With one-fourth of the world's mammals threatened with extinction and limited budget to save them, adopting an efficient conservation strategy is crucial. Previous approaches to setting global conservation priorities have assumed all species to have equal conservation value, or have focused on species with high extinction risk, species that may be hard to save. Here, we identify priority species for optimizing the reduction in overall extinction risk of the world's threatened terrestrial mammals. We take a novel approach and focus on species having the greatest recovery opportunity using a new conservation benefit metric: the Extinction risk Reduction Opportunity (ERO). We discover that 65-87% of all threatened and potentially recoverable species are overlooked by existing prioritization approaches. We use the ERO metric to prioritize threatened species, but the potential applications are broader; ERO has the potential to integrate with every strategy that aims to maximize the likelihood of conservation success.