# Manifold Nonparametrics: Which Way Do Passers Pass?

As a player traverses across the court, they break down and process every event that they see: the assertion of defensive players, the alignment of their teammates, and current state of the game. The ability to perceive all three components simultaneously is what I call court vision. It is one of the primary instigators that…

# Exercising Error: Quantifying Statistical Tests Under RAPM (Part IV)

In the Regularized Adjusted Plus-Minus (RAPM) model, one of the perceived challenges is understanding the error associated with the resulting posterior RAPM value a player receives. In a previous post, we noted that RAPM is a Bayesian model in which we assume that “player contribution” can be estimated through weighted offensive ratings conditioned on the…

# The “80 Point Club”

Whenever we talk about scoring in the NBA, typically the the conversation points towards heroic scoring feats such as Wilt Chamberlain’s 100 point game or Kobe Bryant’s 81 point game. Or Wilt Chamberlain’s 78 point game… Or Wilt Chamberlain’s pair of 73 point games… or Wilt Chamberlain’s 72 point game. Of those other spurious 70+…

# The Potential Assist

In a fairly comical article back in February 2018, Bleacher Report identified the League’s Least Valuable Shooters. In this article, Adam Fromal examined players around the league by extracting their field goal percentage from four particular zones on the court: 3-10 feet, 11-16 feet, 17′-3pt, and 3PA. Fromal would then calculate each player’s points per…

# Applying Role Alignment to Tracking Data

Once of the core applications for tracking data is the ability to apply machine learning to gain insight into player tendencies. Unfortunately, due to small samples, we cannot simply measure a particular player’s track paths and say “this player tends to do x.” Instead, we must adopt methods that lift information off a player and…

# Is Scoring Up (Again) in the NBA?

A couple years ago, I presented an introduction to the Wilcoxon-Mann-Whitney nonparametric test with respect to identifying whether scoring was indeed increasing in the NBA. This was in 2015; and now that we are a few seasons along, we can start tracking the year-to-year trends. The reason for this popping up once again is primarily…

# Curious Tale of 3’s Versus 2’s in the NBA

Over the last decade, the subtle changes from offenses revolving around mid-range jump shots to long-range three point attempts have become much more explicit as teams such as the Houston Rockets had come off a 2017-18 campaign launching over 50% of their field goal attempts from beyond the arc. The mathematics is simple: “3 >…

# Introduction to Pandas Using Play-By-Play

By popular demand, attached you will find basic course materials that I developed for a sports analytics course taught at UW-Madison. The goal is simple: introduce Pandas and show how column manipulations, groupings, and report building could be accomplished. This was a working document at the time; and has not been updated since the course.…

# Understanding Trends in the NBA: How NNMF Works

Over the past decade a true emphasis on three point shooting has emerged. This can be credited to the understanding of effective field goal percentage being a better underlying parameter for points per field goal attempt than raw field goal percentage. And it’s become an emphasis for some top-tier teams such as the Houston Rockets.…

# Stochastic Tracking

In the era of tracking data, a need for a new style of analysis has emerged. Long gone are the regularized regression models and the simple counting techniques. Instead, we require leveraging shot-noise distributed systems such as Dan Cervone’s competing risks model, or Matthias Kempe’s self-organizing maps, or Peter Carr’s Imitation Learning. The list is…