Groundwater stored in weathered crystalline aquifers is an essential resource of drinking water in tropical countries. Previous studies based on the analysis of borehole data in African countries have shown that the productivity of these aquifers is generally low (<1 l/s), but there is considerable variability with some boreholes much more productive (> 5 l/s), and other areas unproductive. Although these observed data allow a quantitative estimation of the groundwater resource, they are too sparse to fully explore the factors controlling the productivity of boreholes. In this work, a large dataset from Northern Ghana was used to develop and parameterise a stochastic groundwater flow model to generate and validate a comprehensive set of synthetic yield data. The model was then used to investigate the sensitivity of aquifer productivity with respect to thirteen hydrogeological and borehole construction parameters. These include the thickness, extent, and hydrogeological properties of different horizons in the weathered profile, annual recharge rates, as well as the borehole and water table depths. Groundwater abstraction is simulated with a 2-D stochastic numerical radial flow model accounting for heterogeneous hydraulic conductivity and porosity profiles. These are consistent with traditional geological conceptualisations of weathered basement aquifers. The synthetic dataset yield data was generated from distributions of input parameters comparable to those derived from borehole data in Northern Ghana. The resulting distribution of simulated yields can be considered representative of the actual productivity given the excellent agreement with the real abstraction data. The synthetic data and the corresponding model input parameters were then considered for global sensitivity analysis using the PAWN method. The estimated sensitivity indices indicate that the main factors influencing the average well productivity over a pumping period of four years are: (1) the maximum hydraulic conductivity of the weathered profile; (2) the thickness of the regolith; (3) the static depth of the water table; and (4) the hydraulic conductivity of the unweathered crystalline rock. The average productivity is relatively insensitive to other factors including recharge rates especially if we take into account the contribution of baseflow. However, recharge and aquifer extent become sensitive parameters when we analyse changes in yield over time. Further exploration of higher and lower yielding boreholes within the synthetic dataset reveals variability in the sensitivities to difference parameters. This has important implications for siting boreholes for irrigation or small town supplies. The developed approach generates realistic distributions of yields in weathered crystalline aquifers that can be used to estimate aquifer productivity in areas with scarce borehole data. Given site-specific distributions of input parameters, we demonstrate that the model can be used to understand which factors are most important for certain classes of productivity, and the probability of encountering different yields within weathered crystalline aquifers.