Synaptic ribbons are classically associated with mediating indefatigable neurotransmitter release by sensory neurons that encode persistent stimuli. Yet when hair cells lack anchored ribbons, the temporal precision of vesicle fusion and auditory nerve discharges are degraded. A rarified statistical model predicted increasing precision of first-exocytosis latency with the number of readily releasable vesicles. We developed an experimentally constrained biophysical model to test the hypothesis that ribbons enable temporally precise exocytosis by increasing the readily releasable pool size. Simulations of calcium influx, buffered calcium diffusion, and synaptic vesicle exocytosis were stochastic (Monte Carlo), and yielded spatiotemporal distributions of vesicle fusion consistent with experimental measurements of exocytosis magnitude and first-spike latency of nerve fibers. No single vesicle could drive the auditory nerve with requisite precision, indicating a requirement for multiple readily releasable vesicles. However, plasmalemma docked vesicles alone did not account for the nerve's precision --- the synaptic ribbon was required to retain a pool of readily releasable vesicles sufficiently large to statistically ensure first-exocytosis latency was both short and reproducible. The model predicted that at least sixteen readily releasable vesicles were necessary to match the nerve's precision, and provided insight into interspecies differences in synaptic anatomy and physiology. We confirmed that ribbon-associated vesicles were required in disparate calcium buffer conditions, and irrespective of the number of vesicles required to trigger an action potential. We conclude that one of the simplest functions ascribable to the ribbon, the ability to hold docked vesicles at an active zone, accounts for the synapse's temporal precision.