Background: While the association between self-efficacy and sports success has been well established in previous studies, little is known regarding whether the basic approach motivation system contributes to this relationship in athletes. The study examines associations between self-reported temperamental approach disposition, self-efficacy, and predispositions to sports success in athletes. Methods: A cross-sectional study was performed between August 3 and 30 November 2020. The participants were 156 athletes, aged 16–34 years (M = 21.57, SD = 3.58, 41.67% women), in two groups: 54 elite athletes in speed skating (EASS) and 102 physical education students (PES). The online survey consisted of the Reinforced Sensitivity Questionnaire (RSQ), General Self-Efficacy Scale (GSES), and Sports Success Scale (SSS). Results: There were no differences in self-efficacy and sports success in terms of gender, sports discipline, and level of competitions. The Behavioral Activation System (BAS) results were lower in the EASS sample compared with in the PES group. Self-efficacy plays a mediating role in the relationships between BAS and sports success among athletes, with sport discipline as a moderator between BAS and self-efficacy. Sports success in speed skating relies strongly on BAS, while a weak link has been found in other sports disciplines. Conclusions: BAS is directly correlated to sports success and indirectly related through self-efficacy. Mental training should be focused on maintaining self-efficacy and reward motivation in athletes to increase their sports success.