The ability to attract and retain talented professors is a distinctive competence of world-class universities and a source of competitive advantage. The ratio of top scientists to academic staff could therefore be an indicator of the competitive strength of the universities. This work identifies the Italian top scientists in over 200 fields, by their research productivity. It then ranks the relative universities by the ratio of top scientists to overall faculty. Finally, it contrasts this list with the ranking list by average productivity of the overall faculty. The analysis is carried out at the field, discipline, and overall university levels. The paper also explores the secondary question of whether the ratio of top scientists to faculty is related to the size of the university.