# 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 Pleasureā¢. (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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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.

Thanks for the note, Bill. That’s not something that even crossed my mind, honestly.

I still had the sheet open, though, with Dickey’s PITCHf/x data. Looks like, using the method you suggest, the No. 1 pitch has the second-most movement; the No. 2, the third-most. There’s another pitch — with 0.7 inches of gloveside movement and 11.5 inches of rise — that would have been the movingest by that method. It’s an 0-0 pitch to Wieters in the 5th inning.

What’s funny is that these knucklers today aren’t that crazy. Last week vs the Rays, Dickey threw a knuckler with 14.41 inches of horizontal movement toward a left-handed batter and -5.827 of vertical movement (relative to what we’d expect only from gravity).

And that pitch WAS IN THE STRIKE ZONE!

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.

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.

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.

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.

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