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Hitting mechanics: the Twisting Model and Ted Williams's The Science of Hitting.

The "Twisting Model" is a biomechanical model of physical movement that explains why our current ideas about baseball mechanics--bat speed, hip rotation, "power"--are insufficient to explain fully what happens when bat hits ball. In this article I would like to introduce the "Twisting Model" by showing how it supports Ted Williams's theory of hitting from The Science of Hitting. The Twisting model is less well known than the conventional Rotational Model. Field study on the Twisting Model has only recently begun.

The Science of Hitting is an excellent book. Everything Ted Williams learned about hitting throughout his career is contained in this book. However, his explanation of hitting mechanics is vague: it is based on his personal perceptions. Recently I found by applying the Twisting Model theory, Williams' explanation on hitting mechanics becomes clearer and allows for a better understanding regarding movement for producing impulse when hitting.


1) Mechanics of the Twisting Model

The Twisting Model assumes that the most important elements of hitting (or throwing) are the structure of body and appropriate movement. This movement is more important than just having big muscles because muscle contraction is not the direct source of hitting power in the model.

In Figures 1 and 2 I am bending bristle grass to demonstrate how energy is stored in the grass. By bending the grass, one stores energy which is released when the grass straightens or "snaps back." To bend the grass, two different forces in opposite directions are needed. The bottom arrow is force added by hand and the top arrow is force from the spike that resists movement, so-called "fictitious" force.

We use our bodies in the same way when we hit (or throw) a ball. When hitting (or throwing), we produce force when the upper body (above hip joints) and lower body (below hip joints) move in opposite directions.

In Figure 3, a tennis player is about to hit a ball using her upper body and lower body in distinct ways. She twists backward first and then moves forward. In the lower body, by her weight shift and inside-step, the force of the rebound twist is gathered and the forward twist of her upper body is delayed. The twist combination stores energy in her body that is used when hitting the ball.

Figures 4-7 depict a major league player throwing a fastball. He is also using his upper body and lower-body in different ways. In Figure 4 he twists backward and steps forward, shifting his weight for the purpose of creating a rebound twist in his lower-body. In Figure 5 the rebound twist and upper-body twist stores energy in the front leg. In these figures, the fictitious force in his left arm--from dragging "arm and ball"--is clearly seen. The combination of these forces stores energy in his body like the bend in bristle grass. I drew a line on the figures to indicate how energy is stored and released like in the bristle grass. Since the "twists" are centered on the hip joints, the bigger the movement around the hip joints, the more energy can be stored to throw the ball.

The Twisting Model assumes the same "energy store and release" process is important to hitting mechanics, too. Figures 8-11 shows a major league player going through the hitting process. Figure 8 shows how the first twist is made in the back--commonly referred to as "cocking the hip." In Figure 9, a rebound twist is produced by shifting weight and stepping in along with a bat drag to store energy. In Figure 10 and 11, the energy is released for hitting the ball. Interesting to note is that in this process bat speed won't be at maximum at the hitting point but rather at the follow-through point. This is because in this model, the energy storage-and-release process of bat deployment relies on the stored energy: this energy can be transformed either into bat speed or transferred to the ball at impact. This means that increasing bat speed would only reduce energy transfer to the ball, reducing batted-ball speed.

Figure 12 shows two waves, one from the left, the other from the right, moving and interfering with each other to generate a bigger wave. The Twisting Model also assumes that like the two opposing waves, lower-body and upper-body movement interference stores greater energy. The movement has the property/profile of a "wave," like a spring, which explains why timing is important for hitting. In the Twisting Model, energy for throwing/hitting can be described as elastic energy, such as compressing a spring.

Often this process is misunderstood as "rotation," but rotation and twisting are different things. Twisting stores energy, but rotation does not. The Twisting Model is based on "twisting," not "rotation." (Figure 13)

2) Mechanics in The Science of Hitting

Williams wrote that the most important thing he could think of is the cocking of the hips: Now, with your weight evenly distributed, your hips start out at level. You don't worry about hips until you actually begin the performance of the swing. The hips and hands cock as you move your lead foot to stride, the front knee turning in to help the hips rotate back. You are cocking your hips as you stride, and it's so important to get that right. It's pendulum action. A metronome-move and countermove. You might not have realized it, but you throw a ball that way. You go back, and then you come forward. You don't start back there. And you don't "start" your swing with your hips cocked. (1)

Let's examine this relative to the Twisting Model. Using two images from Williams's book. Figure 14 and 15 add black and white arrows and lines to show how energy is stored and released under the Twisting Model.

In Figure 14, two gray arrows indicate the "cocking of the hip." In Figure 15, two arrows at the waist and lower body illustrate the pendulum action, "move and countermove," with the line indicating how energy is stored in the body.

Figure 16 and 17 illustrate the process of energy release. The Twisting Model prediction fits quite well with Williams's explanation. It is like putting missing parts of a puzzle together.

Suppose we imagine a player's body as a plate spring. To store energy in the plate spring by bending it, one end needs to be fixed. For this reason the Twisting Model theoretically predicts that the shifting of weight onto the front leg would help to store energy in the body.

