We propose an innovative use of the Leiden Rankings (LR) in institutional management. Although LR only consider research output of major universities reported in Web of Science (WOS) and share the limitations of other existing rankings, we show that they can be used as a base of a heuristic approach to identify “outlying” institutions that perform significantly below or above expectations. Our approach is a non-rigorous intuitive method (“heuristic”) because is affected by all the biases due to the technical choices and incompleteness that affect the LR but offers the possibility to discover interesting findings to be systematically verified later. We propose to use LR as a departure base on which to apply statistical analysis and network mapping to identify “outlier” institutions to be analyzed in detail as case studies. Outliers can inform and guide science policies about alternative options. Analyzing the publications of the Politecnico di Bari in more detail, we observe that “small teams” led by young and promising scholars can push the performance of a university up to the top of the LR. As argued by Moed (Applied evaluative informetrics. Springer International Publishing, Berlin, 2017a), supporting “emerging teams”, can provide an alternative to research support policies, adopted to encourage virtuous behaviours and best practices in research. The results obtained by this heuristic approach need further verification and systematic analysis but may stimulate further studies and insights on the topics of university rankings policy, institutional management, dynamics of teams, good research practice and alternative funding methods.