Bradley-Terry Rankings: Introduction to Logistic Regression

In a recent post, we identified the Colley Matrix methodology for ranking NBA teams. The methodology provided insight but abused the originating statistical construct in an effort to enforce a correlated, solvable, set of equations to identify a “probability” of winning. Unfortunately, we witnessed that not only were those statistical assumptions violated, but the resulting…

Statistics of Colley’s Ranking Methodology

In 2002, Wes Colley (Princeton) developed a methodology that became a part of College Football BCS rankings lore: The Colley Method. In his original paper, Colley claims that his method is “bias free” for estimating the ranking of a team given a particular schedule. The resulting values for each team is identified as a ranking…

Kinematics of Player Motion

After a couple special topics posts in Sketching and Voronoi Tessellation, we take a step back and look at the basic mechanics of player motion: position, velocity, and acceleration. Understanding computation and estimation of such quantities allow us to perform more important calculations such as trajectories, coverage, and crashing. The easiest way to capture these…

The Art of Sketching: Trajectory Analysis

In a recent 2017 paper posted by Andrew Miller (Harvard University / Philadelphia 76ers) and Luke Bornn (Simon Fraser University / Sacramento Kings) titled “Possession Sketches: Mapping NBA Strategies,” the duo takes a well-known manifold learning technique called trajectory analysis and develops a methodology of classifying NBA actions through the use of functional mapping of…