Abstract This paper adopts concepts of systems’ theory and multidimensional scaling to study the competitiveness in soccer leagues of four countries. A season for a given league is read as a dynamical system with states that are measured at discrete time samples corresponding to the rounds. The system state is inferred from the accumulated points won and lost by each team. These data are interpreted as active and reactive power and are processed in the complex plane. The league competitiveness is visualized through 2-dim maps of items that represent the relative positioning of the teams over the season. The results are compared with those obtained with two classic competitiveness measures.

中文翻译：

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足球联赛中的竞争力建模和可视化

摘要 本文采用系统论和多维尺度的概念来研究四个国家足球联赛的竞争力。给定联赛的一个赛季被解读为一个动态系统，其状态是在与回合相对应的离散时间样本中测量的。系统状态是从每个团队赢得和失去的累积积分中推断出来的。这些数据被解释为有功功率和无功功率，并在复平面中进行处理。联赛的竞争力通过代表球队在整个赛季中的相对位置的项目的二维地图进行可视化。将结果与使用两种经典竞争力度量获得的结果进行比较。