R.A. Dickey’s Three Movingest Knucklers from Monday

Mets right-hander and soft-spoken Southern gentleman R.A. Dickey threw his second consecutive one-hitter tonight — in this case, against the Orioles of Baltimore. Nor do his defense-independent numbers suggest that he was anything but excellent on Monday night (box): 9.0 IP, 30 TBF, 13 K, 2 BB, 11 GB on 15 batted-balls (73.3% GB), 1.14 xFIP.

The average knuckleball from Dickey has approximately zero inches of horizontal movement and a single inch of positive vertical movement — or “rise,” a concept the present author discussed briefly earlier on Monday. Of course, the idea of an “average” knuckleball is a bit of a misnomer: given the nature of the pitch, the standard deviation of both sorts of movement is likely quite high. Indeed, this is the strength of the pitch: no one really knows where it’s going, not even Dickey.

As a sort of celebration of Dickey’s last two games — of his entire season, really — I sought out Dickey’s three “movingest” knuckleballs from his Monday start. In this case, I’ve identified the three of Dickey’s knuckleballs with the highest absolute value of total movement (i.e. the sum of the absolute values of both horizontal and vertical movement, in inches).

It’s hard to say if what follows are necessarily Dickey’s three best knuckleballs from Monday. However, each of them really does move quite a bit: indeed, the reader will note that catcher Josh Thole is unable to catch two of the three pitches and has to sort of violently move his glove to catch the other.

Below are those three knuckleballs. Click on individual GIFs for Maximum Pleasure™. (Data from Brooks Baseball.)

No. 3: Wilson Betemit, Third Inning

Movement: 5.2 in. armside, 7.5 in. rise (12.7 in.)

No. 2: Brian Roberts, Third Inning

Movement: 4.2 in. gloveside, 9.9 in. drop (14.1 in)

No. 1: Chris Davis, Seventh Inning

Movement: 6.9 in. armside, 8.8 in. drop (15.8 in)

Bonus

Here’s a bonus: Dickey’s reaction to that last pitch — a reaction that suggests even he was surprised (and/or impressed) by the amount of movement on same.



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Carson Cistulli has just published a book of aphorisms called Spirited Ejaculations of a New Enthusiast.


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Bad Bill
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Bad Bill
4 years 11 days ago

Minor quibble: the movements shouldn’t be added directly, but rather, in a Pythagorean sense (square root of sum of the squares), since that’s the way a batter will perceive them as deviations from a Newtonian trajectory. This said, that last knuckler had a LOT of movement, regardless of how you define it.

samuelraphael
Member
4 years 11 days ago

2 Questions, One stupid, one stupider, because there are no stupid questions:

1) We the people get NERD points for climbing Kilamanjaro or beingBruce Chen.

2) Would a vector of these differ?

Does pitchfx assume a ball will go the full 60 feet six inches, and would this effect the calculations oh a 3 dimensional vector that includes vertical and horizontal movement.

I’m curious if there’s a way to track the ball over 3 dimensions and time.

John Thacker
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John Thacker
4 years 11 days ago

If you assume that they all go the same distance in the third dimension (60.5 feet or whatever), then answer maximizing the three dimensional distance metric is the same as using the two dimensional distance metric.

2-D: d_2 = sqrt(y^2 + z^2), or d_2^2 = y^2 + z^2

3-D: d_3 = sqrt(X^2 + y^2 + z^2) = sqrt(X^2 + d_2^2) (X = 60.5 ft)

We can equivalently write d_3 = f(g(h(d_2))), where h(x) = x^2, g(x) = (60.5)^2 + x, f(x) = sqrt(x). But all of these functions are monotonically increasing over their domains, so it’s obvious that the same pitch that maximizes d_2 maximizes d_3.

Jim
Guest
4 years 10 days ago

Minor Quibble as well –

Neither method is exact. The ball won’t travel directly left/right, then up/down, but it also won’t be a direct line between the start and end point – it will arc. It will usually be between the two values, but not always.

Consider a bowling ball. If I release it one arrow to the right of center, and it is pushed close to the gutter before spinning back to the center pin, the net movement is zero, but the actual distance moved is not.

