Physics and Acoustics of Baseball & Softball Bats
Daniel A. Russell, Ph.D.
Graduate Program in Acoustics
The Pennsylvania State University

The contents of this page are ©2003-2011 Daniel A. Russell

Today is The contents of this page were last modified on May 12, 2008

Explaining the 98-mph BBS standard for ASA softball

In my introductory article about regulating bat performance I argued that the hit-ball speed was the ultimate measure of performance in the field. In this article I'll attempt to explain how the Amateur Softball Association regulates the Batted-Ball Speed directly.

Batted-Ball Speed, Collision Efficiency, and Bat-Ball-Coefficient-of-Restitution

The Batted-Ball Speed, or the speed with which a bat hits a ball, depends on three quantities:
where vball is the pitched speed of the ball, vbat is the linear speed of the bat at the impact location, and eA is a term called the collision efficiency (sometimes referred to as the "apparent coefficient of restitution"). The collision efficiency eA depends on the elastic properties of both the bat and ball, as well as on the moment-of-inertia of the bat, and the location of the impact on the bat barrel. It is also the quantity most easily measured in the laboratory. The ASA has used two different bat performance standards, the first took effect in 2000 and the second in 2004. Both standards directly regulate the Batted-Ball Speed. The two standards differ primarily in the relative speed between ball and bat at which the laboratory test is conducted, and in the manner in which the collision efficiency is measured. In the laboratory currently test used by the ASA to regulate BBS, a softball is fired from a cannon towards a bat which is initially at rest. The ball passes through a light gate speed detector on its way towards the bat, and passes through the same detector as it rebounds from the bat. The collision efficiency for this scenario is simply the ratio of the final ball speed vf after the collision divided by the initial ball speed vball
This measurement is often referred to as a "ball-in, ball-out" measurement (as opposed to the "ball-in, bat-out" measurement used for the BPF standard). If the balls used in the test were exactly the same as the balls used in the field, then calculating a predicted BBS for a particular bat would be as simple as taking the laboratory measurement of eA from equation (2) and plugging it into equation (1) along with a value for the pitched ball speed and bat swing speed.

However, the parameters of a softball (weight, COR, and compression) can vary significantly from ball to ball, and the performance of a bat depends rather strongly on these ball parameters. If the balls typically used in the field have a different weight, COR or compression than the ball used in the laboratory test, then the simple procedure above will not accurately predict BBS in the field. The fix to this problem is to attempt to normalize the laboratory test results to the parameters of a "standard" ball.

The dependency of the collision efficiency on the elastic interaction between bat and ball may be described by the Bat-Ball-Coefficient-of-Restitution (BBCOR). The BBCOR is often represented by the symbol e and represents the ratio of the combined speeds of the ball (vball-exit) and bat (vbat-recoil) after the collision divided by the initial speed of the ball (vball) before the collision.

The depencency of the collision efficiency on the inertia properties of the bat and the location of impact are combined into a kinematic factor which is essentially a ratio of the ball mass m divided by the "effective mass" of the bat[1]
which depends on the moment of inertia of the bat Ip about a pivot point on the handle and the distance z from the pivot point to the impact location. The collision efficiency eA is related to the BBCOR (e) and the kinematic factor k according to

The way the ASA BBS standard works is as follows. The moment-of-ineritia of the bat and the mass of the test ball are measured, so that the kinematic factor may be calculated from equation (3). The collision efficiency is measured using the ball-in/ball-out method in equation (2). Then, equation (4) is rearranged in order to calculate the BBCOR in terms of the measured collision efficiency (as a ratio of ball speeds) and kinematic factor:

This calculated value of the BBCOR is then normalized to the elastic properties of the ball itself to obtain BBCOR*, and the kinematic factor is normalized to the ball weight to obtain k*. A value for the normalized collision efficiency is then obtained
and finally the Batted-Ball Speed is calculated from
where the values for pitched-ball speed and bat-swing speed are appropriate to game conditions. The value of BBS from equation (7) is compared to the limit chosen by ASA and if the bat tests below the limit it is considered to have passed the BBS test and may bear the ASA certification stamp.

