## 1 Introduction  
Change of direction (COD) is the skill of changing movement direction, velocity, or mode and is a crucial aspect of agility [1; 2], significantly impacting athletic performance. A practical evaluation method based on the COD definition should measure the athlete's ability to change direction, velocity, and movement pattern, namely \"actual COD ability\". Measuring the center of mass velocity before and after the braking phase during deceleration and acceleration within a 1 m distance enables an accurate evaluation of the athlete's actual COD ability [3]. However, due to test time and equipment limitations, previous studies have primarily relied on the COD total time (CODT) to assess athletes' COD ability in sports such as football, rugby, basketball, and tennis [3; 4].  
Multiple variables, such as energy metabolism, linear sprint, and actual COD ability, may influence CODT. As the COD test time increases, the impact of the athlete's anaerobic metabolism ability on the CODT also increases [5]. Shorter CODTT tests, like Y-shaped pre-planned agility, 505 agility, and Pro-agility, are less affected by the above factors and are commonly used to assess 45\({}^{\circ}\) and 180\({}^{\circ}\) COD ability [6]. Moreover, numerous studies have reported a significant correlation between CODT and sprint time at the same distance, particularly when measuring COD types involving a significant proportion of short sprint distance [7; 8]. This correlation could introduce noteworthy measurement inaccuracies when assessing an athlete's actual COD ability. As demonstrated in a previous study, rugby players allocated approximately 31% of the total time during the 505 agility test to execute actual COD maneuvers [9]. Furthermore, another investigation distinctly affirmed that,as opposed to the total time taken in the 505 agility test, the center of mass velocity of the athletes before and after braking at 0.3 m, 0.5 m, and 1 m weakly correlated with the 5 m and 10 m sprint speeds [7]. Hence, the evaluation results of COD ability based on the CODTT may not be congruent with the actual COD ability.  
In 2013, a study introduced the COD deficit (CODD) concept as a convenient method to evaluate athletes' actual COD ability, derived from the difference between the times of the same distance COD and sprint test [9]. Although the CODD has received attention and application from relevant scholars in recent years, the evidence that it can accurately reflect the actual COD ability still needs to be improved. Few studies have analyzed the correlation between CODTT, CODD, and sprint time for the same sample under different COD distances, angles, and types [5; 9].  
Research on the impact of CODTT and CODD on the assessment results of athletes' COD ability is also scarce. Therefore, the aim of this study was twofold. The first was to evaluate the relationship between Y-shaped pre-planned agility, Pro-agility, and the 30 m sprint. The second was to compare the differences between CODTT and CODD in evaluating athletes' COD ability. We hypothesized that there would be a trivial correlation between short sprints and CODD and that using CODD as the standard for assessing athletes' COD ability would be more scientific.