Another prediction is about the bat swing itself. The Twisting Model predicts that the bat swing is one action with two processes: a process of storing energy and a process of energy release. Again, suppose a player is a plate spring (Figure 15, Figure 16). A soft spring easily bends so using soft muscles helps for the storage process. Once the plate is bent, a stronger plate is suitable for releasing greater energy. That means in the releasing part of the process, using hard muscles is better for hitting (Figure 17). This is not in the book, but Williams was known to comment: "Slow, slow, slow, quick, quick, quick." (2) Williams may have been trying to make this same point.

Twisting Model and Rotational Model

Figure 18 shows a simplified diagram that no longer seems to resemble a baseball movement. A bat is just a round mass which is projected straight by a compressed coil spring in a body.

This model predicts that while bat speed is slow, force (acceleration) from the spring is high. Likewise, while bat speed is high, force from the coil would be low. So this would be suitable for an inside-out swing model.

In addition, because the bat is projected straight to a ball, the influence of the body at impact should also be taken into consideration. In other words, at the moment of collision, the ball hits not only the bat alone, but the combination of the bat held by the player's body. The influence of body as "inertial mass" should work to provide a big impulse.

Simplified Twisting Model (Figure 18)

If you compare this to the conventional Rotational Model (Figure 19) and its simplified model (Figure 20), the simplified Twisting Model is very different.

Rotational Model / The Physics of Baseball (Figure 19) Simplified Rotational Model (Figure 20)

The difference is not only in appearance. Since the Rotational model considers only impulse in the rotational direction, the optimal condition would be where bat speed is maximum at impact. The Rotational Model does not take impulse from the body into consideration. In fact, since the optimal condition of the Rotational Model is hitting a ball square to the body, impulse from the body won't appear under this condition. Perhaps this is the reason why impulse/ acceleration from the body was not part of the discussion of hitting mechanics for years?

In reality, both impulse in the rotational direction and impulse in the straight direction should work upon impact. For example, to hit to the opposite field, using impulse in the straight direction should be useful. Williams described this inside-out swing in the book, and the Twisting Model predicts it.


Rather than presenting field test results, this article describes an assessment of the Twisting Model in comparison to Ted Williams's explanations of hitting technique in The Science of Hitting. This analysis seems to show that the Twisting Model fits Williams's insights well and explains the mechanics of many professional players. The conventional Rotational Model, which considers only bat momentum based on bat speed, cannot explain the mechanism of hitting with power to the opposite field.

The Twisting Model has many practical applications. Since it predicts the critical point for producing potential energy is flexible movement around hip joints, introducing appropriate exercises to maximize hip flexing could have the following effects:

* Improve power development in young athletes

* Prolong players' careers

* Prevent injuries

* Keep children/players away from using muscle-enhancing drugs, since muscle strength is not critical for the Twisting Model

Further study is needed for developing the Twisting Model's potential for baseball in the future.


My special thanks to the people of SABR especially to Dr. Dave Baldwin, who was a pitcher for the Senators. Without his instruction and guidance I would not be able to write this paper. Thank you very much.

And also I thank my friends with King Industries Inc. Chris Fesenmeyer continuously encouraged me for doing this research. Dan Miller kindly took me to Boston from Norwalk, Connecticut, for my research meeting and Dr. Len Calbo checked my rough draft to correct my English and gave me useful recommendations. I appreciate their kind support a lot. And last but not least my deepest respect to Ted Williams, the author of The Science of Hitting.


The Science of Hitting Ted Williams with John Underwood, 1971, Printed by Simon & Schuster New York.

Batting no Kagaku (The Science of Hitting), Ted Williams with John Underwood, 1978, Printed by Baseball Magazine Sha Co. Ltd.

Kagakusuru Yakyu Jitsugi-hen (Baseball Science for application), Yutaka Murakami, 1987, Printed by Baseball Magazine Sha Co. Ltd.

Baseball no buturigaku (translation of The Physics of Baseball), Robert K. Adair, 1996, Kinokuniya shoten.

"A new batting model for the Twisting Model," Takeyuki Inohiza, 2011, Published at Shintaichi Kenkyukai.

"Elastic energy storage in the shoulder and the evolution of high-speed throwing" in HOMO, N.T Roach, M. Venkadesan, M. J. Rainbow and D. E. Lieberman, 2013, Nature 498.


(1.) Ted Williams with John Underwood, The Science of Hitting, (New York:Simon & Schuster, 1971).

(2.) For example, from Jerome Holtzman's The Jerome Holtzman Reader, "A Splendid Pitch on the Art of Hitting" quotes Williams as saying during a batting clinic, "Be quick quick quick! The only way to be quick is to use your hips. The hips must lead the way." George Will, in a nationally syndicated political column on June 3, 2003, quotes it as "Ted Williams' rule about hitting: 'Wait, wait, wait, then quick, quick, quick.'"
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Author:Inohiza, Takeyuki
Publication:The Baseball Research Journal
Geographic Code:1USA
Date:Mar 22, 2014
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