To prevent the overfishing of marine fish populations, governments often limit fishing access through the allocation of fishing opportunities. While some studies have linked particular systems of fishing opportunities to sustainable outcomes (particularly individual transferable quota), it remains unclear whether it is the use of exclusive access (individual allocation), the use of a market (tradability), the duration of this access or the quota limits themselves that drive the sustainable outcomes. To determine which attributes of fishing opportunities are associated with sustainable fishing, we developed a novel method to systematically classify how fishing opportunities are allocated for 443 global fish stocks from 1990 to 2018 to produce the longest and most comprehensive dataset and longitudinal study of its kind. Our results revealed that quota limits and individual allocation are linked to a reduced probability of overfishing, with the most robust result for quota limits. No attributes were robustly linked to a reduced probability of overfished biomass. Whereas some previous studies have found that systems with market-based features or strong property rights (i.e. a long duration) were linked to sustainable fishing, these benefits were found to be small or not significant once proper controls for other system attributes were introduced. These results highlight the importance of considering all attributes of institutional design in the governance of common pool resources.