Identification of success factors in wrestling as well as establishing their hierarchy are crucial from a cognitive and practical standpoint. It may provide a lot of practical recommendations related to wrestling-specific training. The aim of this study was to identify and establish the hierarchy of success factors in wrestling regardless of a fighting style and weight class. This study included 168 elite male freestyle and Greco-Roman wrestlers. They were divided into two groups: athletes who won medals (successful wrestlers) in high-rank competitions (Polish Championships or higher) and those who did not win any medals (less successful wrestlers) in those competitions. The following elements were assessed: anthropological measurements, body composition, dynamic strength, strength endurance, agility, special endurance, wrestling-specific fitness, response time, technical wrestling skills and anaerobic capacity. For initial data analysis, one-way ANOVA (α = 0.005) was used. Random Forests classifier was employed to identify success factors and to determine the importance of each of these factors in terms of sports performance. Seven key success factors were identified: anaerobic power, strength endurance, response time, special endurance, wrestling-specific fitness and technical wrestling skills performed in a horizontal position. Random Forests turned out to be an effective method of modelling success in wrestling (compared to SVM and KNN, which were also used in the study). These findings suggest that wrestling-specific training can be effectively monitored by controlling several vital indicators of athletes' preparedness: anaerobic power, strength endurance, response time, special endurance, wrestling-specific fitness and technical wrestling skills (the performance of reverse waistlock from a standing position and trunk grip gut wrench assessed by experts).