The Effect of Softball Compression and Coefficient of Restitution on Batted Ball Speed by Dr. Michael V. Cioccoa and Dr. Mark McDowellb aMichael V. Ciocco, Parsons Project Services, Inc., P.O. Box 618, South Park, PA 15129 bMark McDowell, Bomani Sports Research, Inc., P.O. Box 81402, Cleveland, Ohio  44181

Introduction
The performance of different softballs is a much discussed and debated subject in men’s slowpitch softball. Power hitters want to know which ball will maximize distance. While league directors, tournament directors, and associations try to balance performance with safety. Two measured quantities, compression and coefficient of restitution (COR) currently are used to characterize softballs. Softball compression is a measure of the force (lbs) required to compress the ball 0.25 inches. Softball compression is commonly reported as PQI (lbs/0.25 inch compression). The COR is defined as the ratio of the rebound speed of the ball bouncing off of a rigid wall compared to the ball's incoming speed. That is, if the incoming ball speed is 60 mph and the rebound ball speed is 30 mph the COR = 30/60 = 0.50.

Measuring the actual performance of a ball is more difficult. The most direct and reproducible method of quantifying performance is measuring Batted Ball Speed (BBS) with a radar gun.

In a recent article, “On The Ball”, in Softball Magazine[1] the effects of softball compression and coefficient of restitution (COR) on batted ball speed were presented. There are two important points about this article need to be discussed. First, the article states that the BBSs and distances were calculated. Secondly the article states that the calculations for BBS and distance were based on an “A” player with a 70 mph bat speed.
With respect to the first point, the mechanics of batting and bat – ball collision cannot be perfectly modeled via calculations because of inconsistent data on angle of deflection, inconsistent ball compression values, ball cover slippage properties, and varying MOI values for each bat model. Therefore, actual measured values would provide more accurate results. As for the second point, measured bat speeds for “A” level players are typically in the 85 – 100 mph range based on our testing over the past 6 years. This further complicates the use of “calculations” in any attempt to quantify effects of PQI and COR on BBS.

In order to remove the generalizations introduced by using “calculations”, and allow for realistic swing speeds, a study was undertaken in order to provide real world data. This real world data was then used in determining the effect of PQI and COR on BBS. In no way is this study meant to be an attack on the “On The Ball” article. Instead it is hoped that by employing measured BBSs a better understanding of actual effects of PQI and COR on performance can be determined. And this in turn would allow players, directors, and associations to make a better-informed decision when deciding which ball to use.

In this study, a typical “A” level player, swinging two state-of-the-art 30 oz. Multi-walled bats with balls of various PQI and COR values, was used to provide actual BBSs. These BBSs were then used to quantify the effect of PQI and COR on ball performance.

The CORs listed in this study were the stated CORs on the balls. The COR test is an ASTM Test procedure that is intended to standardize a method of measuring the COR of baseballs and softballs. The ASTM COR test is a repeatable and uniform testing procedure based on ball speed measurements before and after impact with either a wood or metal surface. However, the ASTM COR test does not address all safety concerns and states the following: “It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use”. This means that the softball associations are ultimately responsible for controlling the safety of the balls used in the sport of softball.

Swing speed was measured using an ATEC Sports Speed Trainer 2000 bat speed meter that measures the average swing speed at the end of a bat. Note that depending on the swing mechanics of a player and the location of the sweet spot on the bat the speed of the sweet spot will be 85 to 90% of the end-of-bat speed.

A Jugs professional pitching machine was used to pitch the balls. The machine provided consistent pitch speeds (measured via radar gun) in the 16-22 mph range.

The radar gun used was a Jugs Professional Cordless MPH RADAR GUN (model # R1000). This device is used to measure batted-ball speed and is accurate to within ± 0.5 mph. The gun is used to record the batted-ball speed right after impacting a ball and was placed in the same position for all measurements.

The batter hit each ball at least 9 times in order to provide 5 “good” measurements. Good measurements were defined as line drives that had a low trajectory and did not hit the top of the net.

The bats used were chosen because they are extremely popular Multi-walled 2002 models readily available. Both bats were ASA certified. The balls used were chosen to encompass a range of compressions (411 – 553 PQI) and CORs (0.40 – 0.47).

It should be noted that softball compressions vary from about 200 to 600 PQI, a 400 PQI difference, for different balls. The corresponding change in BBS, for a 400 PQI difference, could be as much as 17 mph, correlating to a distance change of about 55 feet. This is most definitely a significant effect.

In order to accurately determine the effect of COR the results first need to be normalized to the same PQI. Adjusting the batted ball speeds using the results from the effect of PQI on BBS can do this. Table 2 summarizes the adjusted BBSs, adjusted to have a standard PQI of 500. Performing statistical analysis on this data yields the effect on COR on BBS. For an increase of 0.07 in COR (0.40 to 0.47 COR) the BBS decreases 3.57 mph (± 0.28 mph). This result was opposite of what was expected.  Again from a previous study[2] this correlates to an approximate decrease in distance of 11-12 feet.

There are a couple of possible explanations for this surprising result. It may be that the actual COR of the ball at real impact speeds (100+ mph, 80+ mph bat plus a 20+ mph pitched ball) may be very different from the ball’s stated COR. The COR test uses an impact speed of 60 mph, much lower than the actual impact velocities of 100+ mph and it has been shown that COR is a strong function of impact speed[3]. Also while the cover of the softball has no real effect on its compression value, cover slippage has a significant effect on batted-ball performance. The better the cover is bonded to the ball, the less cover slippage, the better it will perform.

Another possible explanation for the relationship of decreasing BBS with increasing COR may be that the compression measurements are conducted at somewhat lower forces than are actually present in a bat-ball collision. The force required to change the motion of a 6.5 oz. ball pitched at about 20 mph to a 90 mph hit ball in the 1/1000 of a second of bat-ball contact is over 2000 lbs. And since the compression measurements resulted in compressions of between 400 and 600 PQI it follows that the balls may perform differently at the higher actual forces.

It is clear that the biggest safety factor involved in the game of softball today is the ball.  High-Compression balls have no place in the game of softball at any level. The BPF 1.20 and ASA 2000 testing methods have capped the performance of bats and while both tests have their flaws, they at least keep the performance of bats at a reasonable level.

*  Softball COR was found to have a slight negative effect on batted ball speed. Increasing the COR from 0.40 to 0.47 actually resulted in a decrease in batted ball speed of over 3 mph and correlated to a decrease in distance of about 11 feet.