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In international football (soccer), two-legged knockout ties, with each teamplaying at home in one leg and the final outcome decided on aggregate, arecommon. Many players, managers and followers seem to believe in the `second-leghome advantage', i.e. that it is beneficial to play at home on the second leg.A more complex effect than the usual and well-established home advantage, it isharder to identify, and previous statistical studies did not prove conclusiveabout its actuality. Yet, given the amount of money handled in internationalfootball competitions nowadays, the question of existence or otherwise of thiseffect is of real import. As opposed to previous research, this paper addressesit from a purely nonparametric perspective and brings a very objective answer,not based on any particular model specification which could orientate theanalysis in one or the other direction. Along the way, the paper reviews thewell-known shortcomings of the Wald confidence interval for a proportion,suggests new nonparametric confidence intervals for conditional probabilityfunctions, revisits the problem of the bias when building confidence intervalsin nonparametric regression, and provides a novel bootstrap-based solution toit. Finally, the new intervals are used in a careful analysis of game outcomedata for the UEFA Champions and Europa leagues from 2009/10 to 2014/15. Aslight `second-leg home advantage' is evidenced.

Robust analysis of second-leg home advantage in UEFA football through better nonparametric confidence intervals for binary regression functions