Mathematical models for off-ball scoring prediction in basketball

TL;DR

The paper addresses predicting off-ball scoring opportunities in basketball by extending the OBSO framework from soccer to basketball, introducing two theory-based models: BMOS for pass and dribble sequences and BIMOS which additionally accounts for ball interception. It demonstrates that BIMOS improves scoring prediction accuracy, particularly for pass-to-score situations, using tracking data from 630 NBA games in the 2015-2016 season. The models are built from components of occupancy, ball delivery, and scoring probability, with BIMOS incorporating ball interception via PBCF. This approach provides interpretable, physics-inspired insights for tactical analysis and player evaluation, while highlighting limitations in dribble-to-score predictions and near-basket scoring that point to avenues for future refinement and integration with box-score statistics and counterfactual analyses.

Abstract

In professional basketball, the accurate prediction of scoring opportunities based on strategic decision-making is crucial for spatial and player evaluations. However, traditional models often face challenges in accounting for the complexities of off-ball movements, which are essential for comprehensive performance evaluations. In this study, we propose two mathematical models to predict off-ball scoring opportunities in basketball, considering pass-to-score and dribble-to-score sequences: the Ball Movement for Off-ball Scoring (BMOS) and the Ball Intercept and Movement for Off-ball Scoring (BIMOS) models. The BMOS model adapts principles from the Off-Ball Scoring Opportunities (OBSO) model, originally designed for soccer, to basketball, whereas the BIMOS model also incorporates the likelihood of interception during ball movements. We evaluated these models using player tracking data from 630 NBA games in the 2015-2016 regular season, demonstrating that the BIMOS model outperforms the BMOS model in terms of team scoring prediction accuracy, while also highlighting its potential for further development. Overall, the BIMOS model provides valuable insights for tactical analysis and player evaluation in basketball.

Figures (7)

• Figure 1: Overview of OBSO, BMOS, and BIMOS structures. Attacking and defending players are represented in red and blue, respectively. An attacker at the bottom left currently possesses the ball. The OBSO and BMOS models consist of three components: spatial occupancy (PPCF), ball delivery probability (Transition Model), and scoring probability (Score Model). The BIMOS model consists of two components: ball occupancy (PBCF) and scoring probability, common to all three models. In the BMOS and BIMOS models, dribbling situations for PPCF and PBCF are incorporated as separate components alongside the pass model.
• Figure 2: Transition Model and Score Model. Transition Model distribution after applying a Gaussian filter for noise reduction (left). This model captures the tendency of the ball possessor to choose shorter-range ball movement. Scoring probabilities at various distances (right). The exponential function, depicted in red solid line, models the decreasing trend in scoring probability with increasing distance.
• Figure 3: Ball Velocity and Ball Handler Selection Rate. The left figure illustrates how the ball speed varies based on the type of ball movement (pass or dribble) and the distance traveled. For distance exceeding 10 meters, ball speed is assumed constant. The right figure shows the rate at which the ball possessor chooses to pass or dribble based on the travel distance.
• Figure 4: $\tau_{true}-\tau_{exp}$ Distribution. The figure shows the $\tau_{true}-\tau_{exp}$ distribution, highlighting the better fit of an asymmetric Lorentzian function compared to a logistic function. The heavy tail on the positive side suggests that players might not always move at a constant acceleration, resulting in longer than expected times to reach the target position.
• Figure 5: BMOS and BIMOS distribution. The ball possessor at the bottom left passed to a shooter at the bottom middle, resulting in a successful 3-point shot. The BIMOS effectively captures the higher scoring probability in proximity of the shooter.