Not yet reviewed by Pith; the record is open.

In many real-world complex systems, the behavior can be observed as a collection of discrete events generated by multiple interacting agents. Analyzing the dynamics of these multi-agent systems, especially team sports, often relies on understanding the movement and interactions of individual agents. However, while providing valuable snapshots, event-based positional data typically lacks the continuous temporal information needed to directly calculate crucial properties such as velocity. This absence severely limits the depth of dynamic analysis, preventing a comprehensive understanding of individual agent behaviors and emergent team strategies. To address this challenge, we propose a new method to simultaneously complete the velocity of all agents using only the event-based positional data from team sports. Based on this completed velocity information, we investigate the applicability of existing team sports analysis and evaluation methods. Experiments using soccer event data demonstrate that neural network-based approaches outperformed rule-based methods regarding velocity completion error, considering the underlying temporal dependencies and graph structure of player-to-player or player-to-ball interaction. Moreover, the space evaluation results obtained using the completed velocity are closer to those derived from complete tracking data, highlighting our method's potential for enhanced team sports system analysis.