Estimating the change in soccer's home advantage during the Covid-19 pandemic using bivariate Poisson regression

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.