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 second-leg home advantage', i.e. that it is beneficial to play at home on the second leg. A more complex effect than the well-documented usual home advantage, it is more difficult to identify, and previous statistical studies have not proved conclusive about its actuality. As opposed to previous research, the paper addresses the question from a purely non-parametric perspective, which is 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 non-parametric confidence intervals for conditional probability functions, revisits the problems of bias and bandwidth selection when building confidence intervals in non-parametric regression and provides a novel bootstrap-based solution to them. Finally, the new intervals are used when analysing game outcome data for the UEFA (Union of European Football Associations) Champions and Europa Leagues from 2009-2010 to 2014-2015. A slight second-leg home advantage is evidenced.