The sigmoid(PRR-1.5) term ranges smoothly from 0 to 1. It's equal to 0.5 at PRR = 1.5. When PRR = 6, sigmoid(PRR-1.5)=0.99; so PRR values >= 6 are all treated roughly equivalently by the AE score. Thus, extremely high PRRs due to small counts will not swing the AE score much beyond PRR = 6, and the ln(count) term will down-weight those small-count cases, so that they do not show up at the top of the AE score list.