This study quantifies spatial autocorrelation in agricultural yields in southern Peru and identifies priority provinces for climate adaptation using hierarchical Bayesian CAR models. We analyzed 1368 observations of white potatoes and starchy corn in 20 provinces of 5 departments during 2024 (National Agricultural Survey). Results show significant spatial autocorrelation (I = 0.404, p < 0.001; ρ = 0.402, 95% CI:[0.015,0.915]). Droughts reduced yields by 183 kg/ha (16%, CI: [− 355,− 3]), the only climatic event with a robust effect. Potatoes outperformed corn by 780 kg/ha (104%). Four hotspots were identified within Puno department (1605–2345 kg/ha) and four coldspots in Cusco (538–1229 kg/ha). Agricultural practices showed no effects (low adoption: terraces 1.6%, certified seed 0.4%). The model explained 18.4% of the variance. Four critical provinces in Cusco plus La Unión (Arequipa, 461 kg/ha) require urgent intervention. First estimate of spatial autocorrelation parameter (ρ) in Peruvian agriculture, establishing a methodological framework for evidence-based territorial prioritization.