Batted-Ball Speed Standards used by the ASA

The Amateur Softball Association began regulating the performance of slow-pitch softball bats in 2000.[2] At that time the industry standard for testing the performance of softball bats was to follow the test protocol outlined in ASTM Test Standard F1890[3]. Note that while this test protocol bears the phrase "bat performane factor" in its title, the ASA has never used the BPF performance standard, but instead has always used a Batted-Ball Speed standard. They just followed the test protocol outlined in ASTM F1890 to determine a value for BBS. The version of the test standard in use at the time ASA begain regulating bats is designated F1890-98. This version of the test standard made the following assumptions:
  • typical pitched-ball speeds for the game of slow-pitch softball are around 10-mph.
  • typical bat-swing speeds for adult slow-pitch players are around 60-mph, with some top level players cabable of reaching 70-mph swing speeds.
  • impacts at the Center-of-Percussion (COP) of the bat offer the highest batted-ball speeds due to the optimization of momentum transfer.
  • the pivot point of the bat while being swung is on the handle approximately 6-inches from the knob end.
Based on these assumptions, the test protocol called for a bat to be gripped at the 6-inch point on the handle in a freely rotating pivot. A ball was fired from a cannon at 60-mph towards the initially stationary bat, such that the impact would occur at the measured location of the Center-of-Percussion. The speed of the ball, just prior to impact with the bat, was measured using light gates. The speed with which the bat recoiled after the collision was measured using another set of light gates. The BBCOR (e) was calcualted using the measured ball and bat speeds, and the kinematic factor was calculated. Finally, using a pitched-ball speed of vball = 10-mph and a bat-swing speed of vbat = 60-mph (or 70-mph) the bat's performance as a Batted-Ball Speed was determined from
The ASA made a policy decision to limit the Batted-Ball Speed to 125 feet/second (85 mph), and any bat which produced BBS of 85-mph or lower was certified as passing the ASA-2000 BBS standard, and legal for play.

During the 2002 ASA National Tournament in Montgomery, AL, an extensive field study[4,5] of bat swing speed and bat performance was conducted. The data from this field study, along with other concurrent laboratory studies[6,7] revealed that all of the assumptions made in the F1890-98 test standard were incorrect.

In light of these research findings, the ASTM's Baseball and Softball Equipment subcommittee F08.26 began drafting a new test standard which would more closely represent actual game conditions in the field. The new test standard, ASTM F2219[8], still uses a cannon to propel balls towards an initially stationary bat gripped in a freely rotating pivot. But, the following changes and improvements were made:

One very important discovery from the 2002 field study and subsequent laboratory validation of the new F2219 test standard was the fact that BBS values determined using the old F1890 standard were significantly underestimating bat performance in the field. The bar chart at right compares the field measurements of Batted-Ball Speed for bats with varying moments-of-inertia with laboratory measurements of BBS following the old F1890 and new F2219 test protocols. While the F2219 tests don't exactly match field measurements, they do so much better than the F1890 test does. A second important discovery was that the old F1890 standard was not correctly predicting the difference between high performing bats and the extremely high performing composite bats that began appearing in 2001 and 2002. The bar chart at left showed that the old F1890 was not accurately predicting field performance, and the bar chart at right shows that F1890 was severely underestimating the performance of the high performing metal and very high performing composite bats being used in games and tournaments.
In 2002 the ASA commissioned a study of a wide variety bats encompassing the 30-year history of non-wood bat types as well as covering the entire range of performance.[2,4] Approximately two dozen bats were tested with the F2219 standard using 0.44/375lb softballs. Bats included in this "era" study included wood, single-walled aluminum, double-walled aluminum, titanium, and composite bats. As shown in the bar-chart at right[4], the study showed BBS values ranging from 90-mph to over 110-mph.

Based on the data from this "era" study, the ASA chose to set the maximum BBS value, effective January 2004, to be 98-mph. A bat must produce a BBS of 98-mph or lower to be certified by the ASA and bear the ASA2004 stamp on the barrel. Even though the numerical value of the BBS with the new standard is higher than with the older standard (98-mph compared to 85-mph), the new standard is actually a much stricter standard. Many bats which passed the old 85-mph BBS standard using F1890 no longer passed the new 98-mph standard using F2219. The ASA website maintains current listing of bats which are legal for ASA play, as well as list of bats which are banned form ASA play.

High Speed Ball Cannon and Ball-in Ball-out Measurements

According to the ASTM F2219 test protocol, a softball (with tight restrictions on weight, COR and compression) is fired from a cannon at 110mph towards a stationary bat. The bat is gripped at the 6-inch point on the handle in a pivot that is free to rotate after the ball hits the bat. The photograph below shows the cannon at the Sports Science Laboratory at Washington State University. The ball is held by a sabot and is placed in to the cannon just in front of the breach plate in the photo. The large gray tank on the left provides the compressed air used to fire balls from the cannon. A couple of movies showing the cannon in action are available form the WSU Sports Science Laboratory website.

