The reason the Birthday Paradox is surprising is that there are N people, but the number of possible matches rises like N^2.  The &quot;paradox&quot; occurs because success is defined as any one of the N-choose-2 matches happening.<p>The analog here is there are M people in the database, and N crimes, so the chance of a single failure (mistaken match) is kind of like N<i></i>*M.<p>But I&#x27;m not sure that&#x27;s the correct metric; I think you really care about the amortized cost of a mistaken match across all N crimes.  So you don&#x27;t see the &quot;paradoxical&quot; quadratic increase.<p>I admit I&#x27;m being a bit fussy -- just testing the extent of the analogy.<p>You are of course correct that the database size is growing, and the number of samples that can be collected, even from one crime, also can be made to grow.