ABSTRACT Every halo-finding algorithm must make a critical yet relatively arbitrary choice: it must decide which structures are parent haloes, and which structures are subhaloes of larger haloes. We refer to this choice as percolation. We demonstrate that the choice of percolation impacts the statistical properties of the resulting halo catalogue. Specifically, we modify the halo-finding algorithm rockstar to construct three different halo catalogues from the same simulation data, each with identical mass definitions, but different choice of percolation. The resulting haloes exhibit significant differences in both halo abundance and clustering properties. Differences in the halo mass function reach 6 per cent for haloes of mass $10^{13}\ h^{-1}\ {\rm {\rm M}_{\odot }}$, larger than the few per cent precision necessary for current cluster abundance experiments such as the Dark Energy Survey. Comparable differences are observed in the large-scale clustering bias, while differences in the halo–matter correlation function reach 30 per cent on translinear scales. These effects can bias weak-lensing estimates of cluster masses at a level comparable to the statistical precision of current state-of-the-art experiments.