As the ball exits the cannon, the sabot is caught by the arrestor plate, while the ball continues on and passes through a series of three light gates. Each gate is triggered when the ball breaks the plane of light, and the ball speed is measured as the distance between pairs of light gates divided by the time between trigger signals. Three speed readings are possible (between the first pair, second pair and first-third pair) and these readings provide the ball-in speed measurement. After colliding with the bat, the ball rebounds and passes through the same light gates, only in reverse order. The ball must rebound through at least two of the light gates to be considered a valid hit, and a high-speed camera is used to monitor the trajectory of the rebounding ball. The ratio of ball-out to ball-in speeds determines the collision efficiency or BESR.

This photo shows the bat in its pivot. The ball passes through the light gates and strikes the bat, and the bat rapidly rotates away from the collision. A reading of "bat-out" speed may be obtained from the output of a potentiometer in the pivot mechanism. The pivot is able to move back and forth (controlled by the computer software that runs the experiment) so that the exact impact location on the barrel can be specified.

Limitations of the ASA BBS standard for softball bats

Cannot account for possible "whip action" in flexible handled bats

Since the F2219 test standard fires balls from cannons towards initially stationary bats, it is not possible for the F2219 test to account for, or detect, any improvements in performance of flexible handled bats due to the supposed "whip action" they provide during the swing.

Difficult to test bats with low collision efficiency

Occasionally there are bats which have a very low (or even a negative) collision efficiency. Most often this is a result of the bat having a very low moment-of-inertia, but it also happens with very low performing bats that have a low BBCOR. If the collision efficiency is too low, then the ball does not rebound with enough speed to pass through the light gates and a value for eA cannot be obtained from the "ball-in, ball-out" method of equation (2) above. The same apparatus and F2219 test protocol is used for the ASA BBS standard for softball bats and for the NCAA BESR standard for baseball bats. However, while the test works rather well for most adult softball and adult baseball bats, the low moment-of-inertia of the shorter youth bats makes if very difficult to extract a value for the collision efficiency (or BESR value) from the "ball-in, ball-out" technique.

Why not use bat-out instead of ball-out?

The problem of measuring the performance of bats with very low collision efficiency could be solved by using the recoil speed of the bat after the collision. Even though the ball may not rebound with sufficient speed to pass back through the light gates, the bat recoils with more than sufficient speed. However, early on in the development of the F2219 test standard, the feasibility of using a "bat-out" measurement was studied. Theoretically, the results from a "ball-out" measurement should be exactly the same as for a "bat-out" measurement. However, experimental data showed that while a 1% error in "ball-out" speed results in a 1% error in the measured value of eA the same 1% error in a "bat-out" speed measurement results in a 10% error in the measured value of eA. The "bat-out" method allows for testing over a wider selection of bats and over a wider range of impact locations on the barrel of any given bat. But, the "ball-out" measurement is more precise and "self-calibrating."

An additional problem with "bat-out" measurements is that the bat often vibrates violently while it is rotating and recoiling from the collision. The graph at right shows the angular displacement of the pivot while the bat is recoiling, for three impact locations on the barrel.[4] The blue trace (impact at 24" from the knob) shows strong vibration contributions from the first two bending modes. The magenta trace (impact at 28" from the knob) represents an impact at the node of the first bending mode so that only the higher frequency second bending mode contributes to the vibration. The yellow trace (impact at 32" from the knob) represents an impact at the node of the second bending mode so that only the lower frequency first bending mode contributes to the vibration. This trace is especially interesting because it shows the pivot actually coming to rest and rotating in the opposite direction as the flexing of the handle counteracts the rigid body rotational motion of the bat. This data was measured with a potentiometer in the pivot holding the bat. It may possible to minimize the effects of vibration somewhat by measuring the "bat-out" speed at the location of impact on the barrel.[9]

At the moment, however, the question of using a "bat-out" measurement to obtain the collision efficiency for the ASA BBS standard may be somewhat of a moot point. Richard Brandt, the inventor of the Bat Performance Factor, has patented the "bat-out" technique[10] and subsequently sued the ASA to prevent them from using it to certify bats.* The lawsuit has been settled out of court, and all references to BPF and "bat-out" measurements have been removed from the current version of ASTM F2219.

* As of May 2008, the ASA has apparently reached an agreement wth Dr. Brandt to allow use of a Bat-Out measurement (through a potentiometer in the pivot) for the testing and certification of softball bats for the ASA.

Normalization of results to ball parameters

One of the problems with converting the laboratory measurement of collision efficiency into a reliable field value for Batted-Ball Speed is that the parameters of the ball (compression, COR, and weight) can vary considerably from ball to ball, and this variation in the ball parameters can greatly affect the resulting calculation of BBS enough to cause problems for certification of bats.

