This paper aims to evaluate the criticality of strategic metals by (i) investigating the validity of the Herfindahl-Hirschman Index (HHI) for assessing the supply risk aspect of criticality and (ii) determining an appropriate threshold for using this indicator in the context of criticality studies. Relying on a large panel of 33 strategic metals over the 1995-2021 period, our findings show that the variation of HHI has more impact on metal prices at lower HHI levels and question the existence of a threshold that clearly distinguishes high-risk markets from less risky ones based on their concentration levels. Overall, we show that using the HHI as a supply risk indicator, especially in conjunction with a threshold, may result in underestimating risks in less concentrated markets.