Accurate spatial information on yield potential and gaps is key to determine crop production potential. Although statistical methods are widely used to estimate these parameters at regional to global levels, a rigorous evaluation of their performance is lacking. Here we compared outcomes derived from four published statistical approaches based on highest average farmer yields over time and space against those derived from a 'bottom-up' approach based on crop modelling and local weather and soil data for major rain-fed crops in the United States. Statistical methods failed to capture spatial variation in water-limited yield potential, consistently under- or overestimating yield gaps across regions. Statistical methods led to conflicting results, with production potential almost doubling from one method to another. We emphasize the need for well-validated crop models coupled with local data, robust spatial frameworks and extrapolation methods to provide more reliable assessments of production potential from local to regional scales.