In wake of the Covid-19 pandemic, 2019-2020 soccer seasons across the world were postponed and eventually made up during the summer months of 2020. Researchers from a variety of disciplines jumped at the opportunity to compare the rescheduled games, played in front of empty stadia, to previous games, played in front of fans. To date, most of this post-Covid soccer research has used linear regression models, or versions thereof, to estimate potential changes to the home advantage. But because soccer outcomes are non-linear, we argue that leveraging the Poisson distribution would be more appropriate. We begin by using simulations to show that bivariate Poisson regression reduces absolute bias when estimating the home advantage benefit in a single season of soccer games, relative to linear regression, by almost 85 percent. Next, with data from 17 professional soccer leagues, we extend bivariate Poisson models estimate the change in home advantage due to games being played without fans. In contrast to current research that overwhelmingly suggests a drop in the home advantage, our findings are mixed; in some leagues, evidence points to a decrease, while in others, the home advantage may have risen. Altogether, this suggests a more complex causal mechanism for the impact of fans on sporting events.
翻译:在Covid-19大流行后,全世界2019-2020年的足球季被推迟,并最终在2020年夏季的几个月里补足了2019-2020年的足球季。来自不同学科的研究人员跳跃了一次机会,比较了在空的斯塔迪亚面前玩的更新游戏,比以前在球迷面前玩的更前的游戏。到目前为止,大多数后Covid足球研究都使用了线性回归模型或版本来估计家庭优势的潜在变化。但是,由于足球结果不是线性,我们争辩说,利用Poisson的分布比较合适。我们首先利用模拟来显示,在单季足球比赛中,与线性回归相比,二变波西森回归会减少绝对的偏差。接下来,根据17个专业足球联盟的数据,我们扩展了双变波西森模型来估计因没有球迷而导致的家庭优势的变化。与目前绝大多数显示家庭优势下降的研究相比,我们发现的情况是混合的;在某些联盟中,我们发现有证据表明,在足球比赛中,家庭优势可能会降低绝对偏差,而在其他运动会中,结果会增加。