Maximal quantum randomness in Bell tests

The nonlocal correlations exhibited when measuring entangled particles can be used to certify the presence of genuine randomness in Bell experiments. While nonlocality is necessary for randomness certification, it is unclear when and why nonlocality certifies maximal randomness. We provide a simple argument to certify the presence of maximal local and global randomness based on symmetries of a Bell inequality and the existence of a unique quantum probability distribution that maximally violates it. We prove the existence of N-party Bell tests attaining maximal global randomness by identifying those combinations of two-outcome measurements by each party providing N perfect random bits.