Math in Softball

Pitching

Almost every aspect of softball pitching has an opportunity for mathematical analysis. In softball, a majority of pitchers use a windmill style wind up, instead of the typical overhand throw that most baseball players use. Measurement of the arm angles during a pitch reveals that the windmill style wind ups help extend the upper arm away from the shoulder at an average angle of 156 degrees. Whereas overhand throws only extend the arm 108 degrees. This helps to relieve the repeated stress on the arm and remove long-term health risks.

Reaction Time

To measure reaction time(the time between the release of the ball by the pitcher to the instant at which contact needs to be made) the only required factors are speed of the pitch and distance to the batter. In softball, the distance from the pitcher's mound to the plate is 43 feet and an average fastball of a well practiced pitcher can be measured at 70 miles per hour. The reaction time equals distance divided by speed, and is therefore 0.42 seconds. Compare this reaction time to that of a 95 mph fastball in professional baseball (0.43 seconds).

Batting

Bat quickness (s) and bat velocity (m/s) are two details of a batter's swing that can be evaluated in order to define a successful hitter. An increase in bay velocity will potentially lead to an increase in ball velocity off the bat, and in turn increase the chance of the batted ball being a hit. Many believe if a hitter can complete the swing in a shorter amount of time this will allow the hitter more time to evaluate the incoming pitch thus make a better decision about whether or not to commit to the incoming pitch. However, a quicker swing that was completed in less time would have a slower bat velocity. An effective swing depends on executing the steps of the swing. A common way of evaluating the relationship between bat quickness and bat velocity is to consider bat acceleration (an average acceleration of the bat head calculated by dividing the bat velocity in m/s of a swing at its point of contact by the swing bat quickness time in seconds) A greater bat acceleration come from some combination of maximizing bat velocity and minimizing bat quickness.

Sources

This page by Angelique B. ('18)

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