Assessing the risk of yield loss in African drought-affected regions is key to identify feasible solutions for stable crop production. Recent studies have demonstrated that Copula-based probabilistic methods are well suited for such assessment owing to reasonably inferring important properties in terms of exceedance probability and joint dependence of different characterization. However, insufficient attention has been given to quantifying the probability of yield loss and determining the contribution of climatic factors. This study applies the Copula theory to describe the dependence between drought and crop yield anomalies for rainfed maize, millet, and sorghum crops in sub-Saharan Africa (SSA). The environmental policy integrated climate model, calibrated with Food and Agriculture Organization country-level yield data, was used to simulate yields across SSA (1980-2012). The results showed that the severity of yield loss due to drought had a higher magnitude than the severity of drought itself. Sensitivity analysis to identify factors contributing to drought and high-temperature stresses for all crops showed that the amount of precipitation during vegetation and grain filling was the main driver of crop yield loss, and the effect of temperature was stronger for sorghum than for maize and millet. The results demonstrate the added value of probabilistic methods for drought-impact assessment. For future studies, we recommend looking into factors influencing drought and high-temperature stresses as individual/concurrent climatic extremes. © 2022 The Author(s). Published by IOP Publishing Ltd.