This study examined the selective influences of one-repetition maximum (1RM) values [assessed in the half-squat (HS)] and bar-power production [assessed in both HS and jump squat (JS) exercises] on the physical performance of male and female team sport athletes from four different sports. Three-hundred and three elite players (31 Olympians) from four different disciplines (47 male soccer players, 58 female soccer players, 28 male handball players, 58 female handball players, 49 male rugby players, and 63 male futsal players) participated in this study. The physical tests were performed over 2 consecutive days for soccer and rugby players, and in 1 day for the remaining athletes. On the first day, rugby and soccer athletes performed squat jumps (SJ), countermovement jumps (CMJ), and HS 1RM. On the second day, they executed HS and JS tests (to assess the maximum bar-power output) and the linear and change-of-direction (COD) speed tests. For the other players, the sequence of the measurements was the same; however, they did not perform the HS exercise. Athletes were separated, using a median split analysis, into two distinct groups, according to their bar-power output in both JS and HS exercises and their performance in HS 1RM. The magnitude-based inferences method was used to examine the differences between "higher" and "lower" performance groups. Overall, the bar-power outputs were better connected to improved acceleration, speed, and jump performance than the 1RM measures. From these findings, it is possible to infer that players able to produce higher bar-power outputs are likely to sprint faster and jump higher. Therefore, coaches involved in team sports are strongly encouraged to use the bar-power method to evaluate the athletic performance of their players.