Correcting for Nonstandard Ball Weight
According to the ASTM standard F2219, softballs used to certify bats high speed test must weigh between 6.75 and 7.00 ounces (191.0-198.1 grams). But what if an organization's governing body wanted to use a ball whose weight typically lies outside this narrow range? In order to correctly predict batted-ball speed in the field, the calculated BBS must be normalized to ball weight in order to account for this variation in ball weight. So how does this work? The bat-ball-coefficient-of-restitution (BBCOR) is obtained from the laboratory measurement of the ratio of ball-out to ball-in speeds and the inertia properties of the specific ball and bat
where mball is the weight of the specific ball used in the test, and Meff is the effective weight of the bat,
with Ibat and Ipivot being the moments-of-inertia of the bat and pivot and d2 being the distance from the pivot to the location on the barrel where the ball impacts the bat. Then the normalized collision efficiency is calculated from the BBCOR using the weight of a "standard ball" (mo)
And finally the Batted-Ball Speed (normalized to the "standard" ball weight) may be calculated from the normalized collision efficiency,
Normalizing the calculated Batted-Ball Speed to ball weight appears to work pretty well.[11] The chart at top right shows the COR, compression, and weight for three softballs. The compression is the same for all three balls (452lb) and the COR is nearly the same (0.46), but the weights are significantly different (6.43oz, 6.78oz, and 7.04oz). The bottom chart shows the normalized calculated BBS for four softball bats covering the entire range of performance. The normalized calculated BBS is almost exactly the same for the three different weight balls on all four bats. The slightly lower BBS value for the 104-mph bat with the high weight ball is due to the slightly lower COR and comression for this heavier ball).

Correcting for Nonstandard Ball COR
The effect of varying the Coefficient-of-Restitution (COR) of a softball on bat performance is much more significant, especially for high performance bats. And, the actual COR of a gross of softballs can vary considerably from the value printed on the ball cover. The ASTM standard protocols require that the balls used to test bats have COR values between 0.420 and 0.440. However, several organizations sponsor tournaments and leagues where balls with COR values of 0.40 or 0.47 are used, and it is necessary to normalize the calculated prediction of BBS to the ball COR if one wants to accurately predict bat performance in the field with balls that are different from those used in the laboratory tests.

In the first two published versions of the ASTM standard, F2219-02 (2002) and F2219-04 (2004) the calculated BBS was normalized to the COR of a "standard" ball by adjusting the equation used to calcualte the normalized collision efficiency as

where in addition to the weight normalization, the BBCOR was normalized by multiplying by the COR of a "standard" ball (eo) and dividing by the COR of the actual test ball (e). This was known as "BPF normalization" because the Bat Performance Factor (BPF) is just the Bat-Ball-COR divided by the COR of the ball used in the test. This normalizing approach assumes that the BPF (BBCOR/e) is independent of the value of the COR of the ball (e). However, recent laboratory tests and computational models have shown that this assumption is not valid.

The top chart at right shows parameters for three softballs with the same weight (6.72oz) and compression (464lb), but varying COR values (0.41, 0.46, 0.51).[11] The middle chart at right shows the calculated Batted-Ball Speeds for four softball bats of varying levels of performance when tested with these three balls. The BBS results have been normalized for both weight and ball COR. The BBS values for the 87-mph wood bat are the same - the COR normalization works for a very low performing wood bat. However, the COR normalization does not work as well for the other three bats. The failure is especially evident for the 104-mph high performance bat. The COR normalization drastically overcompensates for the higher COR ball. Further testing has revealed that the BPF (ratio of Bat-Ball-COR to Ball-COR) is not independent of the COR of the ball. This throws into question the entire validity of the BPF standard as a legitimate predictor of performance. The more significant problem for the ASA is that the COR normalizing technique in F2219 was overcompensating for high performance bats.

In light of this data, the COR normalization was removed from the ASTM F2219 test standard in 2005. (ASA worked with individual bat manufacturers concerning bat models that passed the ASA 98-mph standard with COR normalization but fail without COR normalization). Normalizing to ball COR is not part of the most current version of the F2219 standard. The bottom chart at right shows the calculated BBS for the same bats and the same three balls (varying COR) when the results were normalized to weight only. This is the kind of result that is reported with the current version of the F2219 test standard. Low performance bats produce lower calculated BBS values with high COR balls, and high performance bats produce slightly lower calculated BBS values with high COR balls.

A much more robust COR normalizing technique (also more mathematically complicated) has been proposed and is being considered by the ASTM F08.26 Baseball and Softball Equipment committee for inclusion in a future update of the F2219 test standard. Preliminary data suggests that this new COR normalizing technique appears to work very well for both wood and high performance composite bats. Further testing is underway to ensure the stastitical repeatibility of this new technique is before this new normalization technique will be adopted.

