The aim of this study was to evaluate the relation between the maximum mean propulsive power (MPP) obtained in the loaded jump squat (JS) and half squat (HS) exercises and functional performances in vertical jumps, 40 m linear speed (VEL) and change-of-direction (COD) tests, using the median split technique. Twenty-two male rugby sevens players from the Brazilian National Olympic Team (Rio-2016) performed vertical jumping tests (squat and countermovement jumps [SJ and CMJ]), JS and HS exercises, COD speed test and sprinting velocity in 40 m, in this order. Based on the results of the MPP in the JS and HS exercises the participants were divided, using the median split, into four groups as follows: higher JS, lower JS, higher HS, and lower HS. Between-group differences in the functional tasks were detected via magnitude-based inferences. The athletes with higher MPP in the JS were capable of jumping higher and sprinting faster (including the COD speed test) than their weaker counterparts. This pattern was not observed in the HS exercise. To conclude, JS was shown to be more connected to sprinting, COD speed and jumping abilities than HS in elite rugby sevens players and should be preferred for assessing and possibly training elite athletes needing to improve speed-power related abilities.