Intelligent sports video analysis demands a comprehensive understanding of temporal context, from micro-level actions to macro-level game strategies. Existing end-to-end models often struggle with this temporal hierarchy, offering solutions that lack generalization, incur high development costs for new tasks, and suffer from poor interpretability. To overcome these limitations, we propose a reconfigurable Multi-Agent System (MAS) as a foundational framework for sports video understanding. In our system, each agent functions as a distinct "cognitive tool" specializing in a specific aspect of analysis. The system's architecture is not confined to a single temporal dimension or task. By leveraging iterative invocation and flexible composition of these agents, our framework can construct adaptive pipelines for both short-term analytic reasoning (e.g., Rally QA) and long-term generative summarization (e.g., match summaries). We demonstrate the adaptability of this framework using two representative tasks in badminton analysis, showcasing its ability to bridge fine-grained event detection and global semantic organization. This work presents a paradigm shift towards a flexible, scalable, and interpretable system for robust, cross-task sports video intelligence. The project homepage is available at https://aiden1020.github.io/COACH-project-page