Differences in crop yield between different fields in the same region have existed for a long time. Methods for improving the productivity of low-yield fields are a hot topic in large-scale agriculture. This experiment was carried out in potato planting farmland and at a potato experimental station in the Loess Plateau in China to study the effects of soil moisture and soil nutrients on potato yield potential and yield gap. The relationships between potato yield and soil nutrient factors were analyzed using the grey correlation method. The grey correlation method is a new technique for performing prediction, relational analysis and decision-making in many areas. The results indicate that (1) the high-yield group at the potato experimental station (HE) was 72,678 kg/ha; the mean-yield group at the potato experimental station (ME) was 36,083 kg/ha; the high-yield group in the potato planting farmland (HF) was 34,259 kg/ha; and the mean-yield group in the potato planting farmland (MF) was 19,386 kg/ha. (2) The yield gap (YG1) between HF and MF was 14,873 kg/ha; the yield gap (YG2) between ME and the MF was 16,697 kg/ha; the yield gap (YG3) between HE and the MF was 53291 kg/ha. (3) The effects of soil moisture and nutrients on potato yield were ranked from large to small: soil available potassium content > soil nitrate nitrogen content > soil organic matter content > soil water content > soil available phosphorus content. The results of correlation analysis and grey correlation analysis showed that the available potassium had the strongest correlation with potato tuber yield. (4) The content of nitrate nitrogen was significantly correlated with the content of available potassium and available phosphorus, while the water content was significantly correlated with the content of organic matter. According to the influence of soil moisture and nutrients on the potato tuber yield, it is suggested that integrated water and fertilizer cultivation measures be implemented, and the input of potash fertilizer and nitrogen fertilizer be increased.