Our analysis of the effect sizes of mutations underlying HPV+ and HPV− HNSCC tumors not only substantiates the difference in genetic architecture between these tumors based on HPV status, but also identifies some rare oncogenic mutations that contribute strongly to tumorigenesis in both HPV+ and HPV− HNSCC tumors (e.g., FBXW7 R505G), as well as oncogenic mutations that are somatically selected for in either HPV+ (e.g., EP300 D1399N, FGFR3 F249C) or HPV− tumors (e.g., PIK3CA H1047R, oncogenic mutations in HRAS and TP53). This evidence concerns the gene TP53 and head and neck squamous cell carcinoma.