh. You've clearly never met any cricket fans.
Just ask one to describe the Duckworth-Lewis method of calculating scores for a rain-interrupted match.
Duckworth-Lewis System (Score:2)
Hint for curious, it involves taking a hair from each player on the field and burning them so that the oracle can divine a prophesy of how the match *would* have gone, and deciding the score accordingly.
(It actually uses detailed Databases of previous performances of teams and players, but for all effective purposes, you might as well burn the hair)
I am a Pakistani fan, and I remember one of our Coaches, Bob Woolmer (may he rest in peace!) who was know as Mr. Laptop, since he was always on the laptop, alway
Staticians rejoice! (Score:2)
As if there wasn't already one statisticians' wet dream on the form of D/L, here comes another stats-gasm inducing system, which called the VJD.
India tried to enforce it internationally, but it was turned down in the recent meeting.
http://en.wikipedia.org/wiki/VJD_System [wikipedia.org]
Stats (Score:3, Interesting)
That's because if you took the stats out of baseball, there'd be nothing left.
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No, you still have to make decisions on your roster
Mets have two top notch pitchers but they are still barely average in the total standings
nice analysis, now try hitting one (Score:3)
Re:nice analysis, now try hitting one (Score:4, Interesting)
Actually, that's not what he said [baseballprospectus.com]:
So, what has this analysis taught me? For an ordinary pitch, the trajectory follows a smoothly curving line approximated by nearly constant acceleration. For a knuckleball, rather than a line, imagine that the trajectory is confined to lie inside a tube which itself follows a smooth curve. However, the ball is otherwise free to flutter and zig-zag within the confines of the tube. With that picture in mind, the analysis I have presented shows that the diameter of that tube is very small, on the order of a few tenths of an inch at most.
...
The smoothness conclusion appears to contradict the popular belief that knuckleball trajectories are erratic and often experience abrupt changes of direction. Let me speculate that this belief is the result of the randomness of movement, both in magnitude and direction, giving rise to the perception of erratic behavior. We have all seen instances where the catcher and pitcher get their signals crossed, and the catcher has to lunge for the ball at the last moment. The catcher expects a certain movement, and the pitcher throws something with different movement. With the knuckleball, no one really knows what movement to expect, so it is not surprising that the catcher has some difficulty cleanly catching the ball and that the batter has even more difficulty hitting it.
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Yeah, I think what he means is that the tube can point anywhere but that nevertheless the tube itself is a nice and smooth trajectory. Whereas, putting a spin on the ball makes it much more likely the tube will point in one of a few specific directions.
If you've taken differential equations, I imagine the spin makes the trajectories narrow to a few sinks but the knuckleball does not. Many, many curves are valid.
-l
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Well, considering there's only one guy throwing them, my guess is that neither has anyone here.
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He's not the only person on the planet throwing knucklers. I played slow-pitch softball with a guy that could throw a knuckle-softball; we'd be tossing a ball to warm up and he'd drop a knuckler in there. Seeing that coming made you just want to jump out of the way (or fire a fastball back at his knees! :) ).
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Guess again after reading the summary, which states that while the conventional wisdom on the difficulty of hitting knuckleballs is wrong, there still is a reason why they're harder to hit.
Been there, done that! (Score:5, Informative)
Six years ago, from a professor at my alma mater: http://farside.ph.utexas.edu/teaching/329/lectures/node45.html [utexas.edu] This being slashdot, I didn't RTFA but the author seems to come to the same conclusion that Fitzpatrick did. Incidentally, if you ever need to know something about physics, chances are this fellow has excellent lecture notes posted on his website covering the topic (in hyperlinked html, pdf, and even a git repository for the latex code!).
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The wind tunnel data analyzed in your link are in fact mentioned in TFA. Yes, these varying forces exist but the conclusion of the new analysis based on actual trajectories is that their effects are negligible. Also see the article mentioned below for more detailed science; I thought about linking it in the submission but was worrled about slashdotting the poor Prof! Looks like I needn't have worried; fewer people than I thought appear to share my fascination with the knuckler... :P
More detailed rundown of the actual physics (Score:2)
Nathan has a conference paper with a lot more detail about the physics. PDF here: http://webusers.npl.illinois.edu/~a-nathan/pob/ProcediaEngineering34KBall.pdf [illinois.edu]
"Chaotic" != "Random" (Score:3)
I know this is being picky, but if A "causes" B, that is not a "random" chain of events. A chaotic system may be unpredictable by an observer such as a Major League batter, but it is not in any sense of the word, "random".
