The Peruvian Central Andes is a highly important area for potato production. Assessing the potato yield gap and the potential yield is an essential step towards sustainable crop intensification. Fifty-eight smallholder potato farmer's plots in total were monitored at field level during the 2005–2008 and 2010–2015 rainy cropping seasons. All the main crop management inputs were registered. Three field experiments (on-farm trials) established during the 2014–2017 rainy cropping seasons were used to calibrate (2014–2016) and validate (2016–2017) the SUBSTOR-potato model under potential conditions. Potential potato yield (Yp) was estimated for each individual field pilot plot (in kg ha−1) based on the calibrated and validated crop model. Yield gaps (Yg) were calculated as the difference between Yp and farmers' actual yield (Ya). A classification tree-based model predicting the potato gap quantiles was used to elucidate the main biophysical and crop management components inducing Yg. Performance of the SUBSTOR-potato model showed a close agreement of simulated crop biomass, tuber yield, and N-uptake (i.e. N-demand) with the measured data under potential conditions. Redefined index of agreement were 0.84 and 0.80 while the associated mean square error were 2232 and 916 kg tuber dry weight (DW) ha−1 for the calibration and validation, respectively. The mean farmers' actual DW yield was 7118 kg ha−1, however, a high variability due to heterogeneous biophysical conditions and crop management was found (from 710 to 18,885 kg DW ha−1). The potato Yg ranged from 0.1 to 95.8% of the potential yield (x¯ = 42.1%, x~ = 46.0%, σx = 28.14% and CV = 0.67), hence there is an important difference that needs to be reduced. The classification tree analysis showed that inorganic N is the main yield explaining factor. While large yield gaps (Fourth quantile) are induced by low Inorganic N (< 88 kg ha−1) and scarce Human Labour energy (< 4196 MJ ha−1), small yield gap (First quantile) is mainly attributed to high N-inputs (≥ 139 kg ha−1 inorganic and ≥ 154 kg ha−1 organic). Third and Second quantiles (mid potato yield gaps) were characterized by more intricate nutrient input use, being difficult to classify; the Third quantile was partially explained by Inorganic N (< 139 kg ha−1), while part of the Second quantile by Extractable soil phosphorus (< 7.3 mg kg−1) and Inorganic N (< 139 kg ha−1). This classification can be helpful to diagnose the main site-specific crop management and biophysical recommendations towards closing the potato yield gap. The analysis suggests that there is opportunity to enhance potato actual yields in the study zone. More rational amount of inputs together with best management practices might improve potato productivities. However, sustainable potato intensification should be complemented with the expected quantification of environmental burdens under the local socio-economic constraints.