Well...it's not that simple. The comets in the Oort Cloud are presumably the ones that get jostled ever few millions of years by passing stars. These comets have million-year orbits, and get thrown into the inner Oort Cloud or even the Kuiper Belt where further gravitational interactions with the local cometary nuclei perturb THEIR orbits and toss them even further into the inner solar system from their original 'parking' orbits out beyond the orbit of Saturn. The 15-20 comets we see each year are born in the Kuiper belt as short period comets ( periods of a few centuries of less) or we may be treated to a few long period comets like Hyakutake with periods of thousands of years, which have orbits that take them well beyond the orbit of Pluto in the outer Kuiper Belt. Stellar perturbations may simply set up the system for an enhanced 'rain' of comets lasting thousands of years, and perhaps at a mean level of activity a few times more active than what we now see each year.