## 3 Results  
To evaluate the robustness of the algorithm to changes in parameterization, a sensitivity analysis was conducted on the ball speed threshold used to segment pass sequences. Thresholds of 4 m/s, 5 m/s, and 6 m/s were tested. At the baseline threshold of 5 m/s, the algorithm identified 1044 pass sequences. Lowering the threshold to 4 m/s resulted in 1100 sequences (5.37% increase), while raising it to 6 m/s reduced the count to 971 sequences (7.00% decrease). Importantly, the total number of passes identified remained constant across all threshold levels due to a protective mechanism within the algorithm that ensures each pass is always detected. The variation with the threshold reflects the segmentation of each sequence and the exact timing of each pass, as determined by when the ball velocity exceeded the defined threshold. Regarding the differences in the timestamp, the matched passes differed by 23.5 \(\pm\) 16.9 ms between the 4 m/s and 5 m/s thresholds, and by 33.5 \(\pm\) 21.7 ms between the 6 m/s and 5 m/s thresholds. These represent mean relative deviations of 4.2% and 6.2%, respectively. This suggests that, while the core event detection is stable, sequence framing and temporal precision are sensitive to parameter changes. This reinforces the need for careful calibration of velocity thresholds to maintain consistency and interpretability in analyses. The performance of the synchronization algorithm was evaluated by comparing passing events against ground truth labels using a confusion matrix. While the algorithm showed high overall accuracy, several unmatched events were observed (123 events). These mismatches largely stem from the notational dataset containing only completed passes, which omits certain actions necessary for full alignment. The confusion matrix highlights both the algorithm's effectiveness (717 events) and the limitations imposed by incomplete event data (Figure 2). Comparisons between the notational dataset and the two synchronized datasets revealed significant differences (Friedman test, \(\chi^{2}\) = 358, \(p\)! 0.001). MND to RSD showed a mean difference of -21.0 ms (95% CI = [-27.0, -15.0]), whereas MND to OSD showed a mean difference of 13.0 ms (95% CI = [-6.5, 19.5]). This analysis represented a small positive effect for both OSD (r\({}_{\rm{rb}}\) = 0.18) and RSD (r\({}_{\rm{rb}}\) = 0.29). The results showed a similar _RMSE_, with a lower error for OSD (299.49 ms) compared to RSD (300.46 ms). Similarly, it was identified for _MAE_, with 82.63 ms for OSD and 83.42 ms for RSD. Given the potential influence of outliers on the results, a _modified Z-score_ method was employed to identify and exclude anomalous values. This procedure resulted in the removal of 8 outliers from the RSD (-1192.63 \(\pm\) 2481.37 ms) and the OSD (-1181.63 \(\pm\) 2482.65 ms) dataset. While these data points were statistically identified as outliers using Z-scores, it is acknowledged that their origin has not been fully explored. The outliers presented show similar values for both datasets and could reflect data anomalies or measurement errors. The removal of these outliers helped stabilize variance and improve the robustness of subsequent analyses. Normality of the remaining data was then assessed using the Shapiro-Wilk test. The results improved for both _RMSE_ (RSD = 75.98 ms; OSD = 73.53 ms) and _MAE_ (RSD = 61.13 ms; OSD = 60.39 ms), indicating a modest but meaningful enhancement in synchronization accuracy. The reduction in _RMSE_ suggests fewer large alignment errors, which is particularly important in high-tempo game scenarios where even slight timing discrepancies can lead to  
Figure 2: Confusion matrix of synchronized events to notational data. misinterpretation of player actions or physical outputs. Similarly, the lower _MAE_ reflects a more consistent alignment across all data points, enhancing the reliability of time-sensitive performance metrics.