O-Dogg
Guest
O-Dogg
4 years 10 days ago

True, but the bowling pins are inanimate incapable of sight. The net movement on a knuckle ball that goes 2 inches to the right then comes 2 inches back may be zero, but the point of that pitch is that to the batter, it looks like it’s out of the strike zone before it comes back in. The idea is that if you throw a bunch of pitches that move different amounts, but all potentially cross the strike zone, you end up with baffled batters and 1-hit games. The total amount the ball moves is important, the net movement is not.

Garrett
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Garrett
4 years 10 days ago

The city block metric, used in the post, is as valid a metric as the Euclidean.

Ray
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Ray
4 years 11 days ago

Let’s not forget he slid back to third head first to avoid the third out and allow Ike Davis to eventually hit a grand slam. RAdical

Nathaniel Stoltz
Member
Member
4 years 11 days ago

Dang, Cistulli’s on a roll!

Crash Jones
Member
Crash Jones
4 years 11 days ago

I’m off work in 10 minutes. Checking out this performance for sure. Cool article. His reaction to his own pitch is comical.

cs3
Member
cs3
4 years 11 days ago

Carson-
im a littel confused on one point:

Your other article explained how “rise” was actually “lack of gravity induced drop” as relative to a spinless baseball.

However, knuckle balls have zero spin. The pitch in the first GIF clearly drops, yet it registered as “7.5 in of rise”
How is this possible?

Is Pitch FX simply unable to properly calculate relative knuckle ball movement?

cs3
Member
cs3
4 years 11 days ago

and by “littel” i meant “little”

garik16
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garik16
4 years 11 days ago

To answer your question, it’s because of a slight misnomer.

We like to say that Pitchf/x measures movement as compared to a spinless ball, or that it measures “Spin Deflection.”

But this is actually a misnomer that is noticed only when applied to a knuckleball. What the measurements measure is the vertical trajectory of a pitch compared to what it would be if the only force acting on the pitch was gravity. Similarly the horizontal movement figure is the amount in inches that the pitch changes direction from a straight trajectory.

garik16
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garik16
4 years 11 days ago

@Carson no problem. In the comments of one of my old knuckleball articles, Mike Fast noted that instead of “spin-deflection”, the proper terms for knuckleball movement are probably either “drag deflection” or “non-gravity deflection.” I like non-gravity deflection myself, as it can apply to non-knucklers as well.

garik16
Guest
garik16
4 years 11 days ago

Well what’s easiest for a reader tends to be just describing it as “Movement” or “Break”. For Vertical Break, you can just explain it’s “Movement other than that caused by Gravity”. This is generally what I do.

garik16
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garik16
4 years 11 days ago

Nah, the system will work the same way, they’ll just change the movement calculation. Should be an easy adjustment to Lunar baseball.

atigersgrin
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atigersgrin
4 years 11 days ago

Maybe instead of using the “spinless ball” phase it should be “in a vacuum.” Without air creating friction all pitch trajectories would follow a path determined by the initial trajectory and gravity.

Steve
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Steve
4 years 10 days ago

I like the “in a vacuum” suggestion a good deal, here. Earth’s atmosphere is pretty dense, yo, deflecting stuff all over the place, and I wouldn’t want to give it a raw deal just because it’s invisible to humans. It reminds me of that Evel Knievel rocket-car-over-the-grand-canyon trick, which involved a spinless rocket car yet did not quite maintain a parabolic trajectory.

JimNYC
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JimNYC
4 years 11 days ago

What I don’t understand is how knuckleballers don’t get an infinite point bonus on the watchability scores. Outside of Pedro, Randy Johnson, and Gooden in ’85, I’ve never experienced as much joy watching a starting pitcher as Dickey right now.

Condor
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Condor
4 years 11 days ago

Who would have thought Dickey would be the CY Young favorite?

I Agree Guy
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I Agree Guy
4 years 11 days ago

I did.

I swear!

Ira
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Ira
4 years 11 days ago

To answer your question. Anyone in the Texas Rangers organization or fan base is looking at RA Dickey and saying not just WTF, but where has this guy been for the last 8 years or so.

Note that the most notable thing about RA Dickey before this year is that he was born without a UCL in his throwing arm.

Dunston
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Dunston
4 years 11 days ago

That and that he climbed Mt Kilimanjaro, admitted to being sexually abused as a child and that he cheated on his wife in his (ghostwritten autobiography), signed a 7.8 million dollar contract last year, and names his bats after mythical swords from fantasy books.

gobears
Member
gobears
4 years 11 days ago

Or O’s fans…. :( Amazing show, though, I must admit.

smokeybandit
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smokeybandit
4 years 11 days ago

He’s one of the few pitchers in the majors who doesn’t have Dr. James Andrews on speed dial.

