This paper investigates optimal coaching strategies in the combination of players football managers should have on the field. It does so by examining how goal scoring and conceding respond to changes in the number of attacking players on the field in European football matches. The paper tests the hypotheses that more attacking players raise both the rates at which the team scores and concedes goals. The paper shows that managers play more defenders when their team is an underdog and it tests whether this strategy is successful. The estimates show that teams are nearly always better off including more attacking players on the field. In the typical match, teams score at a greater rate and (surprisingly) concede at a lower rate when they have more attacking players on the field. The gain in net goals from playing more attacking players is larger the more a team is favoured over its opponent. Teams that are heavy underdogs playing away from home are the only ones that may be better off playing more defensive players. Coaching strategies should shift toward being less defensive in most cases.
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