> Are they calculated directly based on combinatorial arguments? Yes. Most of the extremely low p-values come from binomial tests with a very low binomial prob

> Are they calculated directly based on combinatorial arguments? Yes. Most of the extremely low p-values come from binomial tests with a very low binomial probability p_bin relative to the fraction of positive outcomes. For example, > We identified 45 point mutations that were introduced in Branch O (hereafter referred to as “pre-outbreak mutations.”) We observed that the pre-outbreak mutations were over-represented in ORF S (P = 1.2 × 10−13, binomial test with the expected probability equal to the length of ORF S relative to the SARS-CoV-2 genome). So p_bin = len(ORF S)/len(genome). The spike protein sequence (ORF S) is roughly 1300 bases and the entire SARS-CoV-2 genome is roughly 30 kilobases long, yielding p_bin ≈ 0.04. If there are 45 total pre-outbreak mutations, and assuming they ought to be uniformly distributed across the genome (big assumption, BTW!), then seeing 17 of them occur in the spike protein sequence would yield a binomial p-value (one-sided test) on the order of 1e-13. The other low p-values either also come from binomial tests with similarly low binomial probabilities relative to positive outcomes, or from Fisher exact tests with gross imbalances between categories (and high counts to back those up).