Bryce Harper
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Bryce Harper
4 years 11 days ago

Those are some clown pitches bro!

BurleighGrimes
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BurleighGrimes
4 years 11 days ago

R.A. Dickey has had everyone who has watched and/or participated in any of his games in the last two months shaking their heads. That knuckler has been ungodly.

Slats
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Slats
4 years 11 days ago

That xFIP is surely unsustainable over the long term.

JimNYC
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JimNYC
4 years 10 days ago

One thing to keep in mind is that FIP in general doesn’t work for knuckleballers.

TFINY
Member
TFINY
4 years 10 days ago

Yes, they generally beat their FIP or xFIP due to weaker than expected contact, and thus a lower BABIP.

Rippers
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Rippers
4 years 11 days ago

Baseball: Where players have career years at age 37!

Carloz
Member
Carloz
4 years 11 days ago

A friendly strike zone, it seemed. As if the ump was too lazy to figure out where the ball was when the ball crossed the plate; gave the benefit of the doubt to Dickey.

Simon
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Simon
4 years 10 days ago

It was a big strike zone, but it was applied pretty evenly to both sides.

Jon L.
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Jon L.
4 years 11 days ago

R.A. Dickey = Johnny Vander Meer, Jr.

WinTwins
Member
WinTwins
4 years 11 days ago

He has to be doing something unprecident here, knuckler aside. I can’t think of any pitcher going from bad/mediocre at best to Cy Young quality (In my mind means top 5 in league for WAR/xFIP/dips stat of your choice/etc) for the first time at age 37. Has this happened before? I understand the knuckler changes things as it is a pitch you can throw when you’re super old as it doesn’t rely on velocity but I’m just speaking of his performance in a general sense.

JimNYC
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JimNYC
4 years 10 days ago

The closest that comes to mind is Spud Chandler, who went from nothing special to one of the best pitchers in the league at age 33… but that’s age 33.

Jon L.
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Jon L.
4 years 11 days ago

It was so weird to watch the batters react to Dickey’s pitches. Many of them look like they’re right there, ready to hit, but the problem is that the pitches have no trajectory, so the batters can’t get their timing. It’s like trying to hit a wiffleball with a wooden bat.

Fatbot
Member
Fatbot
4 years 11 days ago

Have you actually tried hitting a whiffle ball with a wooden bat? Sure it’s hard *at first*, but if you adjust your swing and shorten up, keep your head on it and eyes on contact, it becomes easy.

Now understand — these hitters are supposed to be the best in the world, they are in major league baseball. If they can’t hit a whiffle ball with a wooden bat, they shouldn’t be paid millions of dollars.

Of course, they are paid because they hit HR, not to make contact, which is the problem here. So not one adjusted their approach of their swing like a professional hitter should. Same as hitters who refuse to change against a shift, it’s pathetic.

Giving Dickey credit here is akin to giving a team credit if an opposing player misses a free throw. Like the NBA not having the fundamental skill to make a free throw, batters today lack basic fundamentals. It’s why RA Dickey looks like a Cy Young instead of Tim Wakefield.

Franco
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Franco
4 years 10 days ago

Grandpa learned how to use the computer finally.

Fatbot
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Fatbot
4 years 10 days ago

Looks like Mark Reynolds decided to post a reply. Strikeouts? “So what”…

B N
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B N
4 years 10 days ago

Yah, they should totally choke up on the bat and slap some hits into the infield. What could possibly go wrong other than grounding out weakly and getting a ton of infield flies that are basically sure outs?

Simon
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Simon
4 years 10 days ago

Curious then why Tim Wakefield looked like Tim Wakefield rather than a Cy Young candidate. Did all the batters forget all their fundamentals over the last year or so?

Ned Colletti
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Ned Colletti
4 years 11 days ago

I think that if you aren’t rooting for this man to lead the league in K’s, innings and win the Cy Young, you have not learned anything about him or you have no heart. It should not matter if you hate the Mets with all your being, he’s the best story to come along in this sport in a very, very long time.

I love Dickey!

