A Cornell research team has employed a variation of a theory first used to predict the collective actions of electrons in quantum mechanical systems to a much taller, human system - the National Basketball Association.
A group led by Tomás Arias, professor of physics and a Stephen H. Weiss Presidential Fellow in the College of Arts and Sciences, has adapted density-functional fluctuation theory (DFFT) to predict player positions and rank players based on their defensive contributions. They've also attempted to quantify "player gravity" - how strongly a player attracts defenders, indicating he's a scoring threat.
"Gravity is a frequently used term in basketball, but how you quantify it has been a little tricky," said Boris Barron, M.S. '21, Ph.D. '24, now a postdoctoral researcher at the Max Planck Institute for Demographic Research in Rostock, Germany.
Barron is corresponding author of "Analyzing NBA Player Positions and Interactions With Density-Functional Fluctuation Theory," which published June 5 in Scientific Reports. Co-authors include Arias and Nathan Sitaraman, M.S. '18, Ph.D. '22, a postdoctoral researcher at the Cornell Laboratory for Accelerator-based Sciences and Education.
A relatively new formulation, DFFT seeks to infer interactions and spatial preferences directly from fluctuations in positional data. The theory has already been applied to systems as diverse as insect group organization, racial segregation in urban areas and simulations of crowd dynamics.
This study is a continuation of work the group presented in 2023 at an American Physical Society conference. In the earlier research, the group's model - based on density functional theory (DFT) - suggested the best positioning for each player on a basketball court in a given scenario if they want to raise their probability of either scoring or defending successfully.
Arias said he first thought about DFT in terms of crowd behavior - at a concert, for example - then wrote out some equations and realized "these were exactly the equations we use in our many-body physics and quantum mechanical theories.'"
Sitaraman, who at the time did consulting work for an NBA team and had access to player analytics, helped steer the group toward basketball as a testbed for their DFFT modeling. Neither Arias nor Barron was particularly interested in the NBA at the time.
"Nathan and I joked that they brought me on," Barron said, "so that when I run analyses, I don't actually know which players are supposed to be good at offense, defense, or 3-point shooting - I was largely in the dark."
The researchers' challenge: Given a moment in time on the court - the location of all 10 players and the ball - what is the probability of the offense scoring 0, 2 or 3 points?
For their study, the group used player-tracking data from the first half of the 2022-23 NBA season, and analyzed player and ball positions, during half-court possessions (excluding fast breaks), no more than three seconds before a shot was taken. By training the DFFT model on relevant subsets of the massive dataset, the researchers could predict where an individual player was likely to be, and evaluate probabilities of various scoring outcomes.
The researchers demonstrated that it is possible to improve defensive player positioning and identify player-specific tendencies, such as the consistency with which a player positions himself to help his team collectively defend against 2-point or 3-point shots.
To measure player gravity, the team analyzed the 50 players who were on the court most during the four months in the dataset, along with one special case - Golden State Warriors guard Stephen Curry, who holds the NBA career record for 3-point baskets made and is widely regarded as having the highest gravity in the league.
In fact, it was only after an earlier version of this work was presented at the 2024 MIT Sloan Sports Analytics Conference that Curry was added to the dataset. "Curry was not included at the time," Barron said, "and it seemed that every person who came to our presentation asked us, 'So where's Steph Curry?'"
Curry is unique, Barron said. "Everywhere along the 3-point line, he attracted nearly as much defense to his location - without the ball - as a typical player would with the ball, and at some locations exceeded it," he said, noting that when Curry is in the lane, closer to the basket, his gravity is actually slightly lower than that of a typical player.
The researchers also found that Denver Nuggets center Nikola Jokic produces strong "non-local gravity" - meaning that due to his propensity to pass the ball, defensive density tends to increase on the weak side of the court (opposite the ball).
Future research in this area will explore the concept of "defensive IQ" - a player's instincts and the ability to "see" a play before it develops.
"In terms of what coaches may be interested in," Arias said, "we could potentially do a deep dive on this data here to see what it is that they're not quite getting right."
