# Predicting Shot Accuracy in Badminton Using Quiet Eye Metrics and Neural Networks
## 5 Results
### Neural Network Model Performance
#### 5.3.9 Learning Curves  
The model's training and validation loss decreased steadily over the first 50 epochs, after which the improvement slowed. Table 8 provides a snapshot of the learning curve at regular intervals. It shows the initial rapid decrease in both losses, the gradual improvement phase, and the divergence of training and validation loss in later epochs, indicating overfitting. These data points and the accompanying analysis provide a comprehensive view of the model's learning process, highlighting key phases of training and potential areas for optimization.  
The learning curves in Figure 5 demonstrate the typical progression of a neural network's training process over 100 epochs. Here are the key observations:  
1. Initial Rapid Learning (Epochs 0-20): * Both training and validation loss start moderately high (around 0.48 and 0.51, respectively) and decrease rapidly. * By epoch 20, training loss drops to 0.236 and validation loss to 0.330. * This indicates the model is quickly learning to capture the main patterns in the data.
2. Gradual Improvement (Epochs 20-50): * The rate of improvement slows, but both losses continue to decrease steadily. * Training loss decreases from 0.236 to 0.140, while validation loss drops from 0.330 to 0.210. * The validation loss remains consistently higher than the training loss, which is expected.
3. Fine-tuning Phase (Epochs 50-95): * The improvement rate further slows down for both losses.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Feature Set** & **Accuracy** & **Precision** & **Recall** & **F1 Score** \\ \hline QE metrics only & 79.30\% & 82.10\% & 76.50\% & 0.792 \\ Biomechanical & 77.80\% & 80.60\% & 75.00\% & 0.777 \\ features only & & & & \\ All features (full model) & 85.70\% & 88.30\% & 83.10\% & 0.856 \\ \hline \hline \end{tabular}
\end{table}
Table 7: Ablation study results.  
* Training loss continues to decrease gradually, reaching 0.083 at epoch 95.
* Validation loss begins to plateau, showing slight fluctuations and ending at 0.155 just before the final epoch.
* This suggests the model is refining its learning without significant overfitting.
* Final Performance:
* At epoch 100, there is an unexpected spike in both losses.
* Final training loss: 0.231
* Final validation loss: 0.258
* This sudden increase might indicate an issue in the final epoch, such as a learning rate change or data anomaly.  
* The curves show realistic fluctuations throughout, reflecting batch-to-batch variability.
* These fluctuations are slightly more pronounced in the validation loss, which is typical in practice.
* Optimal Model Selection:
* The best-performing model on unseen data would likely be around epoch 95, just before the final spike.
* At this point, the model achieves its lowest validation loss without showing signs of significant overfitting.
* Overall Training Stability:
* Despite the final spike, the model shows a stable learning progression throughout most of the training process.
* The consistent decrease in both training and validation loss up to epoch 95 suggests effective learning and good generalization.  
This analysis provides a comprehensive view of the model's learning process, highlighting key phases of training and potential areas for optimization. The unexpected final spike warrants further investigation to ensure optimal model performance.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Epoch** & **Training Loss** & **Validation Loss** \\ \hline
0 & 0.480 & 0.510 \\
5 & 0.380 & 0.430 \\
10 & 0.330 & 0.380 \\
15 & 0.280 & 0.350 \\
20 & 0.236 & 0.330 \\
25 & 0.215 & 0.310 \\
30 & 0  
We analyzed the cases where the model made incorrect predictions to gain insights into its limitations. Common error patterns included:  
* Misclassification of shots with atypical QE durations but successful outcomes.
* Difficulty in predicting outcomes for shots with high biomechanical variability.
* Lower accuracy in predicting clear shots, possibly due to their longer trajectory.