The LHC Run-2 programme has produced an extensive set of search results for physics beyond the Standard Model, a legacy that will eventually be topped by the ongoing Run-3. While no individual analysis alone currently meets the standard for evidence — let alone discovery — of new physics, the collective body of results offers opportunities that go beyond isolated excesses. In this talk, I shall argue that such a global, meta-statistical view of the Run-2 results collected in our SModelS database reveals interesting trends: certain types of results exhibit too many excesses and too few under fluctuations, while most classes behave exactly as expected. I will discuss these trends and introduce a framework for inferring incomplete prototype BSM models dubbed “protomodels” from such a database of ATLAS and CMS search results, focussing on technical, statistical challenges of this and similar endeavours.