•First comprehensive application of 15 data mining models to soil erosion.•Game theory was applied to assess the interpretability of the DM models.•BGAM is the most accurate model.•DEM derived factors are the most important controls.•Game theory is a valuable technique for assessing the interpretability of predictive models. This study undertook a comprehensive application of 15 data mining (DM) models, most of which have, thus far, not been commonly used in environmental sciences, to predict land susceptibility to water erosion hazard in the Kahorestan catchment, southern Iran. The DM models were BGLM, BGAM, Cforest, CITree, GAMS, LRSS, NCPQR, PLS, PLSGLM, QR, RLM, SGB, SVM, BCART and BTR. We identified 18 factors usually considered as key controls for water erosion, comprising 10 factors extracted from a digital elevation model (DEM), three indices extracted from Landsat 8 images, a sediment connectivity index (SCI) and three other intrinsic factors. Three indicators consisting of MAE, MBE, RMSE, and a Taylor diagram were applied to assess model performance and accuracy. Game theory was applied to assess the interpretability of the DM models for predicting water erosion hazard. Among the 15 predictive models, BGAM and PLS respectively returned the best and worst performance in predicting water erosion hazard in the study area. The most accurate model, BGAM predicted that 22%, 8.2%, 9.4% and 60.4% of the total area should be classified as low, moderate, high and very high susceptibility to soil erosion by water, respectively. Based on BGAM and game theory, the factors extracted from the DEM (e.g., DEM, TWI, Slope, TST, TRI, and SPI) were considered the most important ones controlling the predicted severity of soil erosion by water. We conclude that overall, game theory is a valuable technique for assessing the interpretability of predictive models because this theory through SHAP (Shapley additive explanations) and PFIM (permutation feature importance measure) addresses the important concerns regarding the interpretability of more complex DM models.