Pitches and Stuff: Arm Angles

Why does a curveball curve? What is the difference between a cutter and a slider? The art of pitching is filled with arcane terms, and even when two players are talking about the same thing, they often use different words. In this series of articles, we are going to look carefully at the motion of a baseball through the air: How does it behave and what a pitcher can do to control it?

Today, we focus on arm angle: the position of a pitcher’s arm as he releases the ball. You may have heard that a fastball thrown with a sidearm motion breaks in a different manner than one thrown over the top. We will define breaks and introduce a diagram based on the size and direction of the break to help classify pitches.

Arm Position Determines the Spin Axis of a Fastball

We view the action from a seat in the outfield, just to the left of center field; it is a common location for television cameras. The pitcher is just releasing a fastball:

To help describe both the pitcher’s arm and the spin of the ball, we will superimpose the face of a clock on the mound, so that the pitcher stands on top of the six:

Since the arm points to the “12” on the clock as the ball is released, we could call this a “12 o’clock arm angle.” The usual term for this position is “over the top.”

With a basic fastball, the ball rolls along the fingers, picking up spin as it goes, and is finally released with pure backspin as the wrist snaps down. Since the fingers are pointing upward, the ball’s spin has the same vertical orientation. Here is a closeup view of the ball, just as it comes out of the pitcher’s hand:

Spin and Break

As you will recall from the first article in this series, the interaction between a spinning ball and the air flowing past it creates a force, the Magnus force. This force acts in the direction towards which the very front of the ball is spinning. In the diagram above, we see that the back of the ball is spinning down, which means that the front of the ball is spinning – and the Magnus force is pushing – up.

In other words, a “12 o’clock fastball” produced by an arm which points to the 12 on a clock face will experience a force pushing it up toward that same 12 on the clock face.

A very exaggerated cartoon of this pitch’s trajectory looks something like this:

A spinning pitch does not actually rise during its motion. However, it does end up striking the catcher’s mitt higher above the ground than a spinless ball thrown with the same initial velocity. If we define break as:

the difference between the final location of a spinning pitch and a spinless pitch with the same initial velocity

then we can say that this particular fastball “breaks straight up.”

Lowering the Arm Angle

Not all pitchers hold their arms vertically above their shoulder as they release the ball. Many extend the arm to the side, so that it makes an angle roughly 45-degree from the vertical. The common term for this arm slot is three-quarters, but it could be called a “1:30 arm angle”:

The fingers of a pitcher using this motion will also point to 1:30 on the clock, and the spin of a fastball rolling off those fingers will therefore be tilted in the same direction:

In this case, the Magnus force does not push the ball purely upward; instead, it deflects the ball both vertically up and horizontally towards third base:

This pitch will break up by a small amount, and also break a small amount towards third base: away from a left-handed batter (as seen in the figure above), or in towards a right-handed batter.

Going Sidearm

If a pitcher “drops down” so that his arm is roughly horizontal, his arm and fingers will point toward the third-base line as he releases the ball:

A fastball thrown from this arm angle will spin “on its side,” so that the front of the ball rotates toward the “3” on a clock face:

The Magnus force has no vertical component on this pitch instead it pushes the ball purely horizontally towards third base. A sidearm fastball breaks away from left-handed batters or towards right-handed batters:

Introducing the Vertical/Horizontal Break Diagram

Now that we have defined what break means, we can use it as a tool to identify pitches. It will also tell us something about the pitcher. First, separate the break of a pitch into horizontal and vertical components and use these to make a diagram. This is not a new idea as people started making similar diagrams as soon as PITCHf/x data became available.

In order to compare our results easily to those of other analysts, we will switch the point of view. The diagram below shows the horizontal and vertical components of a pitch’s break from the point of view of the umpire. Third base is now to the left, and first base to the right:

A pitcher who throws with an overhand motion – so that his arm points to the “12 o’clock” position – will give his fastballs and changeups pure backspin, so that the Magnus force pushes them straight up. His curveballs will have pure topspin, so that they break straight down. His pitches will appear in the locations shown by the red symbols on this diagram.

A pitcher who extends his arm slightly to the side – so that his arm points to the “1 o’clock” position as seen from the center-field seats – will impart a small tilt to the spin axis of his offerings. The resulting Magnus force will nudge his fastballs a bit towards third base as well as lift them vertically. His curveballs will drift a bit towards first base in addition to diving down. The locus of his pitches (the blue symbols) will rotate slightly so that it runs from upper-left to lower-right.

The lower a pitcher drops his arm, the greater this rotation in the horizontal break/vertical break diagram. A right-handed sidearm pitcher throws fastballs that break toward third and curveballs that break sharply toward first. This is one reason that right-handed batters, in general, have trouble facing right-handed pitchers: the curveballs break away from them. A relief pitcher with particularly large horizontal movement (created in part by a low arm angle) can become a “specialist,” brought into the game just to face one or two batters: a “ROOGY” (Right-handed One Out GuY).

What About Southpaws?

Of course, that raises the question: What about the LOOGY? Can lefties take advantage of their arm position, too?

Of course they can! Although some left-handed pitchers throw straight over the top (and so produce pitches which break straight up and down, just like their right-handed counterparts), most lefties extend their arms to the first-base side as they release the ball. Their arm angles end up somewhere between 9 o’clock and 12 o’clock:

In the vertical vs. horizontal break diagram, the locus of a left-hander’s pitches rotates in the other direction, so that it stretches from upper-right to lower-left:

Testing the Theory with Real Pitchers

Does this simple relationship between arm angle and pitch trajectory actually work in practice? We will use the PITCHf/x data from a single game for one righty and one lefty.

Our right-handed pitcher is Stephen Strasburg of the Washington Nationals. The picture below indicates that his arm is roughly 45 degrees away from vertical when he releases the ball.

On July 7, 2014, the Nationals faced the Baltimore Orioles in Washington, D.C., Strasburg pitched seven strong innings, striking out nine and giving up four hits. His repertoire was limited to three pitches: fastball, change, and curve:

Voila! Almost exactly as theory predicts, the symbols run diagonally from upper-left to lower-right. The one difference is the location of the changeups: their horizontal break is a bit larger than that of the fastballs, not smaller. There are several ways to grip a changeup and Strasburg’s circle-change version tilts the spin axis slightly relative to his arm.

Our left-handed example is Jason Vargas of the Kansas City Royals. His arm is nearly vertical at the release, making him an “11 o’clock” pitcher:

On August 13, 2014, he shut out the Oakland Athletics on three hits and no walks. Like Strasburg, he relied on just three pitches:

Again, we see the expected pattern: a diagonal swath of symbols, running this time from upper-right to lower-left. Just as Vargas’ arm is nearly vertical, the overall pattern of his pitches is closer to vertical. The fact that the changeups again have a greater horizontal break than the fastballs might suggest that Vargas uses the same circle-change grip as Strasburg; and, in fact, he does.

The direction of a pitcher’s arm has a very strong effect on the behavior of his pitches, both in theory and in practice. Watch carefully, and you will see that many of the late-inning ROOGYs and LOOGYs use extreme arm angles to make their offspeed pitches run away from from their victims. Every now and then, a starting pitcher will “drop down” to throw an occasional sidearm pitch, surprising the batter with a ball that moves in a different direction. You will also see the vertical-vs-horizontal-break diagram which so neatly encapsulates these effects in many sabermetric discussions and in future installments of this series.

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All data compiled from PITCHfx and Baseball-Reference.com.