A mechanical model of pitching

“Everything should be made as simple as possible, but not simpler.”
-Albert Einstein

That’s a well-worn quote from a very famous physicist, but it is appropriate with regards to this article. I’m going to lay out a model of how pitches are thrown and try to keep it as simple as possible without being too simple. In a way my first article, Why Grounders go one Way and Flies go the Other was about the same thing. The model people had been using for hit balls was too simple and some important details were lost.

Let’s start out with a very simple model of pitching that I will tell you up front is too simple. It’s worth setting up the straw man since tearing him apart will be instructive. The exercise will naturally lead us to the more sophisticated model that is just complex enough to explain what is going on and simple enough to understand.

I think it is common for people to think of pitching as a simple arm that rotates at a certain speed and releases that ball at a certain point so that it flies toward the strike zone. Here’s a little cartoon of what that would look like in three steps:


We start with the arm cocked back and the fingers holding the ball. As the arm accelerates forward, the fingers open at the correct point and release the ball. The ball flies off toward the strike zone and the arm continues to rotate and decelerate. It’s a simple machine that turns rotational momentum into straight line momentum.

Not surprisingly, there are a lot of problems with this model. First of all, how does a pitcher impart spin on the ball? We know that almost all pitches are thrown with spin with the notable and rare exception of the knuckleball. This model shows no mechanism for spin to happen. We have all seen fastballs hop and curves curve, and we know that this is caused by a lot of spin put on the ball when it is thrown. Somehow, from the time the ball is in the pitcher’s hand to the time it is thrown, the ball acquires spin. We know it’s not spinning while he is holding it, but we also know it is spinning once it has been thrown. This model offers no help in explaining this.

There’s also a less obvious problem that really sinks this model for good. Really good pitchers can throw all their pitches with the same arm speed. That’s what makes a good changeup so deceptive. The pitcher does everything the same, but the ball leaves his hand eight to 10 mph slower. That’s a pretty mysterious ability and is not reflected in the simple model we’ve kicked around so far.

The model has no elbow or wrist, but that’s not the key piece that is missing. The real problem is the fingers. A pitcher’s fingers do a lot more than simply release the ball, as we will see. Let’s throw this model away and look at how a fastball is really thrown.

Contrary to what you might think, there are actually two points of release when a pitcher throws a fastball. First it leaves his hand and then, a split second later, it leaves his fingertips. This two step process, happening in the time it takes a ball moving in excess of 80 mph over the space of a few inches, makes all the difference in the world. It allows the fingers to keep adding energy from the arm and wrist even after the hand has released it. This action typically adds about 7 mph to a thrown fastball’s speed.

When a scout says the ball explodes out of a pitcher’s hand it is more than just colorful scout-speak. A fastball really does pick up speed as it is released.
At the same time, the ball also picks up backspin because the force applied at the fingertips is not in alignment with the flight path of the baseball. Some of the energy goes into increasing the speed and some goes into spinning the ball which gives the fastball its hop.
Here’s another threesome of illustrations that shows what I am talking about:


The first picture on the left shows the fastball just as its leaving the pitcher’s hand. At this moment the hand and the ball are moving at the same speed, but their paths begin to diverge as the hand follows an arc and the ball travels straight. A few moments later the ball reaches the fingertips and further force is applied to the ball, but since the ball and hand (one travelling straight and the other in an arc) are no longer going in the same direction. The fingertip force is applied in a direction that is out of line with the path of the ball.
This does two things:
1. Adds velocity to the ball (The part of the force that is in line with the path of the ball)
2. Adds spin to the ball (The part of the force that is perpendicular to the path of the ball)

The last frame just shows the results of this action. The fingers follow through and the ball heads off with a speed boost and a lot of backspin.
All fine and dandy, but how does a pitcher throw a fastball at 90 mph, a cutter at 88 mph, a slider at 83 mph, a changeup at 81 mph, and a curveball at 77 mph, all with the same arm speed? It’s all about applying inefficiencies to the hand action.

To throw a cutter the pitcher simply holds the ball off center. Let’s take a look at the cutter from a top view compared to a fastball on the left and a cutter on the right.


