Softball pitching has a unique set of attributes that enable interesting mathematical analysis. These attributes result from specific aspects of the game of softball, such as the size of the ball, the distance from the pitcher's mound to the batter and the distinct windmill windup that many pitchers use. By describing the role of each of these characteristics mathematically, we can very accurately analyze and compare different pitchers and different sports.

## Significance

Mathematical calculations describe physical processes in discrete terms. This allows us to accurately measure different aspects of softball pitching. For example, math enables a calculation of reaction time for different pitchers. Reaction time depends specifically on speed of a pitch and distance to the batter. Comparison of reaction time across different sports shows exactly how softball pitching relates to baseball pitching or even tennis serving. In addition, mathematical assessment of a pitcher's windup can identify potential health and injury risks that are common to the sport.

## Considerations

To measure reaction time, the only required inputs are speed of the pitch and distance to the batter. In female professional softball, the distance from the pitcher's mound to the plate is 43 feet. In softball, a very good fastball 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), and it is easy to see that softball hitters can have to make the same reaction that a baseball player makes.

## Benefits

Another set of mathematical measurements benefits the health of a softball pitcher. In female professional softball, most pitchers use a windmill style windup, instead of the typical overhand throw that most baseball players use. Measurement of the arm angles during a pitch reveals that windmill style windups extend the upper arm away from the shoulder at an average angle of 156 degrees. Overhand throws only extend the arm 108 degrees. Repeated stress of the arm is this way can have long-term health risks to softball pitchers.

## Identification

Almost every aspect of softball pitching is an opportunity for mathematical analysis. An insightful observer will identify these characteristics readily. For example, softball pitchers don't throw only fastballs. They can utilize curve balls, sinker balls and rising pitches as well. Math enables an analyst to identify not only how long it takes each of these pitches to arrive at the plate, but how far the pitch moves on its way there. This overall movement during the pitch is part of the measurement of its displacement. Displacement, a mathematical attribute, is the precise measurement of a change in position.

## Potential

Mathematical description of softball pitching has the potential to solve many arguments or dispel any misconceptions about the sport. Comparison of reaction time shows exactly how softball and baseball relate, and can also be used to compare these sports with others that have reaction time as a critical component. Finally, the potential to identify exactly why injury risks occur for pitchers can lead to changes that will preserve their health while allowing them to continue to pitch at a high level.