The reason the Birthday Paradox is surprising is that there are N people, but the number of possible matches rises like N^2. The "paradox" occurs because succe

The reason the Birthday Paradox is surprising is that there are N people, but the number of possible matches rises like N^2. The "paradox" occurs because success is defined as any one of the N-choose-2 matches happening. 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*M. But I'm not sure that's the correct metric; I think you really care about the amortized cost of a mistaken match across all N crimes. So you don't see the "paradoxical" quadratic increase. I admit I'm being a bit fussy -- just testing the extent of the analogy. 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.