The Biomechanics of Baseball Pitching — Appendices

This work is part of my dissertation submitted at the University of Aberdeen in partial fulfilment of the BSc in Physics in May 2021.

During this research I was supported by physicists and experts to whom I am grateful. In particular I would like to thank Prof. Jan Skakle, Alessandro Rosa Colombo, Gary McCoy, Brent Strom and Ron Wolforth.
I want this work to be publicly available to athletes, coaches and researches as a source of information to support athletes development.

Appendix A — Standard Naming of the Positioning of Shoulder and Elbow

This information is based on Sabick et al. (2004).
The shoulder joint has three degrees of freedom: flexion, abduction and rotation.

• Shoulder flexion, (Fig.A1.D) is also referred to as horizontal abduction or adduction. The shoulder is in neutral flexion if it lays on the frontal plane, (Fig.A2). The shoulder is in 90° adduction (or flexion) if the hand is pointing straight forward, and if the hand is pointing behind the plane, the shoulder is in horizontal abduction.
• Shoulder abduction, (Fig.A1.C) is also referred to as lateral abduction. The arm is in neutral abduction if parallel to ground, and is adducted when moving down along the trunk.
• Shoulder rotation, (Fig.A1.B) allows the shoulder to point the forearm at different angles on the median plane, (Fig.A2) while keeping the elbow bent at 90°.

The elbow has two degrees of freedom: flexion and pronation.

• Elbow flexion, (Fig.A1.A) allows the elbow to bend. The arm is in neutral position when is fully extended, and measures 90° if the forearm and upper-arm are perpendicular to each other.
• Elbow pronation, (Fig.A3) allows the forearm and hand to be supinated (facing up) and pronated (facing down).

Appendix B — Conversion Table

In this dissertation, the speed of pitches is reported in mph as it is the unit adopted in the game of baseball, however, every velocity is also converted into m/s in parenthesis.
A useful conversion table it provided, (Table.B1):

Appendix C — The Game of Baseball (field, rules)

Rules reported from MLB (2019).

The game of baseball is played on a field that has a shape similar to a 90° sector of a circle, (Fig.C1). At the centre of the infield grass is placed the pitcher’s mound. The pitcher’s mound is 18.44 m away from home plate and is 25 cm tall, (Fig.C2). On top of the mound there is the pitching rubber, a plate where the pivot foot of the pitcher must be placed during the pitching motion. The batter stands in the batter’s box beside home plate, (Fig.C3).

Each batter has a strike zone that has the width of home plate (43 cm), and the height between the hollow of the kneecaps and the midpoint between shoulders and waist (approx. 68 cm).
A pitch that crosses the strike zone is called a “strike”, otherwise is called a “ball”. If the batter swings and doesn’t hit the baseball, this is counted as a strike. The pitches are caught by the catcher, behind whom is standing the umpire deciding strikes and balls. During the “At Bat” between batter and pitcher, a “count” of strikes and balls is kept. With 3 strikes the batter is “out” (eliminated), with 4 ball the batter receives a “walk” (or base on ball) that grants him access to first base.
If the batter hits the baseball, the game evolves into other scenarios that are not relevant for this dissertation.

A pitcher has an arsenal of different pitches. The most common pitches are: fastball (93.2 mph or 41.7 m/s), changeup (81.7 mph or 36.5 m/s), curveball (77.2 mph or 34.5 m/s), and slider (85.7 mph or 38.3 m/s), (eFastball, 2014c), and while the fastball follows a straight trajectory, the changeup drops vertically, the curveball moves vertically and horizontally, and the slider moves horizontally only, as shown in this animation, (Brady, 2019).

[https://twitter.com/BaseballFreak_9/status/1105630404227194881?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1105630404227194881%7Ctwgr%5E%7Ctwcon%5Es1_c10&ref_url=https%3A%2F%2Ffivethirtyeight.com%2Ffeatures%2Fmlb-curves-and-sliders-have-gotten-alarmingly-nasty%2F]

A game is made of 9 “innings”. In each inning there is a “top part” and a “bottom part” where attacking team and defending team are swapped.
The MLB season is composed by 162 games played over 181 days. Due to the limited rest days, clubs need many pitchers on their roster. A club has 12 pitchers: 5 starters set to start the games in turns, and 7 relievers ready to substitute them and finish the game. Starters pitch 5–6 innings, and relievers only 1–2 innings.