This article describes the equipment and technology advances in baseball and softball games. Research efforts are currently being pursued by the authors to develop a layer-by-layer finite element model of a baseball. While work on improved ball models is ongoing, a number of significant accomplishments have been made with current models. These include comparing bat performance, describing the plastic deformation (denting) observed in metal bats, and the failure modes observed with wood bats. To simulate the bat/ball impact at game-like speeds, a durability machine is used to fire balls at a bat at speeds up to 200 mph, at the rate of 10 per minute. After a ball is shot, it falls into a trough and is loaded back into the magazine, which holds up to 36 balls. The bat-support mechanism simulates the grip and flexibility of a batter and can be programmed to rotate the bat between hits to simulate the use of hollow bats or to remain “label up” as is needed for wood bats.


Professional baseball has not changed appreciably in over 100 years. Major League Baseball goes to great lengths to ensure that its game does not change. It still permits only solid wood bats, for instance. Major League Baseball is a game founded on tradition, and keeping the equipment uniform throughout the years allows a common basis to compare players over time.

That isn’t the case, however, with amateur level baseball and with softball. Equipment advances have been embraced in those areas because innovation is seen as a way to encourage participation in the game and to increase sales of sporting goods. And the most obvious equipment advances at the amateur level have been in the design of bats.

As engineers, we are trained through education and experience to find ways to make things better. So naturally as new design options become available, engineers explore ways to improve product performance.

There is also the economic incentive: for sporting goods companies, improved performance on the field translates to increased market share.

In the 1970s with the advent of high-strength aerospace-quality aluminums, designers were able to develop bats that had lighter swing weights than wood bats. These lighter bats translated to increased swing speeds and more control for the batter. Designers soon realized that the bats could be tuned to achieve varying levels of batted-ball speeds. Some have likened the pursuit of increased bat performance to a Cold War arms race as manufacturers sought stronger alloys and metals. Fiberreinforced composites brought yet another material choice that allowed increased design flexibility over metals.

Improved bats have benefited the offense, and some believe that bats have become too good and have changed the balance of the game. Accordingly, regulating associations have encouraged the development of tests to quantify equipment performance. At the professional level, the tests are used to ensure the game does not change, while at the amateur level the testing is used to ensure the game doesn’t change too much.


As engineers entrenched in the game, our task is to design tests to ensure the game is played as desired by the respective governing body. Mechanical engineering has made considerable contributions in quantifying and understanding ball and bat performance in baseball and softball.

Eye on the Ball and Bat

Bat performance is a joint property of the bat and ball. The ball primarily affects bat performance in two ways: by elasticity and stiffness. Because of the importance of these properties, tests have been developed to measure ball elasticity and stiffness independently. Ball elasticity is found from its coefficient of restitution, or COR. The COR is obtained by firing the ball at a flat rigid wall. The COR is the ratio of the rebound and the inbound ball speeds, which are measured using light gates placed in front of the wall. The COR of baseballs and softballs is close to 0.5. Thus, the ball dissipates about 75 percent of its energy during impact.

Ball stiffness is measured in two ways. A quasi-static test, termed compression, squeezes the ball between two flat platens. Ball compression is the force needed to compress the ball one-quarter inch. Another test, termed dynamic stiffness, is similar to the COR test. The ball is fired at a rigidly mounted solid half-cylinder. Load cells between the cylinder and rigid wall measure the impact force, which is used to determine the ball stiffness.

Ball response has been found to be sensitive to temperature and humidity. To improve test reproducibility, balls are conditioned and tested at 72 ̊F and 50 percent relative humidity.


Humidity affects a baseball and a softball differently. Going from a dry to humid environment has a relatively small effect on a baseball (a 5 percent decrease). There is a comparatively large effect on the stiffness of a polyurethane softball (a 40 percent decrease).

To assure that Major League Baseball remains the same from year to year, compliance testing on a random sample of baseballs is conducted. The baseballs are tested for COR and compression. Per MLB specifications the COR of the baseball must be between 0.514 and 0.578. MLB does not have a specification for compression, so the compression component of the compliance testing is only used at this time as another measure for exploring the relative hardness of the baseballs from year to year.

