Paradoxical popups: Why are they hard to catch?

TL;DR

This paper explains why certain baseball pop-ups are difficult to catch by analyzing their complex trajectories influenced by Magnus force, revealing how these paradoxical paths mislead fielders and affect their pursuit strategies.

Contribution

It introduces a physics-based model of paradoxical pop-up trajectories, highlighting the role of Magnus force in causing misleading flight paths for fielders.

Findings

Magnus force causes pop-ups to have cusps and loops near the apex.

Trajectory analysis explains fielders' difficulty in catching paradoxical pop-ups.

Model aligns with former major league infielders' experiences.

Abstract

Even professional baseball players occasionally find it difficult to gracefully approach seemingly routine pop-ups. This paper describes a set of towering pop-ups with trajectories that exhibit cusps and loops near the apex. For a normal fly ball, the horizontal velocity is continuously decreasing due to drag caused by air resistance. But for pop-ups, the Magnus force (the force due to the ball spinning in a moving airflow) is larger than the drag force. In these cases the horizontal velocity decreases in the beginning, like a normal fly ball, but after the apex, the Magnus force accelerates the horizontal motion. We refer to this class of pop-ups as paradoxical because they appear to misinform the typically robust optical control strategies used by fielders and lead to systematic vacillation in running paths, especially when a trajectory terminates near the fielder. In short, some of the dancing around when infielders pursue pop-ups can be well explained as a combination of bizarre trajectories and misguidance by the normally reliable optical control strategy, rather than apparent fielder error. Former major league infielders confirm that our model agrees with their experiences.