Understanding the principles of real-world biological multi-agent behaviors is a current challenge in various scientific and engineering fields. The rules regarding the real-world biological multi-agent behaviors such as those in team sports are often largely unknown due to their inherently higher-order interactions, cognition, and body dynamics. Estimation of the rules from data, i.e., via data-driven approaches such as machine learning, provides an effective way to analyze such behaviors. Although most data-driven models have non-linear structures and high predictive performances, it is sometimes hard to interpret them. This survey focuses on data-driven analysis for quantitative understanding of behaviors in invasion team sports such as basketball and football, and introduces two main approaches for understanding such multi-agent behaviors: (1) extracting easily interpretable features or rules from data and (2) generating and controlling behaviors in visually-understandable ways. The first approach involves the visualization of learned representations and the extraction of mathematical structures behind the behaviors. The second approach can be used to test hypotheses by simulating and controlling future and counterfactual behaviors. Lastly, the potential practical applications of extracted rules, features, and generated behaviors are discussed. These approaches can contribute to a better understanding of multi-agent behaviors in the real world.

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