## 3 Results
### DTW Validation Study  
With the establishment of DTW stability, we began to validate the correlation of the normalized DTW function with human evaluation. We performed an experiment with a much larger group consisting of 25 beginner players (with no prior table tennis experience: M: 22; F: 3; age: 18-25) and 25 intermediate players (with at least 2 years of table tennis experience: M: 22; F:3; age: 18-25). After obtaining consent, they received 2 h of basic training on the forehand stroke. Then, their hitting poses were recorded with the system to obtain a 15 s video stream, and, for each of them, the normalized DTW value was displayed. At the same time, the recording was sent to two professional table tennis coaches (certified national level two table tennis players) to evaluate the hitting position with a composite score of 0-100, where 100 stands for most effective, and 0 stands for least effective. The coaches' score criteria included timing, speed, landing point, and movement rationalization. These four criteria were weighted equally at both the beginner and intermediate levels when giving a composite score--timing (25%), landing point (25%), movement rationalization (25%), and speed (25%)--and the sum of all the scores formed the composite score. Specifically, timing was assessed by observing the players' ability to execute shots at the optimal moment during rallies, such as anticipating the opponent's movements or reacting quickly to fast-paced exchanges. The landing point was judged by the accuracy of the ball's placement on the table, focusing on whether the players consistently targeted advantageous positions for their shots. Movement rationalization was assessed by analyzing the players' decision-making and movement efficiency, such as whether they used the most effective and economical movements to reach the ball or position themselves strategically. Speed was evaluated based on the players' reaction time and the efficiency of their movements, including how quickly they transitioned between positions and how fast they hit the table tennis balls. Each coach independently evaluated each video, using a standardized scoring sheet. The coaches reviewed the videos as much as needed using slow motion and freeze frame. The method of using two independent observers could improve internal validity; however, interpretation bias from coaches could still affect validity. Therefore, we first examined the composite score from the two coaches to ensure cross-reliability. The data are summarized in Figure 8, and the raw data are presented in the Supporting Information. For the beginners, the two coaches gave similar ratings of 54.6 \(\pm\) 20.96 (coach 1) and 50.80 \(\pm\) 17.06 (coach 2), with a \(p\) value of 0.48. The same trend was observed for the intermediate group, where coach 1's rating was 81.61 \(\pm\) 10.54, and coach 2's rating was 80.71 \(\pm\) 8.01, with a \(p\) value of 0.72. We did notice, however, that there were individual score fluctuations between the coaches. For example, player 6 in the beginner group received a score of 30 from coach 1 and 50 from coach 2, while player 20 received a score of 80 from coach 1 and 50 from coach 2. Since each player can have a very different style of play and each coach will have interpretation bias, this kind of individual variation could influence the reliability of the composite score. Therefore, we can only say that, for the average composite score, the scores of the two coaches yielded no statistical difference between the beginners and intermediates. \begin{table}
\begin{tabular}{c c c c} \hline
**Day** & **Player 1** & **Player 2** & **Player 3** \\ \hline
1 & 45.92 \(\pm\) 0.20 & 48.48 \(\pm\) 1.16 & 31.83 \(\pm\) 1.86 \\ \hline
3 & 46.98 \(\pm\) 0.75 & 50.13 \(\pm\) 1.69 & 35.97 \(\pm\) 2.32 \\ \hline
7 & 46.61 \(\pm\) 1.10 & 47.48 \(\pm\) 0.77 & 35.96 \(\pm\) 1.47 \\ \hline \end{tabular}
\end{table} 
Table 1: DTW pilot study for 3 players. For the beginners vs. intermediates, the coaches' average composite scores were statistically different.