Home advantage of European major football leagues under COVID-19 pandemic.

Since March 2020, the environment surrounding football has changed dramatically because of the COVID-19 pandemic. After a few months' break, re-scheduled matches were held behind closed doors without spectators. The main objective of this study is a quantitative evaluation of ``crowd effects'' on home advantage, using the results of these closed matches. The proposed analysis uses pairwise comparison method to reduce the effects caused by the unbalanced schedule. The following conclusions were drawn from the statistical hypothesis tests conducted in this study: In four major European leagues, the home advantage is reduced in closed matches compared to than in the normal situation, i.e., with spectators. The reduction amounts among leagues were different. For example, in Germany, the home advantage was negative during the closed-match period. On the other hand,in England,statistically significant differences in home advantage were not observed between closed matches and normal situation.