## 4 Discussion  
One of the aims of this study was to analyze the correlation between CODTT, CODD, and sprint time. We observed significant correlations between CODTT of Y-shaped pre-planned agility, Pro-agility 0-10 m, and Pro-agility and sprint times at 0-5 m, 0-10 m, and 0-30 m, consistent with some previous findings. For instance, a study involving 25 high school American football players revealed a significant relationship between total time in the 505 agility test and sprint times at 5 yards, 10 yards, and 40 yards [15]. Another study, which included 36 male university students participating in team sports, detected a significant correlation between CODTT in the context of the 90\({}^{\circ}\) COD test and the 505 agility test and sprint times at 5 m, 10 m, and 20 m distances [10]. The previously highlighted facts indicate that CODTT is commonly affected by short sprint times. A primary reason for this phenomenon may be that the COD and sprint tests involve similar acceleration movement patterns and running distances. In this study, Y-shaped pre-planned agility, Pro-agility 0-10 m, involved two 5 m sprints, while Pro-agility covered two 5 m sprints and one 10 m sprint. Similar to the 30 m sprint, athletes must adopt a running strategy of quick steps and short strides in the acceleration phase to achieve the desired speed in the shortest time. However, a study investigated the center of mass velocity using three motion-capture techniques at distances of 0.3 m and 0.5 m following deceleration in rugby players [7]. They found that the center of mass velocity was not significantly correlated with 5 m and 10 m sprint speeds. Thus, we can infer that the CODTT may not accurately reflect an athlete's COD ability. As researchers increasingly recognize the importance of accurately measuring COD ability, more and more scholars have challenged the validity of the CODTT. The investigation of the CODD began in 2013, suggesting that the CODD might reflect the actual COD ability [9]. Previous studies have shown that there is a significant correlation between the CODD and the CODTT in the 505 agility test [11], the Pro-agility test [9], the L-shaped COD test [10], and the Zigzag test [16]. This study showed a significant correlation between the CODTT and the CODD in the Y-shaped pre-planned agility, the Pro-agility 0-10 m, and the Pro-agility, further confirming previous findings. Additionally, the results show that the CODD in the Y-shaped pre-planned agility, Pro-agility 0-10 m, and Pro-agility tests only had small to moderate correlations with the 0-5 m, 0-10 m, and 0-30 m sprint times, which is similar to previous research findings. Studies have confirmed that the correlation between the CODD in Pro-agility 0-10 m and the 10 m sprint time [9], the CODD in the 505 agility test and the sprint times at 10 m and 30 m [5], and the CODD in the L-shaped COD test and the sprint times at 5 m, 10 m, and 20 m [10] have no statistical differences. Reducing the possible influence of the short sprint time on the CODD might be possible because the CODD is obtained by subtracting the sprint time from the CODTT over the same distance. Therefore, the CODD is an essential component of the CODTT, and the COD and the short sprint time are two independent variables. Furthermore, we found that compared to the Y-shaped pre-planned agility, the CODD of the Pro-agility 0-10 m test was more significant, and its prediction degree of CODTT variables was higher. The reason may be the different cut angles requiring different COD abilities. From a sports biomechanics perspective, the deceleration amplitude of an athlete before the braking stage is proportional to the cut angle [17], resulting in an increased ground contact time of the cut action with an increase in the cut angle.