Multi-agent statistically discriminative sub-trajectory mining and an application to NBA basketball
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Rory Paul Bunker
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Vo Nguyen Le Duy
Abstract
Improvements in tracking technology through optical and computer vision systems have enabled a greater understanding of the movement-based behaviour of multiple agents, including in team sports. In this study, a multi-agent statistically discriminative sub-trajectory mining (MA-Stat-DSM) method is proposed that takes a set of binary-labelled agent trajectory matrices as input and incorporates Hausdorff distance to identify sub-matrices that statistically significantly discriminate between the two groups of labelled trajectory matrices. Utilizing 2015/16 SportVU NBA tracking data, agent trajectory matrices representing attacks consisting of the trajectories of five agents (the ball, shooter, last passer, shooter defender, and last passer defender), were truncated to correspond to the time interval following the receipt of the ball by the last passer, and labelled as effective or ineffective based on a definition of attack effectiveness that we devise in the current study. After identifying appropriate parameters for MA-Stat-DSM by iteratively applying it to all matches involving the two top- and two bottom-placed teams from the 2015/16 NBA season, the method was then applied to selected matches and could identify and visualize the portions of plays, e.g., involving passing, on-, and/or off-the-ball movements, which were most relevant in rendering attacks effective or ineffective.
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 19H04941
Award Identifier / Grant number: 20H04075
Funding source: Japan Science and Technology Agency
Award Identifier / Grant number: JPMJPR20CA
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Research ethics: Not applicable.
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Author contributions: The authors have accepted responsibility for the entire content of this manuscript and approved its submission.
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Competing interests: No competing interests to declare.
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Research funding: This research was partly funded by JSPS (Grants 19H04941, 20H04075) and JST PRESTO (Grant JPMJPR20CA).
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Data availability: The raw data was sourced from https://github.com/neilmj/BasketballData/tree/master/2016.NBA.Raw.SportVU.Game.Logs. The code is available from https://github.com/rorybunker/ma-stat-dsm.
Code
The MA-Stat-DSM code is available on GitHub: https://github.com/rorybunker/ma-stat-dsm
Statistical testing & pruning properties of (MA)-Stat-DSM
The statistical testing and pruning properties of MA-Stat-DSM are essentially analogous to the original Stat-DSM (Le Vo et al. 2020). Therefore, in this subsection (and in Figure 2 in the main text), we provide a brief explanation of the statistical testing and pruning properties of (MA-)Stat-DSM and refer the reader to (Le Vo et al. 2020) for full details.
Stat-DSM (MA-Stat-DSM) represents sub-trajectories (sub-matrices) in the form of a tree, which is pruned to remove sub-trajectories (sub-matrices) that are guaranteed to not be discriminative (this pruning criterion is shown in line 18 of the MA-Stat-DSM algorithm pseudo-code in Algorithm 1). Stat-DSM (MA-Stat-DSM) uses Fisher’s Exact Test (FET) (Agresti 1992; Fisher 1922) to determine the statistical significance of a sub-trajectory (sub-matrix) using a contingency table with the number of trajectories (matrices) that, respectively, contain and do not contain sub-trajectories (sub-matrices) within a distance of ɛ. A correction for multiple-testing bias is also incorporated, which is necessary due to the calculation of p-values for a large number of trajectories (trajectory matrices), and is conducted using the Westfall-Young (WY) method (Terada et al. 2013; Westfall and Young 1993). Sub-trajectories (sub-matrices) are only identified as SSD if their p-value is less than their adjusted significance level, δ, which is, in turn, less than α = 0.05. The dataset labels are permuted B = 1,000 times as part of this procedure. The pruning and WY methods are applied simultaneously to reduce complexity (Step 1, Figure 2).
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