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A model for competitiveness level analysis in sports competitions: Application to basketball

机译：体育比赛中竞争水平分析的模型：在篮球中的应用

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摘要

The degree of overall competitiveness of a sport league is a complex phenomenon. It is difficult to assess and quantify all elements that yield the final standing. In this paper, we analyze the general behavior of the result matrices of each season and we use the corresponding results as a probably density. Thus, the results of previous seasons are a way to investigate the probability that each team has to reach a certain number of victories. We developed a model based on Shannon entropy using two extreme competitive structures (a hierarchical structure and a random structure), and applied this model to investigate the competitiveness of two of the best professional basketball leagues: the NBA (USA) and the ACB (Spain). Both leagues' entropy levels are high (NBA mean 0.983; ACB mean 0.980), indicating high competitiveness, although the entropy of the ACB (from 0.986 to 0.972) demonstrated more seasonal variability than that of the NBA (from 0.985 to 0.990), a possible result of greater sporting gradients in the ACB. The use of this methodology has proven useful for investigating the competitiveness of sports leagues as well as their underlying variability across time.
机译：体育联赛的整体竞争力是一个复杂的现象。很难评估和量化产生最终地位的所有要素。在本文中，我们分析了每个季节的结果矩阵的一般行为，并使用相应的结果作为可能的密度。因此，前几个赛季的结果是一种调查每个团队必须获得一定数量胜利的概率的方法。我们使用两种极端的竞争结构（层次结构和随机结构）开发了基于Shannon熵的模型，并将该模型应用于调查两个最佳职业篮球联赛：NBA（美国）和ACB（西班牙）的竞争力）。两个联盟的熵水平都很高（NBA平均为0.983; ACB平均为0.980），表明竞争能力很高，尽管ACB的熵（从0.986到0.972）表现出比NBA更大的季节变化（从0.985到0.990）， ACB中更大运动坡度的可能结果。实践证明，该方法的使用对于调查体育联赛的竞争力及其随时间变化的潜在变化非常有用。

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