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You're nitpicking to a fault. It's like spinning a roulette wheel. We consider it random exactly because it is unpredictable to the players as normally played, but if you had some technology with you, you could predict where the ball was going to land.
Nice to see skill over brawn (Score:5, Interesting)
It's nice to see the pracitioner of a fine skill be successful where traditionally the best pitcher is the one who can throw the fastest (under control of course).
A similar scenario happens in cricker where a great spin bowler can dismantle a team. Until the 1990's bowling in cricket was dominated by extreme speed where the best bowlers could bowl at over 150 Km/Hr. Along comes Shane Warne, considered the 2nd most influential cricketer in the 20th century who bowls at less than 100 Km/Hr but with a wicked spin and fantastic control.
Check out the "Gatting ball" video below for a delivery of pure beauty.
http://www.youtube.com/watch?v=rOVei8iTyM8 [youtube.com]
It was Warne's first Test Match delivery in England!
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I don't think so. If it was just familiarity, catchers would have no trouble with their own pitcher. But catchers often have just as much trouble as the batters.
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Even the personal catchers have trouble catching them. Some even use softball mitts, or first basemen's gloves, to improve their chances of getting leather on the ball.
Defective article (Score:2)
TFA states that if there is no initial spin on the ball, the curve of its trajectory will be constant. However, if a ball starts with no spin and a seam is oriented to make more air friction than the opposite side of the ball, that will impart a spin to the ball as it travels.
Furthermore, TFA states that the uncertainty of the ball's position is 0.3 inches, and the claim is that they can reliably declare that the knuckleball has an rms unpredictability of 0.45 inches versus other pitches' 0.4 inches (choosi
Stats and Sports (Score:1)
Baseball really does have the best sports stats geeks.
Well, the author should meet some Cricket fans.
What ever happened to Dave Steib anyhow? (Score:1)
The balls and strikes argument (Score:2)
There was a great exchange (usually attributed to Hack Wilson) between a batter and umpire that eloquently describes the umpire's role in calling balls and strikes.
Wilson stepped to the plate and waited on the first pitch. He didn't swing, and the umpire called "strike." Wilson stepped back and said "That's a strike? Boy, you sure missed that one." The umpire didn't miss a beat and replied "I wouldn't have if I had your bat, Hack."
The strike zone is generally described as being the belt to the knees. When H
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I believe the strike zone now is from the bottom of the knee to the midpoint between the top of the shoulders and the belt, not from the belt.
physics aside... (Score:2)
Since there is only one current pitcher that throws it, I wonder if school bans on this pitch have led largely to its death. I was banned from throwing the knuckleball in Jr High and High School because it was "too hard on a pitcher's arm," even though I used it in sandlot games fairly effectively. Ultimately lack of arm strength did me in as a pitcher (I could throw harder with a submarine pitch, which I had started using in sandlot games, but the school didn't allow that either), and I wasn't much of a ba
Knuckleball Pitcher here.... (Score:2)
Knuckel-balls are not as simple as "a tube .... that follows a smooth curve." That is a wobbling knuckle-ball, and is generally what people think of. This is usually the first pitch knuckle-ball, does not really move much but you can control it better to get that first strike. But if that is all you have got, then you are going to hit around a bit. That is not the strike-out knuckle-ball. By making minor changes in the grip, you can produce more movement that can cause it to dive, cut-in, and break-awa
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And again, what the analysis of actual pitch trajectories shows is that the supposed effect of the varying forces on the ball due to the slight rotation in-flight is totally negligible! If they were not, the knuckleball trajectories would not be fittable to the 9-parameter equation, which assumes that the forces on the ball are constant after leaving the pitcher's hand. What the article suggests is really happening is that things like seam orientation do play a role in determining the forces on the ball at