A technique for managing storage space in a data storage system generates liability values on a per-family basis, with each family including files in the file system that are related to one another by snapping. Each family thus groups together files in the file system that share at least some blocks among one another based on snapshot activities. Distinct files that do not share blocks based on snapping are provided in separate families. The file system leverages the snap-based relationships among family members to produce more accurate estimates of liability than would otherwise be feasible.