量化2018年FIFA世界杯预选赛的不公平性
Quantifying the unfairness of the 2018 FIFA World Cup qualification
摘要：
采用蒙特卡罗模拟方法对2018年世界杯足球赛预选赛的公平性进行了研究。预选赛的概率是为102个国家计算的，除了非洲和欧洲国家。提出了一种量化不公平程度的方法。虽然四个国际足联联盟的资格是公平的，但各大洲之间存在严重差异：例如，南美球队在亚洲比赛的机会可能会增加两倍。在洲际附加赛中选择固定的对决，而不是现在的随机抽签，可以减少比赛的不公平性。澳大利亚从大洋洲区转移到亚洲区，将使其参加2018年世界杯的概率增加约65%。我们的研究结果提供了重要的见解，管理员如何重新分配合格的泊位。
英文摘要：
This paper investigates the fairness of the 2018 FIFA World Cup qualifying competition via Monte Carlo simulations. The qualifying probabilities are calculated for 102 nations, all teams except for African and European countries. A method is proposed to quantify the degree of unfairness. Although the qualifications within four FIFA confederations are constructed fairly, serious differences are found between the continents: for instance, a South American team could have tripled its chances by playing in Asia. Choosing a fixed matchup in the inter-continental play-offs instead of the current random draw can reduce the unfairness of the competition. The move of Australia from the Oceanian to the Asian zone is shown to increase its probability of participating in the 2018 FIFA World Cup by about 65%. Our results provide important insights for the administrators on how to reallocate the qualifying berths.
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