Crop biodiversity has the potential to enhance resistance to strains due to biotic and abiotic factors and to improve crop production and farm revenues. To investigate the effect of crop biodiversity on crop productivity, we build a probabilistic model based on ecological mechanisms to describe crop survival and productivity according to diversity. From this analytic model, we derive reduced forms that are empirically estimated using detailed field data of South African agriculture combined with satellite derived data. Our results confirm that diversity has a positive and significant impact on crop survival odds. We show the consistency of these results with the underlying ecologic and agricultural mechanisms.