Quantifying the contribution of stratospheric processes to extreme weather events is a challenge. This study breaks new ground in the quantitative attribution of weather extremes to dynamical processes in the stratosphere. It applies two complementary statistical indicators (relative risk and quantile shift) to a coordinated set of experiments with several models to study the role of the stratosphere in three detailed case studies. The paper has the potential to be an authoritative study in this area due to its combination of rigor, depth and range of impacts.