We calculate the statistics of diffusion-limited arrival-time distribution by a Monte Carlo method to suggest a simple statistical resolution of the enduring puzzle of nanobiosensors: a persistent gap between reports of analyte detection at approximately femtomolar concentration and theory suggesting the impossibility of approximately subpicomolar detection at the corresponding incubation time. The incubation time used in the theory is actually the mean incubation time, while experimental conditions suggest that device stability limited the minimum incubation time. The difference in incubation times-both described by characteristic power laws-provides an intuitive explanation of different detection limits anticipated by theory and experiments.