Bip
Member
Member
Bip
4 years 11 days ago

So how “fast” is Dickey’s knuckleball? I mean, I know it hovers around 80, but what I mean is, is it pretty fast or is it unbelievably fast? I’ve watched some of Wakefield’s recent games, for instance, and his seems to be under 70.

garik16
Guest
garik16
4 years 11 days ago

Dickey throws at a variety of speeds. Prior to this year he threw knuckleballs around 73-74 MPH early in counts and finished batters off with knuckleballs that were around 78-81 MPH. He’d also occasionally mix in a super-slow knuckler (the Dickeephus) which normally is in the low 60s, but has hit as low as 54 MPH.

This year Dickey is throwing the super-slow knuckler as usual, the slow knuckler at roughly 75, and is regularly throwing the fast knuckler in the 80s.

ZenMadman
Guest
4 years 10 days ago

When they show that in Tampa Bay, for instance, he threw like 100 knuckle balls and 6 fastballs, it’s easy to think he’s more or less a 1-pitch pitcher. But he’s got at least 3 different knuckleballs. The fast knuckle, the knuckle change, and the Dickeephus. I don’t think it’s accurate to call all of these pitches simply knuckleballs.

Bip
Member
Member
Bip
4 years 11 days ago

For those who can’t rewatch the whole thing on mlb.tv

http://mlb.mlb.com/video/play.jsp?c_id=mlb&content_id=22397883&topic_id=28033182

I like the third and seventh strikeouts in the video.

Fatbot
Member
Fatbot
4 years 11 days ago

Thanks for the link. It reinforces how sad the state of hitting is in baseball now. Thanks to the steroid era these hitters grew up swinging out of their shoes to hit the HR with no concept of how to change your swing with 2 strikes, shorten up and put the ball in play.

Watch the video and look at every single hitter pulling their head out and almost falling down swinging. Not one is looking at the bat hitting the ball. Little league coaches everywhere are spitting up their coffee, because none of these batters have the basic little league fundamental of putting the ball in play with 2 strikes.

Matt Mosher
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Matt Mosher
4 years 11 days ago

What a load. Hitting is no different now than it was years ago.

Fatbot
Guest
Fatbot
4 years 10 days ago

Do some research before posting please. Have you looked at MLB league-wide K%? Do you know hitters are striking out more now than ever in history? 2008-2012 is the greatest strikeout range in the history of baseball. I assume like the hitters of today you are too lazy, so here’s the link:

http://www.fangraphs.com/leaders.aspx?pos=all&stats=bat&lg=all&qual=0&type=8&season=2012&month=0&season1=1871&ind=0&team=0,ss&rost=0&age=0&players=0&sort=9,d

Thanks to growing up in the steroid era, hitters approach is home run or strike out now. But you can keep thinking that RA Dickey is the greatest knuckleballer in history if it makes you feel better.

Bip
Member
Member
Bip
4 years 10 days ago

Do you know hitters are striking out more now than ever in history? 2008-2012 is the greatest strikeout range in the history of baseball.

You’re sure the pitchers have nothing to do with that? Cause I’m not.

Dave I
Guest
Dave I
4 years 10 days ago

OK, so you’re saying Dickey is a product of a generation of bad hitters – I assume that because his pitches are so different from a normal pitch he becomes even more difficult for a batter to hit it squarely.

Currently, Dickey ranks here in the NL:
1st in Wins, Winning Percentage, WHIP, Strikeouts, tied for 1st in ERA, 1st in WPA, tied for 4th in fWAR, 7th in K/9, 12th in BB/9, 5th in K/BB, 3rd in K% and 3rd in Batting Ave against.

Put another way, here is how Dickey compares YTD vs each NL Cy Young winner (excluding relievers) since 1984: 1st in W%, 5th in ERA, tied for 6th in ERA+, 3rd in WHIP, 3rd in H/9, 5th in BB/9, 12th in K/9, 7th in K/BB. With two more shutouts this season, he’ll tie for the most since 1988 (Hershiser and Gooden each had 8, Scott had 5). And he’s 3rd in Age behind Clemens and Johnson.

Tell me again how he’s not really that good?

TFINY
Member
TFINY
4 years 10 days ago

@Dave I; While I agree with your point, using WPA for a starting pitcher tells us only how his own offense did, and not how he pitched. If he struck out three in an inning, or walked three and then got three line drive outs at the warning track, his WPA would be the exact same. While a useful stat for relievers, it only WPA only changes when there is a run or the inning ends, and does not account for how the inning ends.

