Aneuploidy has been recognized as a hallmark of cancer for more than 100 years, yet no general theory to explain the recurring patterns of aneuploidy in cancer has emerged. Here, we develop Tumor Suppressor and Oncogene (TUSON) Explorer, a computational method that analyzes the patterns of mutational signatures in tumors and predicts the likelihood that any individual gene functions as a tumor suppressor (TSG) or oncogene (OG). By analyzing >8,200 tumor-normal pairs, we provide statistical evidence suggesting that many more genes possess cancer driver properties than anticipated, forming a continuum of oncogenic potential. Integrating our driver predictions with information on somatic copy number alterations, we find that the distribution and potency of TSGs (STOP genes), OGs, and essential genes (GO genes) on chromosomes can predict the complex patterns of aneuploidy and copy number variation characteristic of cancer genomes. We propose that the cancer genome is shaped through a process of cumulative haploinsufficiency and triplosensitivity. Display omitted •There exists a continuum of cancer drivers of progressively diminishing potency•Cancer drivers have high betweenness and greater interactivity than neutral proteins•Cumulative haploinsufficiency and triplosensitivity of TSGs and OGs drive aneuploidy•The vast majority of sporadic tumor suppressors are likely to be haploinsufficient A large number of tumor suppressors and oncogenes are identified to exhibit a continuum of potency. The cumulative effect of CNVs of these genes can be used to explain and predict patterns of aneuploidy and chromosome arm deletion/amplification in cancer.