^{Sports Science Laboratory}

_{Bat-Ball Science Bat Performance Measures}

## Bat Performance Measures

*The following describes the common measures of bat performance: BPF, BESR, BBCOR and BBS.*

Once a bat has been tested, the data can be used to measure performance in a variety of ways. While some measures have been shown to correlate with field performance better than others, the best measure ultimately depends on the objectives of the association regulating performance.

Little League, USSSA, and NSA use the Bat Performance Factor (or *BPF*) to regulate bat performance.The *BPF *involves the bat-ball coefficient of restitution or *BBCOR*. Its definition is similar to that used for the ball (Eq. 2.1). We take the ratio of the relative speed after impact to the relative speed before impact. For an initially stationary bat, *Vi*=0, this is

(10.1)

The *BPF* found from the ratio of the *BBCOR* to the ball *COR* as

(10.2)

The Ball Exit Speed Ratio (or *BESR*) involves the collision efficiency, *ea*. For an initially stationary bat ea is defined as the ratio of the outgoing to incoming ball speeds as

(10.3)

The collision efficiency is between 0.1 and 0.2 for many bats. The *BESR* is obtained by adding ½ to the collision efficiency. The NCAA and High School Federation have used a modified *BESR* to regulate performance.

The NCAA desires to regulate bat performance relative to wood bats, where the *BESR *increases with length. Thus, the allowed *BESR* limit is a function of the length of the bat being tested. The *BBCOR* of wood bats is constant, independent of length. The NCAA and High School Federation have recently adopted a 0.5 *BBCOR* limit.

The batted ball speed (or *BBS*) is intended to represent the speed a ball would be hit in field conditions and is found according to

(10.4)

where *vp* is the pitch speed, *ea* is the collision efficiency and *Vb* is the bat speed (*ea *and *Vb* are taken at the impact location). The ASA regulates the performance of its bats using the *BBS* based on nominal game conditions found from the slow pitch field study, where *vp*=25 mph and *Vb* is found from

(10.5)

Equation 10.5 describes the linear speed of the bat at the impact location (in mph), while the analogous Eq. 8.1 describes the rotational speed of the bat (in rpm or rad/s). The nominal speed of 85 mph in Eq. 10.5 is the average players from the slow pitch field study (Fig. 8.7) [m].The additional terms in Eq. 10.5 account for the change in speed with impact location. The nominal 9000 oz in2 was the average bat *MOI* in the slow pitch field study. The speed should be referenced to the bat’s center of rotation in play. The impact location, *Q*, is taken at the test pivot point, 6 inches in from the knob. The field study found that the center of rotation is on average 2.5 inches out from the knob. Thus, the speed is scaled by adding 8.5 to *Q *and dividing it by 22 + 8.5. Any bat certified for ASA play must have a *BBS* less than 98 mph. The ISF adopted this method in 2006, but uses a 100 mph *BBS* limit.

One may ask how ASA’s approach to regulating bat performance (taken from the slow pitch game) applies to fast pitch softball. A 9,000 oz in2 bat that just meets the 98 mph *BBS* limit at Q=22 inches will have *ea*=0.12. In a fast pitch game where *vp*=*Vb*=60 mph, the *BBS* would be 74 mph. Said another way, a fast pitch bat that just meets the ASA *BBS* 98 mph limit, would actually produce a *BBS* closer to 74 mph in a typical fast pitch game.

[m] While this nominal bat speed has a large effect on the BBS, its primary significance is relative to the allowable BBS limit. If the nominal bat speed were 80 mph, for instance, the BBS limit becomes 92.4 mph. Similarly, if the nominal bat speed was 90 mph, the BBS limit becomes 103.6 mph. In both cases the allowable field bat performance has not changed. We have only adjusted the scale used to compare performance.