In professional basketball, the accurate prediction of scoring opportunities
based on strategic decision-making is crucial for space and player evaluations.
However, traditional models often face challenges in accounting for the
complexities of off-ball movements, which are essential for accurate predictive
performance. In this study, we propose two mathematical models to predict
off-ball scoring opportunities in basketball, considering both pass-to-score
and dribble-to-score movements: the Ball Movement for Off-ball Scoring (BMOS)
and the Ball Intercept and Movement for Off-ball Scoring (BIMOS) models. The
BMOS adapts principles from the Off-Ball Scoring Opportunities (OBSO) model,
originally designed for soccer, to basketball, whereas the BIMOS 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 outperforms the BMOS in terms of
scoring prediction accuracy. Thus, our models provide valuable insights for
tactical analysis and player evaluation in basketball.

我们提出了两个数学模型来预测篮球比赛中的无球得分机会，分别考虑了传球得分和运球得分的动作，我们利用 630 场 NBA 比赛中的球员追踪数据评估了这些模型，结果表明 BIMOS 在得分预测准确性方面优于 BMOS，因此我们的模型为篮球的战术分析和球员评估提供了有价值的见解。

篮球中无球得分预测的数学模型

Mathematical models for off-ball scoring prediction in basketball

Evaluating the individual movements for teammates in soccer players is
crucial for assessing teamwork, scouting, and fan engagement. It has been said
that players in a 90-min game do not have the ball for about 87 minutes on
average. However, it has remained difficult to evaluate an attacking player
without receiving the ball, and to reveal how movement contributes to the
creation of scoring opportunities for teammates. In this paper, we evaluate
players who create off-ball scoring opportunities by comparing actual movements
with the reference movements generated via trajectory prediction. First, we
predict the trajectories of players using a graph variational recurrent neural
network that can accurately model the relationship between players and predict
the long-term trajectory. Next, based on the difference in the modified
off-ball evaluation index between the actual and the predicted trajectory as a
reference, we evaluate how the actual movement contributes to scoring
opportunity compared to the predicted movement. For verification, we examined
the relationship with the annual salary, the goals, and the rating in the game
by experts for all games of a team in a professional soccer league in a year.
The results show that the annual salary and the proposed indicator correlated
significantly, which could not be explained by the existing indicators and
goals. Our results suggest the effectiveness of the proposed method as an
indicator for a player without the ball to create a scoring chance for
teammates.

利用图变分循环神经网络对足球比赛中球员的轨迹进行预测，并对球员在没有球的情况下对进球做出贡献的能力进行评估，结果显示提出的指标与球员的年薪相关性显著，表明该方法可以有效评估球员在没有球的情况下为队友创造进球机会的能力。