Caribbean coral reefs are declining due to a mosaic of local and global stresses, including climate change-induced thermal stress. Species and assemblage responses differ due to factors that are not easily identifiable or quantifiable. We calculated a novel species-specific metric of coral bleaching response, taxon-α and -β, which relates the response of a species to that of its assemblages for 16 species over 18 assemblages. By contextualizing species responses within the response of their assemblages, the effects of environmental factors are removed and intrinsic differences among taxa are revealed. Most corals experience either a saturation response, overly sensitive to weak stress (α > 0) but under-responsive compared to assemblage bleaching (β < 1), or a threshold response, insensitive to weak stress (α < 0) but over-responsive compared to assemblage bleaching (β > 1). This metric may help reveal key factors of bleaching susceptibility and identify species as targets for conservation.