Missense driver mutations in cancer are concentrated in a few hotspots1. Various mechanisms have been proposed to explain this skew, including biased mutational processes2, phenotypic differences3-6 and immunoediting of neoantigens7,8; however, to our knowledge, no existing model weighs the relative contribution of these features to tumour evolution. We propose a unified theoretical 'free fitness' framework that parsimoniously integrates multimodal genomic, epigenetic, transcriptomic and proteomic data into a biophysical model of the rate-limiting processes underlying the fitness advantage conferred on cancer cells by driver gene mutations. Focusing on TP53, the most mutated gene in cancer1, we present an inference of mutant p53 concentration and demonstrate that TP53 hotspot mutations optimally solve an evolutionary trade-off between oncogenic potential and neoantigen immunogenicity. Our model anticipates patient survival in The Cancer Genome Atlas and patients with lung cancer treated with immunotherapy as well as the age of tumour onset in germline carriers of TP53 variants. The predicted differential immunogenicity between hotspot mutations was validated experimentally in patients with cancer and in a unique large dataset of healthy individuals. Our data indicate that immune selective pressure on TP53 mutations has a smaller role in non-cancerous lesions than in tumours, suggesting that targeted immunotherapy may offer an early prophylactic opportunity for the former. Determining the relative contribution of immunogenicity and oncogenic function to the selective advantage of hotspot mutations thus has important implications for both precision immunotherapies and our understanding of tumour evolution.