  In international football (soccer), two-legged knockout ties, with each team
playing at home in one leg and the final outcome decided on aggregate, are
common. Many players, managers and followers seem to believe in the `second-leg
home 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 is
harder to identify, and previous statistical studies did not prove conclusive
about its actuality. Yet, given the amount of money handled in international
football competitions nowadays, the question of existence or otherwise of this
effect is of real import. As opposed to previous research, this paper addresses
it from a purely nonparametric perspective and brings a very objective answer,
not based on any particular model specification which could orientate the
analysis in one or the other direction. Along the way, the paper reviews the
well-known shortcomings of the Wald confidence interval for a proportion,
suggests new nonparametric confidence intervals for conditional probability
functions, revisits the problem of the bias when building confidence intervals
in nonparametric regression, and provides a novel bootstrap-based solution to
it. Finally, the new intervals are used in a careful analysis of game outcome
data for the UEFA Champions and Europa leagues from 2009/10 to 2014/15. A
slight `second-leg home advantage' is evidenced.
