Aneuploidies-whole-chromosome or whole-arm imbalances-are the most prevalent alteration in cancer genomes. However, it is still debated whether their prevalence is due to selection or ease of generation as passenger events. Here we developed a method, BISCUT, that identifies loci subject to fitness advantages or disadvantages by interrogating length distributions of telomere- or centromere-bounded copy-number events. These loci were significantly enriched for known cancer driver genes, including genes not detected through analysis of focal copy-number events, and were often lineage specific. BISCUT identified the helicase-encoding gene WRN as a haploinsufficient tumour-suppressor gene on chromosome 8p, which is supported by several lines of evidence. We also formally quantified the role of selection and mechanical biases in driving aneuploidy, finding that rates of arm-level copy-number alterations are most highly correlated with their effects on cellular fitness. These results provide insight into the driving forces behind aneuploidy and its contribution to tumorigenesis.