Past exam of the mathematical and Computational Biology course of the University of Cambridge / 2024 / Paper 1 / C4 / b / Solution

A diagonal substitution matrix score measures enrichment over a background match, rather than simply rewarding an identical letter. tryptophan residues are comparatively rare, so a W–W match has a small chance background frequency $p_W^2$. Its observed conservation produces a much larger ratio $q_{WW}/p_W^2$ than the corresponding ratio for the more common leucine. The BLOSUM62 diagonal therefore awards W–W more than L–L. Both the background frequency and the observed pair frequency matter; rarity alone does not determine a diagonal score.^[ref]