## 3 Results
### Kinematic Analysis of Racket  
Table 1 shows the racket's maximum velocity at impact in different directions. The resultant velocity of AB was significantly greater than AT's (\(p=0.023\), ES = 1.026), which was mainly due to the difference in the vertical velocity component (\(p=0.001\), ES = 6.210). The racket angles within the XY and YZ planes had significant differences between AT and AB at the end of the backward swing in Table 2. The racket angle of AT within the XY plane was less than AB's (\(p=0.007\), ES = 1.336) and the racket angle of AT within the YZ plane was significantly greater than AB's (\(p=0.001\), ES = 3.096). \begin{table}
\begin{tabular}{c c c c c} \hline
**Racket Velocity (m/s)** & **AT (Mean \(\pm\) SD)** & **AB (Mean \(\pm\) SD)** & \(p\)** & **ES** \\ \hline X component value & 10.35 \(\pm\) 0.88 & 8.27 \(\pm\) 2.01 & 0.028 * & 0.973 \\ Y component value & 4.26 \(\pm\) 1.85 & 2.81 \(\pm\) 2.33 & 0.037 * & 0.906 \\ Z component value & 7.62 \(\pm\) 0.93 & 11.70 \(\pm\) 0.68 & 0.001 ** & 6.210 \\ The resultant value & 13.67 \(\pm\) 0.90 & 14.83 \(\pm\) 1.55 & 0.023 * & 1.026 \\ \hline \end{tabular} The statistical significance is marked with **, * indicates \(p<0.05\), and ** indicates \(p<0.01\). Values are the mean \(\pm\) SD (N = 8). ES: effect size. AB: against topspin, AT: against backspin, X component value: the racket velocity in the anterior-posterior direction, Y component value: the racket velocity in the lateral direction, and Z component value: the racket velocity in the vertical direction.  
\end{table} 
Table 1: The racket velocity at impact (N = 8). The racket angles within the XY and YZ planes differed significantly between AT and AB at impact. The racket angle of AT within the XY plane was significantly less than AB's at impact (\(p\) = 0.001, ES = 2.538) and the racket angle of AT within the YZ plane was significantly greater than AB's at impact (\(p\) = 0.001, ES = 3.074). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Angle Variable** & **AT (Mean \(\pm\) SD)** & **AB (Mean \(\pm\) SD)** & \(p\)** & **ES** \\ \hline T\({}_{2}\) & & & & \\ XY plane (\({}^{\circ}\)) & 47.3 \(\pm\) 17.7 & 66.9 \(\pm\) 20.5 & 0.007 ** & 1.336 \\ YZ plane (\({}^{\circ}\)) & 56.9 \(\pm\) 14.5 & 42.0 \(\pm\) 17.0 & 0.001 ** & 3.096 \\ XZ plane (\({}^{\circ}\)) & 69.1 \(\pm\) 22.5 & 63.6 \(\pm\) 16.2 & 0.291 & 0.404 \\ T\({}_{3}\) & & & & \\ XY plane (\({}^{\circ}\)) & 58.5 \(\pm\) 6.0 & 74.7 \(\pm\) 5.4 & 0.001 ** & 2.538 \\ YZ plane (\({}^{\circ}\)) & 34.6 \(\pm\) 5.3 & 18.7 \(\pm\) 2.9 & 0.001 ** & 3.074 \\ XZ plane (\({}^{\circ}\)) & 82.6 \(\pm\) 11.0 & 81.1 \(\pm\) 4.1 & 0.067 & 0.159 \\ \hline \hline \end{tabular} The statistical significance is marked with “**”, and **” indicates \(p<0.01\). Values are the mean \(\pm\) SD (N = 8). ES: effect size, AB: against topspin, and AT: against backspin.  
\end{table} 
Table 2: The racket angle within each plane (N = 8). Figure 6: The joint moment of the lower limbs. Solid lines are the mean group values of AT, with one SD (black shading) after normalizing to 100% of the stroke phase. Dash–dotted lines indicate mean group values of AB with one SD (red shading). The statistically significant differences (for \(p<0.05\)) are marked on the horizontal blue bar at the top of each graph. Hip flexion, \(+\): flexion and \(-\): extension. Right hip abduction, \(+\): adduction and \(-\): abduction. Right hip rotation, \(+\): internal rotation and \(-\): external rotation. Left hip abduction, \(+\): abduction and \(-\): adduction. Left hip rotation, \(+\): external rotation and \(-\): internal rotation. Knee flexion, \(+\): extension and \(-\): flexion. Ankle dorsiflexion, \(+\): dorsiflexion and \(-\): plantar flexion. The top marker of the racket was chosen to represent the racket's trajectory during the movement.