Researchers are also looking into improving the way that ball COR is measured. Currently, COR is measured as the ratio of ball-out to ball-in speeds when a ball is fired from a cannon with an initial speed of 60-mph towards a rigid wall. 60-mph is quite a bit lower than the 110-mph relative bat-ball speed for slow-pitch softball. Plentiful data exists showing that ball COR decreases as ball speed increases. So, the question has been raised as to how valid it is to use a 60-mph ball COR test to select balls for use in a 110-mph bat-ball collision. Research is currently underway to determine a more approriate speed for COR measurements. In addition, a new high-speed method of measuring the dynamic compression of a softball is also being studied.

Three softballs with the same weight and compression but different COR.

Calculated BBS normalized to both weight and COR.

Calculated BBS normalized to weight only.

Correcting for Nonstandard Ball Compression
Static compression is measured as the amount of force in pounds required to squish a softball (or baseball) a distance of 0.25-inches. Typical compression values for softballs are 150-lb ("mush" balls), 375-lb mid-compression balls, and 525-lb high compression balls. Variations in the compression of the ball in use can also have a noticeable effect on the performance of the bat being used to hit the ball. And variations in the actual compression of a box of softballs from the same manufacturer can be significant. The top chart at right shows parameters for three softballs with nearly the same weight (6.95oz) and COR (0.44), but varying static compression values (341lb, 391lb, and 452lb).[11]

The bottom plot at right shows the calculated BBS for four softball bats, of varying performance, tested with these three softballs. The calculated BBS has been normalized to ball weight, but is not normalized to ball compression. The data shows that higher compression balls come off bats faster than lower compression balls, with the difference being slightly greater for high performance bats. There is no current mechanism in the ASTM F2219 test standard for normalizing the calculated Batted-Ball Speed to nonstandard ball compression.

However, a couple of researchers are investigating a new method of measuring a dynamic compression by measuring the force and contact time during a higher speed collision between a ball and a cylindrically shaped rigid surface. Initial results suggest this new dynamic compression test might be able to distinguish between new multi-layer softballs that have the same COR and the same 0.25-inch static compression as traditional softballs, but which - when used with the same bat - produce batted-balls speeds that are 7-mph faster. Several research labs are attempting to collect and correlate data for this new measurement technique, and once the results are verified a new ASTM standard may be written for dynamic compression.

Three softballs with the same weight and COR but different static compresison.

Calculated BBS normalized to weight only.


[1] A.M. Nathan, "Characterizing the performance of baseball bats," Am. J. Phys. 71(2), 134-143 (2003)
[2] ASA Bat and Ball Certification Program Overview downloaded from (www.asasoftball.com)
[3] ASTM F1890-98 Standard Test Method for Measuring Softball Bat Peformance Factor. NOTE: this version of the standard has been superceded by the updated and revised version F1890-05.
[4] L. V. Smith, "Why ASTM 2219?" presented to the Fall 2003 meeting of the Sporting Goods Manufacturer's Association (SGMA), Dallas, TX, (October 2, 2003).
[5] L. Smith, J. Broker, and A. Nathan, "A Study of Softball Player Swing Speed," in: Sports Dynamics Discovery and Application, Edited by A. Subic, P. Trivailo, and F. Alam, (RMIT University, Melbourne Australia, 2003), 12-17.
[6] L. V. Smith, "Evaluating baseball bat performance," Sports Engineering, 4(4), 205-214 (2001).
[7] L. V. Smith and J. T. Axtel, "Mechanical Testing of Baseball Bats," Journal of Testing and Evaluation, 31(3), 210-214 (2003).
[8] ASTM Standard F2219-02, "Standard Test Methods for Measuring High-Speed Bat Performance," Annual Book of ASTM Standards, (ASTM, 2005). NOTE: this version of the standard has been superceeded by the updated and revised version F2219-05. A new revision, combining protocols for both softball and basebgall is currently being considered by the ASTM F08.26 Baseball and Softball Equipment subcommittee.
[9] Alan M. Nathan, "A Comparative Study of the Ball-Out and Bat-Out Techniques," Unpublished Document (March 23, 2004).
[10] Richard A. Brandt,"Method and Apparatus for Determining the Performance of Sports Bats and Similar Equipment." U.S. Patent #5,672,809 awarded September 30, 1997.
[11] Joseph G. Duris, Experimental and Numerical Characterization of Softballs, M.S. Thesis, Washington State University (2004).

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