DEVELOPMENT OF SOFTWARE FOR TACTICAL DECISION IN VOLLEYBALL USING GAME THEORY

在排球比赛中，已经开发了各种比赛分析系统，用于使用个人计算机记录比赛数据。在本研究中，除了收集数据的功能外，我们还利用博弈论开发了排球战术分析软件。用Visual Basic编写软件程序，并通过建立零和博弈的攻阻策略数学模型，计算出最小最大策略。在实践中，我们不仅可以在比赛结束后在屏幕上输入观看录制场景的数据，还可以在现场输入实时数据，以便在比赛中立即分析战术。我们还安装了一个服务器，通过连接日本体育科学研究所开发的视频数据库系统（SMART system）来分发录制的场景。因此，我们可以通过互联网观看录制的场景，并使用我们的系统对场景进行注释。在此基础上，利用校际排球联赛的数据，研究并提出了一种战术决策分析方法，并对进攻战术分配进行了讨论。此外，我们还研究了足球比赛的数学模型，以分析零和和非零和博弈模型下阵型的战术变化。利用这些模型，我们定量地展示了管理者的决策对比赛获胜概率的影响，并展示了联赛积分制度下球队间合作的效果。

In volleyball, a variety of game analysis systems have been developed for recording game data using a personal computer. In addition to the function of collecting data, we have developed software for analyzing tactics in volleyball using game theory in this research. We program this software with Visual Basic code and calculate the minmax strategy by formulating a mathematical model of attacking-blocking tactics as zero-sum game. In practice, we can input not only data watching a recorded scene on the screen after a match, but also real-time data on the site to analyze tactics immediately during a match. We also install a server for distributing a recorded scene by connecting with the video database system (SMART System) developed by Japan Institute of Sports Sciences. Thus, we can watch the recorded scene through the Internet and write annotation on the scene with our system. Further, using the data taken from an intercollegiate volleyball league, we study and propose a method for analyzing tactical decisions, and discuss the assignment of attacking tactics. Furthermore, we also study a mathematical model of a soccer game for analyzing the tactical changes of formations with a zero-sum and a non-zero-sum game model. Using these models, we quantitatively show how the managers' decisions affect the probability of winning the match, and demonstrate the effect of cooperation between teams under the league point system.