Several marginally significant associations between high-energy neutrinos and potential astrophysical sources have been recently reported, but a conclusive identification of these sources remains challenging. We explore the use of Monte Carlo simulations to gain deeper insight into the implications of, in particular, the IC170922A-TXS 0506+056 observation. Assuming a null model, we find a 7.6% chance to mistakenly identify coincidences between flaring blazars and neutrino alerts in 10-year surveys. We confirm that a blazar-neutrino connection based on the γ-ray flux is required to find a low chance coincidence probability and, therefore, a significant IC170922A-TXS 0506+056 association. We then assume this blazar-neutrino connection for the whole population and find that the ratio of neutrino to γ-ray fluxes must be 10 −2 in order not to overproduce the total number of neutrino alerts seen by IceCube. For the IC170922A-TXS 0506+056 association to make sense, we must either accept this low flux ratio or suppose that only some rare sub-population of blazars is capable of high-energy neutrino production. For example, if we consider neutrino production only in blazar flares, we expect the flux ratio of between 10 −3 and 10 −1 to be consistent with a single coincident observation of a neutrino alert and flaring blazar. These conclusions are robust with respect to the uncertainties in our modelling assumptions.