BurleighGrimes
Guest
BurleighGrimes
4 years 10 days ago

Man, this is silly. Not believing that R.A. Dickey’s success has anything to do with Dickey’s work and evolution as a pitcher is unnecessarily cynical — more for you than for anyone else. Last night, Dickey became the first pitcher since 1900 (!!) to throw back to back CG one-hitters in which 10 or more batters were struck out. If you’d rather *not* enjoy that feat b/c of some hare-brained belief that his success is entirely due to how bad hitters are nowadays, that’s your prerogative…but it’s kinda goofy (and sad for you!) if you ask me.

Antonio Bananas
Guest
Antonio Bananas
4 years 10 days ago

Pretty sure pitchers in general throw harder now than ever before, especially bullpen guys. There is a lot less of an emphasis on pitching to weak contact than there was before. All the DIPS and FIP findings mean that more focus is on missing bats.

dudley
Member
Member
dudley
4 years 11 days ago

has anyone written a piece about how the knuckleball is the perfect game theory pitch? you can’t possibly out-guess dickey, because not even he knows where the hell it’s going.

kevinguy
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kevinguy
4 years 10 days ago

63:5 K:BB ratio over his last 48.2 IP… I think he knows where it’s going

Mike
Guest
Mike
4 years 11 days ago

I think, the point about Dickey’s knuckler is that it normally does not have huge movement and therefore he can reliably throw strikes in comparison to previous knuckle ball pitchers. He does not want to throw those unpredictably moving balls, that could just go all over the place, he just wants a little movement to miss the bats but not enough to miss the zone…

rjbiii
Guest
rjbiii
4 years 11 days ago

This is really interesting. In cricket you have swing and spin bowlers who thrive off movement. The really successful ones always appear those who, while able to make the ball move a long way, have mastered only moving it a little or not at all. Someone who can only get lots of movement, often gets a lot of press and have remarkable short-term success, but don’t make it long-term. In the end, it becomes too easy to sit back and pick off the bad balls. Dickey — and the really good spin and swing bowlers — don’t give you that option. Accuracy, with a hint of movement and the promise of more doesn’t leave the batter much room to figure out what the right play is.

Keith
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Keith
4 years 11 days ago

To be fair, WinTwin, he wasn’t bad/mediocre in a while. His era over the last 500 or so innings is under two, and like 23 of 24 of his last outings have been quality starts, the lone exception being a game in the rain. He’s been good for quite a while, since becoming a Met.

BurleighGrimes
Guest
BurleighGrimes
4 years 10 days ago

By bWAR he’s been significantly better (than by fWAR) in the 2 years leading up to this. Now, I prefer fWAR in general, but knucklers have been documented to routinely outperform their peripherals, so by bWAR’s standard Dickey has been a borderline All-Star pitcher since 2010, and totally otherworldly this year. We’re not talking about a worst to first scenario here, but a guy who has obviously improved piece by piece since he started throwing the knuckleball.

Keith
Guest
Keith
4 years 11 days ago

Sorry era should be under 3.00 there obviously for the last 500.

Kevin Martin
Guest
4 years 11 days ago

Someone has to address the elephant in the room – has anyone tested Mr Dickey for HGH (Heckling Gravity Hormone)?

MC
Guest
MC
4 years 11 days ago

Dickey’s run is really incredible in the sense that I think it underscores how little people still know about pitching. I remember watching a Mets telecast in which Ron Darling said that many of the old-school pitchers (I guess 1950’s and before) pitched no so much with an emphasis on velocity (i.e. the classic modern 95mph fastball guys), but movement – palmballs, screwballs, other kinds of pitches that perhaps have since been forgotten.

I think what Dickey shows baseball is that you can’t really define how a pitcher “should” pitch and that pitching always was and always will be much more art than science.

Sandy
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Sandy
4 years 11 days ago

Looks like he needs to find a catcher who can catch the knuckleball.

Zach Reynolds
Member
Zach Reynolds
4 years 11 days ago

Bring back Doug Mirabelli!

Franco
Guest
Franco
4 years 10 days ago

Thole has his defensive issues, but he’s actually the best at catching Dickey and much better than most of the Sox catchers with Wakefield.

reillocity
Guest
reillocity
4 years 10 days ago

I seriously wonder if the proverbial powers that be would even allow Dickey to pitch in the All-Star Game for that reason. Perhaps only if the manager chose Thole for the team with one of his selections solely for the purpose of catching Dickey?

