Nanocrystalline (NC) metals are exceptionally strong because they contain an unusually high density of grain boundaries (GBs) that act as sources and sinks for dislocations and significantly modify dislocation motion. In this study, we seek to understand the relationship between discrete dislocation emissions from GBs and grain size effects seen in the strength of NC metals. We propose a statistical GB dislocation source model responsible for discrete dislocation slip events. We find that the grain size limitation on dislocation source sizes gives rise to grain size effects on the statistical distribution for the critical resolved shear stress (CRSS) for discrete slip events. To establish its impact on mechanical behavior, this GB source model is integrated into a 3D crystal plasticity finite element model for NC Ni. We observe that a Hall-Petch scaling in yield strength emerges from the calculations. Further the predictions achieve quantitative agreement with experimental data from several studies across a wide range of average nanograin sizes. It is revealed that statistical dispersion in the CRSS for discrete slip events causes (a) strain hardening in the macroscale flow stress-strain response and (b) the fraction of grains that accommodate the applied strain and the fraction of active grains that undergo multi-slip to strongly depend on grain size. It is also found to lead to an unusual texture effect on slip activity that is significant in the finer nanograins but weak in larger grains (>100 nm). In addition, it causes increases in heterogeneity in strain concentrations with decreasing grain size, suggesting that plastic instabilities are more likely to form as nano-scale grain sizes decrease.