By holding the ball a little off-center the pitcher changes how the force is applied to the baseball. The spin axis is no longer perpendicular to the direction of travel of the baseball so it has cutting action instead of the hop of a traditional four seam fastball. Another effect is that now the pitcher can’t push on the ball as efficiently as he could with the fastball because of the misalignment of the fingers and the hand action. That explains the modest loss of speed for the pitch. A sinker is similar to a cutter, but the misalignment happens on the other side of the ball and causes movement in the opposite direction.

A slider isn’t much different in kind from a cutter. It’s just a matter of degree. With a slider the fingers end up all the way on the side of the ball. The resulting spin resembles a football spiral more than a variety of fastball. This maximizes the side to side movement, and further erodes the efficiency of the pitching motion. Because of this radical misalignment, almost no energy from the fingers can be applied to the path of the ball and it ends up going about the same speed as the hand speed. There’s a lot of variation among sliders, but a garden variety slider will clock in at about 83mph.

How about changups then? It’s no accident that the slider and changeup are similar in speed even though the mechanism of how the pitch is thrown is very different. With a changeup the pitcher deliberately holds the ball deeper in his hand, killing the finger extension and letting the ball roll off his fingers instead tapping into the arm and wrist rotation and driving it like he would with a fastball.

A Hardball Times Update
Goodbye for now.

The ball leaves his hand slower than the arm speed, usually about 2 mph although pitchers such as Trevor Hoffman and Johan Santana can subtract significantly more speed than that. By letting the ball roll off the finger tips instead of driving it, the pitcher adds no speed with his fingers and actually reduces the speed of the pitch. Some of that forward momentum the ball has at release is converted into backspin which further reduces the pitch speed.

To wrap things up let’s look at the curveball. Although the grip is completely different, in many ways it resembles a changeup. With the fingers positioned in front of the ball there is no way for the pitcher to use his fingers to add speed to the ball. In fact, the only thing he can do is exchange velocity for spin. Also, with the ball choked so far down in the hand it reduces the amount of speed at release since the mechanical advantage of the arm length is reduced several inches and this subtracts about 4 mph to the speed of the ball at release. That is why a curve is one of the slowest pitches a pitcher will throw—typically 13 mph slower than his fastball. The ball might leave his hand at 79 mph and then he will steal an additional 2 mph and convert it to topspin ending up with a 77mph curve that, due to topspin and reduced speed, takes a sharp dive as it reaches the plate and is very difficult to hit.

The model shows that it is impossible for a pitcher to throw a curveball faster than a slider. In fact, where baseball lore describes discrete pitches, there are actually a continuum of pitches that are available. The only rule is that the fastball is the most efficient pitch and the more you drift away from the pure backspin of a fastball the more speed you sacrifice. A pitch that is somewhere between a curve and a slider, known as a slurve, will be thrown at a speed somewhere between a curve and a slider.

Of course a pitcher could deliberately slow his arm down to get a better speed differential, but this is counterproductive. Changing arm speeds means tipping your pitches. Professional batters pick up on this stuff. If they know what’s coming, you won’t be pitching in the major leagues. A consistent arm speed is what every pitcher aspires to.

Besides getting a really good handle on how grips and pitching works in a physical sense, we can also use this model to decipher some baseball phenomena that didn’t make sense before. Have you ever heard a coach or scout complain that a pitcher was “overthrowing” his fastball? It always puzzled me. Wouldn’t you want to throw the fastball as fast as possible? Overthrowing is throwing the ball harder yet straighter. Major league hitters can generally catch up to even an exceptionally fast pitch. If it’s not moving much they will hit it on the screws more often than not. The movement that a fastball has is very important—it’s more than just about the speed.

Looking at the model we can see that a pitcher could theoretically use his fingers in such a way as to apply more of his force budget to accelerating the ball and less to spinning it. Voila, an overthrown fastball: faster, but with less movement. Likewise, a pitcher could theoretically do the opposite and apply too much spin while sacrificing speed. I’m sure there’s a happy medium. The more elements a batter has to worry about the better so keeping him worrying about the speed and the movement is the best approach.

Just to wrap up I’d just like to say that our first model that we thoroughly bashed is not totally useless. It does describe how a knuckleball is thrown quite nicely. In part two of this article, A Pitching Model: Playing the Slots, we will look at arm slots and how they affect a pitched ball.

References & Resources
I would like to thank THT’s own Mike Fast and University of Illinois Prof. Alan Nathan who both assisted with this article. Mike provided the pitching data and Prof. Nathan reviewed the article and his input resulted in many improvements.

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