Breakdown of hard classifications in case of overlapping clusters. Deviation μ̂_A − μ_A of estimated and true means vs. two-cluster separation Δx for class A for hard estimator (red line), soft estimator (blue line), and predicted bias of hard estimator for Δx → 0 (dashed line). From 1000 realisations of data samples we estimated errorbars, which are shown but too small to be visible.