Unlike competitive higher education systems, non-competitive systems show relatively uniform distributions of top professors and low performers among universities. In this study, we examine the impact of unproductive and top faculty members on overall research performance of the university they belong to. Furthermore, we analyze the potential relationship between research productivity of a university and the indexes of concentration of unproductive and top professors. Research performance is evaluated using a bibliometric approach, through publications indexed on the Web of Science between 2004 and 2008. The set analyzed consists of all Italian universities active in the hard sciences.