## 4 Discussion
Muscle strength affects the distance and time required to produce GRF for jumping, and it also affects the stability of landing [35]. The research results show that the reaction forces of the left and the right foot were very similar regardless of the pre-test or post-test results, which may be due to the coordination of the hands and feet caused by the body's arm swinging [36; 37]. The lateral jump's R-GRF had a direct relationship with the \(\theta\) value. When the \(\theta\) value was between 60.7\({}^{\circ}\) and 67.2\({}^{\circ}\), the best lateral jump distance could be achieved [5; 38; 39]. In addition, an athlete's weight and height may indirectly affect their jumping distance. The results of the force plate evaluation revealed that the ASTP increased the participants' ability to produce greater force when taking off, and the reaction force of the lower limbs on the ground increased significantly. The slope of the vertical jumps in the post-test ranged from \(-\)0.815 to \(-\)0.962; thus, the slope of all participants was steep and produced a centripetal output curve. This phenomenon also showed that there was a highly linear relationship between the changes in force and speed during jumping [40]. The time required by the participants in this study to produce force ranged from 0.116 to 0.220 s. These players could be called athletes with excellent explosive power. According to research by [PERSON] et al., it only takes 0.1 to 0.2 s for excellent athletes to generate an explosive force from the moment that their jumping foot touches the ground to the moment that their jumping foot leaves the ground [41]. Similar studies have also pointed out that there are better RFDs that can allow for faster and more explosive movements [14; 42; 43]. This study found that some participants' GRF and RFD showed reverse linearity. This phenomenon shows that these three basketball players belong to the middle peak body, and their body weight and muscle mass were higher than those of the other participants. Their body weight affected the depth of their hip and knee joint squats and the vertical impulse when taking off; thus, they required more time to generate force, resulting in a decrease in the RFD [44]. Similarly, some studies have confirmed that the RFD is indicated by the slope of the force-time curve. The lower limbs could exert a greater force in a shorter period of time, which also shows that the number of muscle fibers determines the amount of force generated [45; 46; 47]. Some studies have pointed out that an excellent vertical jump is dominated by the hip joint. The muscle strength required by the hip joint was also the focus of the ASTP training in this study, because the hip extensor muscles have a higher correlation with the improvement of the vertical jump height than the knee extensor muscles [48]. In addition, the relationship between the RFD and explosive power will confuse players. The basis of explosive power is muscle strength, and explosive power is a manifestation of the RFD [14]. Explosive power is the ability to generate the most force in the shortest amount of time possible. From a biological perspective, the more fast-twitch muscle fibers there are and the thicker the cross-sectional area, the greater the speed force [6]. The formula is explosive power (P) = strength (F) \(\times\) speed (V). In short, the RFD is related to instantaneous time, and explosive power is related to speed, so there is a gap between the two, and many scholars also hold the same view [9; 42; 49]. Although there is a gap between the two, according to the formula comparison, if the two run a 100 m race, the faster one takes less time, which proves that speed is inversely proportional to time. Therefore, there is a high correlation between the force generation rate (RFD = F \(\div\) time) and explosive power (P = F \(\times\) V) [42]. Therefore, the RFD is often called explosive power, and the better the RFD, the steeper the kurtosis.