In most countries, basic research is supported by research councils that select, after peer review, the individuals or teams that are to receive funding. Unfortunately, the number of grants these research councils can allocate is not infinite and, in most cases, a minority of the researchers receive the majority of the funds. However, evidence as to whether this is an optimal way of distributing available funds is mixed. The purpose of this study is to measure the relation between the amount of funding provided to 12,720 researchers in Québec over a 15-year period (1998–2012) and their scientific output and impact from 2000 to 2013. Our results show that in terms of both the quantity of papers produced and their scientific impact, the concentration of research funding in the hands of the so-called ‘elite’ of researchers generally produces diminishing marginal returns. Also, we find that the most funded researchers do not stand out in terms of output and scientific impact.