 where \(\Pr(S \pmid H_d)=\varphi\) and \(S\) stands for the proposition that someone in the database is the source of the crime traces. Donnelly and Friedman (1999) derived a similar formula for this ratio. As the database gets larger, \(\varphi\) increases and the database search ratio increases. This ratio equals one only if no one in the database could be the source.