Saturday, August 22, 2015

Kind of a Drag

Just a heads up that this post is pretty heavy on math and physics: differential equations, integrals, drag coefficients, air density at varying altitudes, etc. You know, in case you're into that kind of thing.

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.

Thursday, August 20, 2015

Vegas Never Doubted Clayton Kershaw

Baseball diamond marines.jpg
San Diego's Petco Park
The most "pitcher friendly" park in the
league according to the market
After a long hiatus, betting market rankings for major league baseball are now available and will update daily for what's left of the season. Similar to my rankings for the NFL, NBA, College Football, and College Basketball, these attempt to reverse engineer an implied power ranking from the betting lines and totals for each game. I now have all five sports on a common mathematical framework and intend to share the technical underpinnings of the methodology in a future post.

The Los Angeles Dodgers currently sit atop the market based rankings, despite having just the sixth best record in the league.


Ranking Starting Pitchers

In addition to the standard team rankings, I can also derive a ranking of starting pitchers. Each MLB team is more like 5 to 6 distinct teams, depending upon who takes the mound to start. According to the market, the best pitcher in the league is, and has been, the Dodgers' Clayton Kershaw. Teams facing Kershaw are expected to score 1.27 less runs on average when compared to a league average starter. And despite Kershaw's early season bout with mediocrity, the market didn't blink. Kershaw has remained the top ranked pitcher throughout the season according to my Vegas rankings (check the sparkline next to each starter in the ranking table for a snapshot of their season progression).