Baseballs are also peeled layer by layer to measure the weights and circumferences of the respective layers and to determine the wool content of the yarns. The data that have been collected over the years have shown that Rawlings is making a very consistent baseball. The application of Six Sigma manufacturing practices helps to ensure this consistency.

Common Bat Myth: The Sweet Spot

The swinging motion of a bat can be visualized as a rod pivoting about a point. If we limit our time frame to the instant that the bat and ball are in contact, the pivot point is nearly stationary.

If a pivoting rod is impacted at its center of percussion (COP) there will be no reaction force at the pivot (i.e. without constraint the rod would tend to rotate about the pivot point). All batters have observed that poorly hit balls can sting the batter's hands, while well hit balls do not.

The impact location on the bat that produces high hit ball speed and minimal sensation to the hands is often termed the “sweet spot” of the bat. Many claim that the sweet spot and the COP are the same location on a bat. While the sweet spot and COP are often close to each other, they are not identical locations.

The COP will move as the weight distribution in the bat is changed, while the sweet spot will not. The sweet spot is actually not a point, but a region of the bat where the vibrations from impact are minimized. As bat impact vibration is reduced, more energy is imparted to the ball, producing a higher hit ball speed, and less sensation to the batter's hands.

Once the ball has been characterized, we can consider bat performance. To measure bat performance, we need only consider the motion of the bat and ball just prior to and just after impact. On the field, in a fixed frame of reference, the bat is swung at an incoming ball.

If we choose a moving frame of reference, a laboratory test encompassing a bat-ball impact, representative of play conditions, can be simplified. Consider a moving frame of reference located on the bat where it impacts the ball. If the bat speed at this location is 70 mph, the frame of reference is moving at 70 mph toward the pitcher.

This moving frame of reference can be duplicated in the laboratory, with a bat that is stationary prior to impact and a ball traveling at the sum of the pitch and bat speeds. If the pitch speed was also 70 mph, then the laboratory ball speed would need to be 140 mph to simulate play conditions.

All manufacturers and regulating associations use this type of test to measure bat performance. Delivering the ball at a high speed is not trivial, but easier than controlling bat motion. The bat is supported on a pivot, with a moment of inertia that is small compared to the bat. The rebound speed of both the ball and bat are relatively slow, so that ball capture and bat deceleration are readily achieved.

The most common approach to accelerate the ball uses a sabot (French for shoe) style air cannon. The ball rides inside the sabot as they both travel down the barrel. The sabot centers the ball in the barrel to achieve accuracy of the impact location. The sabot is made of a durable plastic (polycarbonate or polyethylene) and provides improved speed control in comparison to a ball in direct contact with the barrel as is done in a burp style cannon. At the end of the barrel, a plate mounted on shock absorbers captures the sabot, allowing the ball to continue toward the bat.

Bat Performance Measures

To compare the performance of different bats, they must be evaluated on a common scale. One performance scale is to consider the speed of the ball coming off the bat. The speed of a hit ball in play (vh) depends on the pitch speed (vp), the bat speed (vb) and a term called the collision efficiency (ea): 

The collision efficiency is readily obtained from the bat performance test described above, and is found from the ratio of the ball rebound speed to the ball inbound speed. (The collision efficiency is different from the ball's COR, since the bat recoils after impact.) The collision efficiency is a measure of the energy imparted to the ball by the bat, is a function of the bat design, and is typically between 0.1 and 0.2. This value implies that the bat speed is 5 to 10 times more important than the pitch speed in determining the hit ball speed. The bat speed will, in turn, depend on the bat weight, or more precisely, its moment of inertia.

Bats or trampolines?

In 1970 aluminum bats were introduced as a cost-effective alternative to using wood bats. Teams would need fewer aluminum bats during a season compared to wood bats. Manufacturers quickly learned that hollow bats had a “trampoline effect” that allowed the ball to be hit farther than with a wood bat.

When a ball impacts a solid wood bat, essentially all of the deformation occurs in the ball. The ball only returns about 25 percent of its energy after the impact. Thus, impacts that reduce ball deformation will dissipate less energy and increase hit distance. Hollow bats can do this because their barrels are softer than solid wood.

Hollow barrel bats have another advantage. The barrel stores energy during impact and returns the energy to the ball after impact. The trampoline effect also occurs in golf and has motivated manufacturers to develop stronger materials to further thin and soften the impact surface.