Josh
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Josh
4 years 11 days ago

Can’t wait to see how he does against the streaking Bombers. Thr ultimate test of RA’s pitch.

RobDiablo44
Guest
RobDiablo44
4 years 11 days ago

I feel like his reaction to that last pitch is less “whoa, that one even surprised me” and more “whew, that was almost the equivalent of a hung change-up… thank God that thing is wigglin’ because it was almost tee’d up”

LowcountryJoe
Guest
LowcountryJoe
4 years 10 days ago

I’m not sure why you didn’t make the gif of the 2-2 knuck he threw to Steve Pearce, striking him out for the second out in the 8th. I don’t care what pitch f/x claims as movement, that pitch was unhittable unless, maybe, if one had squared up to bunt it. And even then…

Well, see for yourself at the 1:04 mark

Jesse
Member
Jesse
4 years 10 days ago

People need to realize that R.A. has been very good for the two seasons preceding this one. This did not come out of nowhere. The Ks obviously make a massive difference, and he is better now because of them, but he didn’t go from bad or just serviceable to ace caliber overnight. He has slowly been refining his use of the knuckleball over the last three seasons.

Daniel
Guest
Daniel
4 years 10 days ago

I’m curious more about velocity than movement. Is RA Dickey’s knuckleball significantly faster than others’, and if so, does that explain his mostly unprecedented success?

Antonio Bananas
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Antonio Bananas
4 years 10 days ago

I think it’s how he varies his speed and how he’s pretty accurate with his knuckler.

tenags
Member
tenags
4 years 10 days ago

I wish Pitch F/x would come up with a system to measure the movement of a pitch halfway to the plate (30 ft 3 inches), and then compare the difference between the release point, to the halfway point, to the end point. A knuckleball is a perfect example of how measuring the Net Movement does not do the pitch justice. Look at GIF #2, at the halfway point the pitch was at the batter’s collar bone, but the pitched ended at his knees.

A measurement like this would also be interesting to see for other big moving pitches (12-6 Curve, Cutter, Splitter et al), and it also would help to accurately show if a pitcher gets any late movement on his FB.

Jeremiah
Guest
Jeremiah
4 years 10 days ago

That type of information is actually calculated by pitchF/X. It uses a nine parameter system to determine the location, velocity, and acceleration of the baseball during its flight. The method assumes constant acceleration, which means that there is no such thing as “late movement”, at least in the way that most people think of it. It’s not possible for a baseball to fly straight for most of the trajectory and then turn sharply at the end.

Check out Dr. Alan Nathan’s page on pitchF/X for more information on how the system works and an analysis of the constant acceleration assumption.

Steve
Guest
Steve
4 years 10 days ago

Shouldn’t a constant acceleration assumption be untrue for a knuckleball, which would dart around after encountering masses of air on its way to the plate, as opposed to accelerating due to an unchanging rate of spin on the ball as in other pitches?

underscoremx
Member
underscoremx
4 years 10 days ago

About four starts ago, the SNY crew were attributing his recent success to the development of the “rising” knuckler. There was an inning where the on-field reporter for SNY, Kevin Burkhardt, was repeating to Gary Cohen what was said to him by Mike Nickeas, about what the rising knuckler looks like as it tries to catch it. In one of the following games they mentioned that it was a pitch that he accidentally threw, and was able to repeat the delivery of.

R.A. Dickey started his streak of 8+ strikeouts per game after this discovery. I’m pretty sure that pitch is the one in the third GIF, Where I’m going with this? I don’t really know, but Dickey is awesome.

Dan
Guest
Dan
4 years 10 days ago

A true measurement of the movement requires time as a variable and how the ball moves in all three axes. One needs to consider that the batter not only has to predict the vertical and horizontal location, he must also know when the ball crosses the area of hittable space (~40 degrees of the baters swing). It would seem logical that the rate of decelartion is not constant for a knuckleball adding this third hitting variable. A true measure would use his angle of release and instantaneous intial velocity to create a normal tragectory. At time intervals between release and catch the RMS of the deviation of the pitch from a normal pitch of each the x,y, and z axis should be added either in each direction or as a unitless sum. Ideally the time interval would approach zero (limit as delta t ->0). i think some calculus may be required.

wpDiscuz