Most physics problems, especially the undergraduate variety, require simplifying assumptions in order to make them workable - frictionless surfaces, perfect vacuums, spherical cows. This past May, I employed some simple physics to analyze the shooting trajectories of NBA players. The raw location data came from the SportVU location tracking system, and is somewhat noisy. To tease signal from that noise, I assumed the ball's path followed a simple trajectory, the kind which physics majors cut their teeth on as freshman. I then used linear regression to pick a path that best matched the raw data.
One key simplifying assumption made was to ignore the impact of drag on the flight of the ball. As the ball moves through the air, it is pushing that air out of the way, and the air pushes back, slowly degrading the ball's velocity. As it turns out, this effect, while small, was not negligible, and its omission was creating persistent bias in the modeling of free throws and field goals.
In this post, I'll outline my attempts to incorporate drag into my model of a basketball's trajectory, and then test that model's predictions against the raw SportVU data (science!). As a bonus project of sorts, I will also examine whether drag effects are noticeably different for thin air arenas such as those of the Denver Nuggets and Utah Jazz.