Insider Brief
- Cornell physicists adapted a quantum physics method to analyze NBA player tracking data, revealing new ways to quantify defense, predict outcomes, and measure player influence.
- The study uses density-functional fluctuation theory (DFFT) to model player positions as continuous probability fields, reducing data complexity while preserving predictive accuracy.
- Results highlight player-specific defensive tendencies, quantify off-ball “gravity” effects, and lay the groundwork for future analysis of non-local player influence and defensive anticipation.
A team of physicists at Cornell University has adapted quantum theory to analyze NBA player behavior, revealing new ways to quantify defense, predict play outcomes and measure that elusive force known as player gravity. Their study, published in Scientific Reports, suggests that basketball may be governed not just by coaching strategies and raw talent — but equations typically used to model electrons and atoms may also earn an assist.
The researchers employed a method known as density-functional fluctuation theory (DFFT), a mathematical tool from quantum physics that simplifies complex systems by turning the positions of interacting particles into smooth probability maps. In this case, the “particles” are basketball players, and the maps describe their on-court tendencies and interactions during play.
To The Hoop, Y’all
By transforming player-tracking data — down to the centimeter — into continuous densities, the team could predict where a player is likely to be at any given moment. This isn’t just about who’s guarding whom, but about how likely a player is to be in the best spot to prevent a shot or create a scoring chance. And unlike traditional metrics that rely on basic stats or box scores, this method works by learning from the actual geometry and flow of the game.
The model proved surprisingly accurate. In tests, it could identify a missing defender’s location to within 3% of the half-court area about half the time. It also showed strong correlation with play outcomes, such as whether a shot attempt would likely result in 0, 2, or 3 points. The researchers say these results match or even outperform traditional probabilistic models while using far fewer assumptions and data points.
More impressively, the approach allowed the researchers to assess which defenders consistently put themselves in the right place at the right time, something even advanced stats often miss. Players were evaluated based on their ability to reduce scoring probability by positioning alone, without factoring in size, speed, or vertical leap.
Among the findings: centers like Brook Lopez and Nikola Jokic stood out as elite at defending against 2-point shots, while Max Strus and Royce O’Neale were better at thwarting 3-point attempts. Notably, the model picked up on an inherent trade-off. Players who excelled at protecting the paint — that’s the rectangular area near the basketball hoop, my fellow non-sporty nerds — tended to be weaker perimeter defenders, and vice versa. The researchers dubbed this a spatial tension in defensive coverage, akin to Heisenberg’s uncertainty principle, if Heisenberg had been into zone defense.
Player Gravity
The team also tackled the long-discussed but rarely quantified idea of “player gravity” — or, how much attention a star draws from defenders even without the ball.
Using DFFT, the researchers calculated how much a player’s mere presence warps the distribution of defensive players across the court. Steph Curry, unsurprisingly, bent defensive space near the 3-point line like a black hole bends light. Luka Doncic pulled defenders wherever he went, while Shai Gilgeous-Alexander generated the most pull near the rim.
What sets this method apart is its ability to separate a player’s individual influence from that of teammates. Earlier attempts to measure gravity often muddled the two, but by comparing models trained on specific players to those trained on generic ones, the Cornell team could isolate the gravitational field — so to speak — of a single star.
“Gravity is a frequently used term in basketball, but how you quantify it has been a little tricky,” Boris Barron, one of the Cornell researchers, now a postdoctoral researcher at the Max Planck Institute for Demographic Research in Rostock, Germany, said in the Cornell Chronicle.
The researchers also hinted at broader applications. With further refinement, DFFT could help optimize player positioning in real time, or even serve as a coaching tool to simulate different lineups and defensive schemes. It might even measure “defensive IQ”—how quickly a player adapts to the developing play — by tracking how their position changes in the seconds before a shot.
Limitations And Future Plans
The approach isn’t without limitations. It assumes that player densities behave smoothly and that variations in location can be mapped reliably across a grid. And while the technique drastically reduces the number of parameters needed — from 40,000 to 600 — it still relies on high-resolution tracking data not publicly available.
As sports become more scientific and rely more heavily on increasingly complex analysis, the results have opened the door to a new kind of basketball analytics, one that borrows more from physics journals than playbooks. Rather than labeling players as guards or forwards, the model considers them dynamic agents in a probability field, reacting not to static positions but to evolving game states. (But try adding that to the playbook.)
In the future, the researchers plan to extend the model to study non-local effects — like how Jokic’s passing reputation increases defensive density away from him — or evaluate players’ adaptability in the final seconds of a shot clock. These are the kinds of insights traditional stats can’t capture, but a physics engine for basketball just might.
Nathan Sitaraman, a postdoctoral researcher at the Cornell Laboratory for Accelerator-based Sciences and Education, and Tomás Arias, professor of physics and a Stephen H. Weiss Presidential Fellow in the College of Arts and Sciences, Cornell, worked with Barron on the study.
