Causally‐induced asymmetry reflects the principle that an event qualifies as a cause only if its absence would prevent the occurrence of the effect. Thus, uncovering causal effects becomes a matter of comparing a well‐defined score in both directions. Motivated by studying causal effects at extreme levels of a multivariate random vector, we propose to construct a model‐agnostic causal score relying solely on the assumption of the existence of a max‐domain of attraction. Based on a representation of a generalised Pareto random vector, we construct the causal score as the Wasserstein distance between the margins and a well‐specified random variable. The proposed methodology is illustrated on a simulated dataset of different characteristics of catchments in Switzerland: discharge, precipitation, snowmelt, temperature, and evapotranspiration.