It is not uncommon for a player to remark that one bat is significantly better than another. Indeed, the Internet is full of such claims. Our measurements show that the difference is much less than many believe. The performance of wood bats has not changed—wood is wood, and there is no performance advantage of maple over ash. Nonwood bat performance reached its peak around 1998 before performance tests had been fully developed.

At that time, the maximum difference between a wood and hollow bat (metal or composite) was in adult softball and was about 15 percent (using a hit ball speed performance scale, as in the equation). Today the largest difference is still in softball, but has been reduced to about 10 percent. Most governing associations feel this performance level provides a good balance between offense and defense. Given the similarity of many bat designs, the difference of bats in play is usually less than 5 percent.


In college and high school baseball, the difference between wood and hollow bats was 10 percent and is now about 5 percent. Because of the relatively small difference between bats available on the market, batters seeking to maximize hit distance will find improving technique yields greater benefits than bat selection.

Digital Models

A number of finite element models have been developed to describe bat performance. While favorable comparisons with experiments have been achieved, currently all numerical models have shortcomings.

The primary challenge is creating an accurate model of the ball. Consider the common baseball, composed of a rubber pill, wool windings, and a leather cover. While the pill is relatively straightforward to model, the dynamic response of the wool and leather are not. Softballs have a simpler construction (polyurethane core with a leather cover), but are just as difficult to model.

The challenge is controlling the ball's material stiffness and energy dissipation, which depend on the impact speed. The best models are developed phenomenologically (often using a viscoelastic material model), by modeling instrumented rigid wall impacts. These models show good agreement at the test speed and impact geometry from which they were created, but the correlation between the model and the physical system diminishes as the speed or impact geometry is changed.

Research efforts are currently being pursued by the authors to develop a layer-by-layer finite element model of a baseball. While work on improved ball models is ongoing, a number of significant accomplishments have been made with current models. These include comparing bat performance, describing the plastic deformation (denting) observed in metal bats, and the failure modes observed with wood bats.

It is not uncommon for a bat to break in play. Two separate trends in bat failure have motivated increased scrutiny recently: the failure of maple bats in Major League play, and increased performance of composite bats at the amateur level. (Impacts can cause internal delamination that softens the barrels of composite bats and leads to higher performance.)

To simulate the bat/ball impact at game-like speeds, a durability machine is used to fire balls at a bat at speeds up to 200 mph, at the rate of 10 per minute. After a ball is shot, it falls into a trough and is loaded back into the magazine which holds up to 36 balls. The bat support mechanism simulates the grip and flexibility of a batter and can be programmed to rotate the bat between hits to simulate the use of hollow bats or to remain “label up” as is needed for wood bats.

Until recently, it was assumed that ash and maple bats should be labeled so that the baseball is always making contact with the edge grain of the bat. During a 2008 wood bat study using the durability machine, it was found that, while ash bats are more durable when hit on the edge grain, maple bats are more durable when hit on the face grain.

Ash has distinct grain lines (ring porous) that are weaker than the bulk wood and collapse when compressed. When the grain regions collapse, cracks form causing the wood to flake. Impacting on the edge grain reduces the load in the weaker regions of ash. The grain of maple is more evenly distributed (ring diffuse) and is not sensitive to flaking. Thus, edge grain impacts provide no benefit for maple.

In response to this information, MLB revised its wood bat regulations on placement of the label on maple bats to have the baseball hit the face grain rather than the edge grain. As a result, the rate of breakage for maple bats dropped between 2008 and 2009.

It is remarkable how little equipment has changed in professional baseball over the past 100 years, and at the same time how much technology has changed equipment at the amateur level over the past 40 years. It has not been until the past 10 years, however, that significant progress has been made in evaluating the effect of technology on bat and ball performance.

We now have a good understanding of the mechanisms affecting bat performance and have developed methods to accurately measure performance. With the aid of science and engineering, it is now possible to bring the performance of nonwood bats in line with the wood counterparts they replaced. It is up to the regulating associations to decide where “acceptable” performance lies, however. These same advanced testing methods are being used to ensure that the Major League game is not being compromised by any change in the baseball.

Reference: To Explore in More Detail

Reference: To Explore in More Detail
The Sports Science Laboratory at Washington State University:∼ssl/
The Baseball Research Center at University of Massachusetts-Lowell: