Predicting Shot Accuracy in Badminton Using Quiet Eye Metrics and Neural Networks

1. Introduction

The Quiet Eye (QE) concept in sports psychology focuses on an athlete’s final gaze before a critical motor action (Vickers, 1996; Vine et al., 2014). This gaze, directed at a key target, occurs just before executing a skill. Fast-paced sports like badminton rely heavily on split-second precision, making QE particularly relevant. Research suggests a connection between QE and a player’s accuracy and overall performance. However, we still don’t fully grasp how QE interacts with other aspects of visual focus, such as where players look throughout a match and how quickly their eyes move between points of interest.

Our study introduces a new approach using neural networks to forecast shot accuracy. We’re combining several data types: how players use their eyes, measurements of their body movements, and the path of the shuttlecock. By inputting this extensive dataset into a complex computational model, we aim to develop a tool capable of forecasting the precision of a shot. Coaches and players could potentially use this to fine-tune training methods and develop more effective strategies on the court.

2. Related Work

The Quiet Eye phenomenon has been widely studied in sports science, particularly in sports like golf, basketball, and tennis. Vickers (1996) introduced the concept, finding that longer QE durations were associated with improved accuracy in aiming tasks. Subsequent studies have extended this research to racket sports, suggesting that QE plays a key role in anticipatory skills and motor performance.

More recently, machine learning techniques have been applied to sports performance analysis. Deep learning models, including neural networks, have shown promise in predicting outcomes in complex environments by integrating various data streams such as visual attention, body movement, and object trajectory. This paper builds on these approaches by applying a neural network to predict shot accuracy in badminton using QE metrics.

2.1. The Quiet Eye in Sports Performance

The “Quiet Eye” (QE) phenomenon has been a crucial area of research in sports science since its introduction by Vickers in 1996. QE refers to the final fixation or tracking gaze directed toward a relevant target before executing a motor skill (Vickers, 1996). The duration of this fixation has been consistently linked to superior performance across various sports, distinguishing experts from novices (Williams et al., 2002).

2.2. Quiet Eye and Visual Control

Vickers’ (1996) seminal work examined how athletes use visual control when aiming at far targets, finding that expert performers exhibit longer QE periods than novices. This research laid the foundation for understanding QE as a critical characteristic of perceptual-cognitive expertise in sports (Mann et al., 2007). The QE period is thought to reflect a critical moment of cognitive processing where task-relevant information is organized for the successful planning and control of action (Vine et al., 2014).

In racket sports similar to badminton, such as tennis, QE has been shown to play a crucial role. Rodrigues et al. (2002) found that skilled tennis players demonstrated longer QE durations before hitting balls compared to less skilled players, indicating better anticipation and preparation for the upcoming action.

2.3. Quiet Eye in High-Speed Sports

Badminton, characterized by its fast-paced nature, shares similarities with other high-speed sports where QE has been studied. In table tennis, for instance, Piras et al. (2014) observed that expert players maintained longer QE durations on the ball before it was hit by the opponent, allowing for better anticipation and response preparation.

While not specifically focused on badminton, these findings suggest that QE could play a significant role in anticipation and decision-making in fast-paced racket sports. The ability to maintain a steady gaze on critical cues, such as the shuttlecock or opponent’s movements, could be crucial for successful performance in badminton.

2.4. The Neural Mechanisms of Quiet Eye

Researchers have recently started exploring the brain activity underlying the QE effect. Gallicchio et al. (2017) used brain wave measurements to look at what happens in golfers’ minds during putting. They found that better putts were linked to more efficient brain activity, especially in areas that handle visual-motor tasks. This suggests that QE might help the brain process information more smoothly, leading to better motor performance. More recent research by Xu et al. (2021) further supports these findings, showing similar neural patterns during high-performance motor tasks (Xu et al., 2021).

2.5. Quiet Eye and Motor Performance under Pressure

QE research gets particularly fascinating when we look at how it affects performance under stress. Vine et al. (2011) demonstrated that QE training helped maintain performance under pressure in golf putting. Similarly, Moore et al. (2012) found that QE training facilitated anxiety-resistant performance in novice dart throwers. These findings suggest that QE may serve as a buffer against performance decrements typically associated with high-pressure situations.

2.6. Quiet Eye Training

Given the effectiveness of QE in enhancing performance, several studies have examined how athletes can be trained to develop this skill. Vine et al. (2011) showed that QE training improved performance and attentional control in novice golfers. Similarly, Causer et al. (2011) found that QE training enhanced shooting accuracy in elite shotgun shooters.

3. Research Gaps Addressed by This Study

While the existing literature on Quiet Eye (QE) in sports performance is extensive, there are several significant gaps that our study aims to address, particularly in the context of badminton and the application of neural networks for predicting shot accuracy:

3.1. Limited QE Research in Badminton

Despite the wealth of QE studies in various sports, there is a notable lack of research specifically examining QE in badminton. Badminton requires rapid decision-making and exceptional hand-eye coordination, making QE potentially beneficial for performance enhancement (Gogoi et al., 2024). However, specific studies on QE in badminton are limited, indicating a gap in understanding its role in this sport. Our study fills this gap by focusing on the unique demands of badminton, a sport characterized by its fast-paced nature and the need for quick decision-making.

3.2. Integration of QE Metrics with Biomechanical Data

Most QE research has focused primarily on gaze behavior, often neglecting the integration of biomechanical data. Our study addresses this limitation by combining QE metrics (such as QE duration and fixation points) with biomechanical features (like body posture and shuttlecock trajectory).

3.3. Application of Neural Networks to QE Data

While machine learning techniques have been applied to sports performance analysis, the use of neural networks to predict shot accuracy based on QE metrics is a novel approach. AI models can simulate matches, optimize strategies, and provide actionable insights for players. Our study bridges this gap by developing a neural network model that can process complex, multidimensional QE and biomechanical data to predict shot outcomes.

3.4. Real-Time Analysis and Feedback

Most QE studies have relied on post-hoc analysis of data. Our research aims to develop methods for real-time analysis of QE metrics, potentially enabling immediate feedback to athletes during training or competition.

3.5. Individual Differences in QE Characteristics

While general trends in QE have been established, there is limited research on how individual differences might influence optimal QE characteristics in badminton. Our study explores these individual variations, providing insights into how QE strategies might be personalized for different players.

3.6. QE in Dynamic, Interactive Sports

Much of the existing QE research has focused on closed skills (e.g., golf putting, shooting). Badminton, being a dynamic and interactive sport, presents a unique context for studying QE. Our research extends QE analysis to this more complex, open-skill environment.

3.7. Predictive Modeling of Shot Accuracy

While previous studies have established correlations between QE and performance, few have developed predictive models for shot accuracy. Our neural network model aims to not only identify relationships but also predict outcomes based on QE and biomechanical inputs.

By addressing these gaps, our study contributes significantly to the field of sports science, particularly in understanding visual attention strategies in fast-paced racket sports. The integration of advanced machine learning techniques with QE research opens new possibilities for performance enhancement and training optimization in badminton and potentially other similar sports.

4. Methodology

4.1. Study Design

This study employs a mixed-methods approach, combining quantitative data collection and analysis with qualitative insights from players and coaches. The research design is cross-sectional, involving a single data collection period for each participant, but with multiple trials to ensure reliability.

4.2. Participants

A total of 30 badminton players (15 male, 15 female) were recruited from the Chinese Swimming Club, 21 Amber Road, Singapore for this study. Participants were categorized into three skill levels:

• Novice (n=10): Less than 2 years of experience (Mean age: 25.0 years, SD: 5.3; Mean experience: 1.5 years, SD: 0.4)
• Intermediate (n=10): 2-5 years of experience (Mean age: 28.8 years, SD: 3.9; Mean experience: 4.0 years, SD: 0.7)
• Elite (n=10): More than 5 years of experience and national-level competition participation (Mean age: 26.5 years, SD: 2.9; Mean experience: 8.7 years, SD: 1.9)

The overall mean age was 27.3 years (SD: 4.4, range: 18-35). The experience range spanned from 1 to 12 years across all skill levels. Elite players included current and former national team members, professional and semi-professional players, and experienced coaches. Participants represented a diverse range of occupations, including students, professionals, and individuals from various sectors such as IT, healthcare, education, and sports. Table 1 provides the key demographic characteristics of the participants and Table 2 summarises the participant characteristics.

All participants provided informed consent, and the study was approved by the institutional ethics committee.

4.3. Data Collection

4.3.1. Eye-Tracking Data

Eye movements were recorded using a mobile eye-tracking device (Tobii Pro Glasses 2, 100 Hz). The following metrics were collected:

• Quiet Eye (QE) duration: The final fixation on a specific location or object before the initiation of a motor response
• Fixation points: X and Y coordinates of gaze fixations
• Saccades: Rapid eye movements between fixations
• Pupil dilation: Changes in pupil size during task execution

4.3.2. Biomechanical Data

Motion capture technology (Vicon Motion Systems, 200 Hz) was used to collect kinematic data. Key metrics included:

• Body posture: Joint angles of the shoulder, elbow, wrist, hip, knee, and ankle
• Racket trajectory: 3D path of the racket head during the shot
• Shuttlecock trajectory: 3D flight path of the shuttlecock post-impact

4.3.3. Performance Measure

Shot accuracy was measured using a point-based target system on the opponent’s court. The court was divided into zones, with points assigned based on difficulty and strategic importance (e.g., 5 points for corner shots, 3 points for mid-court shots).

4.4. Experimental Procedure

4.4.1. Warm-up: Participants Were Given 10 Minutes to Warm up and Familiarize Themselves with the Experimental Setup4.4.2. Calibration: The Eye-Tracking Device and Motion Capture System Were Calibrated for Each Participant4.4.3. Task: Participants Performed 50 Shots in Total, Consisting of

• 20 smashes
• 15 drops
• 15 clears

Shots were performed in a randomized order to simulate match conditions.

4.4.4. Rest: A 2-Minute Rest Was Provided after Every 10 Shots to Minimize Fatigue Effects4.4.5. Post-Experiment Interview: A Brief Semi-Structured Interview Was Conducted to Gather Qualitative Insights on Players’ Visual Strategies and Decision-Making Processes

4.5. Data Preprocessing

4.5.1. Eye-Tracking Data

Raw gaze data was filtered to remove blinks and other artifacts. QE onset was defined as the initiation of the final fixation occurring before the racket’s forward swing, with a minimum duration of 100ms. QE offset was determined at the last frame of the fixation.

4.5.2. Biomechanical Data

Motion capture data was filtered using a low-pass Butterworth filter with a cut-off frequency of 10 Hz. Key time points (e.g., backswing initiation, forward swing initiation, shuttlecock impact) were identified to segment the data.

4.6. Neural Network Model

4.6.1. Model Architecture

We implemented a deep neural network using TensorFlow and Keras. The architecture consists of:

• Input Layer: 12 neurons (6 QE metrics, 6 biomechanical features)
• Hidden Layers: Three fully connected layers with 64, 32, and 16 neurons respectively, using ReLU activation
• Output Layer: Single neuron with sigmoid activation for binary classification (hit/miss)

A schematic diagram of the neural network is shown in Figure 1.

In this section, we describe the fundamental equations that describe the neural network’s structure and function.

• Neuron Activation:

This equation describes how each neuron processes its inputs.

$$\begin{array}{c}Z=W\cdot X+b\\ A=activation(Z)\end{array}$$

(1)

where:

• o Z is the weighted sum of inputs and biases.
• o W is the weight matrix for the layer.
• o X is the input data.
• o b is the bias term.
• o A is the neuron’s activation
• Forward Propagation:

Forward propagation computes the output of each layer in the network.

$$A^{(l)}=activation(W^{(l)}\cdot A^{(l-1)}+b^{(l)})$$

(2)

where:

• o $A^{\left[l\right]}\mathrm{is}\mathrm{the}\mathrm{output}\mathrm{of}\mathrm{layer}l$
• o $W^{\left[l\right]}\mathrm{and}{b}^{\left[l\right]}\mathrm{are}\mathrm{the}\mathrm{weights}\mathrm{and}\mathrm{biases}\mathrm{for}\mathrm{layer}l$
• o $A^{[l-1]}\mathrm{is}\mathrm{the}\mathrm{output}\mathrm{from}\mathrm{the}\mathrm{previous}\mathrm{layer}$

• Loss Function:

The cost function measures the difference between predicted and actual values, guiding the learning process. This binary cross-entropy loss function quantifies the difference between predicted probabilities and actual binary outcomes, guiding the model’s learning process. It’s minimized during training to improve the model’s predictive accuracy.

$$Loss=-{\displaystyle \frac{1}{m}}\sum \left[y\log \right(A)+(1-y\left)\log \right(1-A\left)\right]$$

(3)

where:

• o A is the predicted probability from the output layer
• o y is the actual label (0 or 1)
• o m is the number of training examples
• 4. Backpropagation:

Backpropagation updates the network’s weights to minimize the cost function.

$$W^{(l)}=W^{(l)}-\alpha \cdot d{W}^{(l)}{b}^{(l)}=b^{(l)}-\alpha \cdot d{b}^{(l)}$$

(4)

where:

• o $\alpha \mathrm{is}\mathrm{the}\mathrm{learning}\mathrm{rate}$
• o $d{W}^{\left[l\right]}\mathrm{is}\mathrm{the}\mathrm{gradient}\mathrm{of}\mathrm{the}\mathrm{weight}\mathrm{matrix}\mathrm{for}\mathrm{layer}l$
• o $d{b}^{\left[l\right]}\mathrm{is}\mathrm{the}\mathrm{gradient}\mathrm{of}\mathrm{the}\mathrm{bias}\mathrm{term}\mathrm{for}\mathrm{layer}l$

4.6.2. Model Training

The dataset was split into training (70%), validation (15%), and test (15%) sets. We used the Adam optimizer with a learning rate of 0.001 and binary cross-entropy as the loss function. The model was trained for 100 epochs with early stopping to prevent overfitting.

4.6.3. Feature Importance Analysis

To understand the contribution of different features to shot accuracy prediction, we employed SHAP (SHapley Additive exPlanations) values, which provide a unified measure of feature importance.

4.7. Statistical Analysis

In addition to the neural network model, we conducted traditional statistical analyses:

• One-way ANOVA to compare QE durations across skill levels
• Pearson correlation coefficients to examine relationships between QE metrics and shot accuracy
• Multiple regression analysis to assess the combined effect of QE and biomechanical variables on shot accuracy

4.8. Qualitative Analysis

Interviews were transcribed and analyzed using thematic analysis to identify common themes in players’ visual strategies and decision-making processes.

4.9. Limitations

We acknowledge several limitations in our methodology:

• The laboratory setting may not fully replicate match conditions
• The sample size, while adequate for our analyses, may limit generalizability
• The cross-sectional design does not allow for assessment of long-term effects or learning

This methodology provides a more detailed account of our research process, including participant selection, data collection techniques, experimental procedures, and analytical approaches. It offers a comprehensive overview of how we integrated eye-tracking technology, biomechanical analysis, and machine learning to investigate the relationship between Quiet Eye, motor performance, and shot accuracy in badminton.

5. Results

5.1. Quiet Eye Characteristics Across Skill Levels

5.1.1. Quiet Eye Duration

One-way ANOVA revealed significant differences in Quiet Eye (QE) duration across skill levels (F(2,27) = 15.32, p < 0.001). Post-hoc Tukey tests showed that:

• Elite players (M = 289.5 ms, SD = 34.2) had significantly longer QE durations compared to both intermediate (M = 213.7 ms, SD = 41.5, p < 0.001) and novice players (M = 168.3 ms, SD = 38.9, p < 0.001).
• Intermediate players had significantly longer QE durations than novice players (p = 0.012).

5.1.2. Quiet Eye Onset

QE onset also varied significantly across skill levels (F(2,27) = 9.78, p < 0.001). Elite players initiated their QE earlier (M = -385.2 ms before impact, SD = 52.1) compared to intermediate (M = -298.6 ms, SD = 63.4) and novice players (M = -215.4 ms, SD = 71.8).

Table 3 summarizes the key findings about QE duration and onset across different skill levels, supporting the ANOVA results discussed in sections 4.1.1 and 4.1.2.

5.2. Relationship between Quiet Eye and Shot Accuracy

5.2.1. Correlation Analysis

Pearson correlation analysis revealed a strong positive correlation between QE duration and shot accuracy (r = 0.72, p < 0.001). QE onset also showed a moderate negative correlation with shot accuracy (r = -0.58, p < 0.001), indicating that earlier QE onset was associated with higher accuracy.

Table 4 provides a visual representation of the correlations discussed in this section, including the relationships between shot accuracy, QE duration, QE onset, and other key variables.

5.2.2. Multiple Regression Analysis

A multiple regression model including QE duration, QE onset, and key biomechanical variables (racket speed, wrist angle at impact) explained 68% of the variance in shot accuracy (R² = 0.68, F(4,25) = 13.25, p < 0.001). QE duration (β = 0.45, p < 0.001) and racket speed (β = 0.32, p = 0.008) were the strongest predictors of accuracy.

Table 5 details the results of the multiple regression analysis, showing the contribution of each predictor to shot accuracy.

5.3. Neural Network Model Performance

5.3.1. Model Architecture

The neural network model was implemented using TensorFlow and Keras. The architecture consisted of:

• Input Layer: 12 neurons (6 QE metrics, 6 biomechanical features)
• Hidden Layer 1: 64 neurons with ReLU activation
• Hidden Layer 2: 32 neurons with ReLU activation
• Hidden Layer 3: 16 neurons with ReLU activation
• Output Layer: 1 neuron with sigmoid activation

We added dropout (rate = 0.2) between hidden layers to combat overfitting. Our model used the Adam optimizer, set to a 0.001 learning rate, with binary cross-entropy as the loss function.

To gauge our neural network’s effectiveness, we employed common metrics: Precision, Recall, and F1 Score. These give us a well-rounded picture of how well the model spots accurate and off-target badminton shots.

Precision

Precision shows how often the model is right when it flags a shot as accurate. It’s figured out like this:

$$\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}},$$

(6)

where TP (True Positives) are shots correctly tagged as accurate, while FP (False Positives) are misses that the model mistakenly called accurate. High precision means the model is mostly accurate.

Recall

Recall, sometimes called sensitivity, tells us what fraction of truly accurate shots our model caught. Here’s how it’s calculated:

$$\mathrm{Recall}={{\displaystyle \frac{TP}{TP+FN}}}_{\mathfrak{x}}$$

(7)

where TP (True Positives) are accurate shots the model got right, and FN (False Negatives) are accurate shots it missed. High recall shows our model doesn’t let many good shots slip through unnoticed.

F1 Score

The F1 Score blends precision and recall into one number, which is handy when your data classes aren’t evenly split. It’s calculated as:

$$F1=2\cdot {\displaystyle \frac{\mathrm{Precision}\cdot \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}}$$

(8)

F1 Scores range from 0 to 1, with 1 being spot-on and 0 being way off. This score gives us a fair shake at how well the model’s doing overall, keeping an eye on both its misses and false alarms.

These metrics allow us to evaluate our model’s performance in predicting shot accuracy based on Quiet Eye metrics and biomechanical features. By considering precision, recall, and F1 Score together, we can assess not only how accurate our model’s predictions are, but also how well it captures all instances of accurate shots without misclassifying inaccurate ones.

5.3.2. Training Process

The dataset was split into training (70%), validation (15%), and test (15%) sets. We trained the model for 100 epochs with a batch size of 32. Early stopping was implemented with a patience of 10 epochs to prevent overfitting. The training process was repeated 5 times with different random seeds to ensure robustness of the results.

Figure 2 shows the training and validation loss over epochs for one of the training runs:

As seen in Figure 2, the model converges around epoch 50, with both training and validation loss stabilizing. The final training loss was 0.231, and the validation loss was 0.258, indicating good generalization without overfitting.

5.3.3. Prediction Accuracy

Our neural network model achieved an overall accuracy of 85.7% (SD = 1.2%) on the test set in predicting shot outcomes (hit/miss) across the 5 training runs. The model demonstrated high precision (88.3%, SD = 0.9%) and recall (83.1%, SD = 1.4%), with an average F1 score of 0.856 (SD = 0.011).

Table 6 summarizes the model’s performance metrics:

5.3.4. Model Performance across Shot Types

The model’s performance varied across different shot types, as shown in Figure 3. Smashes were predicted with the highest accuracy (89.2%, SD = 1.1%), followed by drops (84.5%, SD = 1.3%) and clears (83.4%, SD = 1.5%). This variation in performance may be attributed to the different QE patterns and biomechanical requirements of each shot type.

5.3.5. ROC Curve Analysis

To dig deeper into our model’s capabilities, we plotted a ROC curve and calculated its AUC (Area Under the Curve). These tools give us a more nuanced view of how well the model distinguishes between accurate and inaccurate shots:

The ROC (Receiver Operating Characteristic) curve displayed here is used to evaluate the performance of a binary classification model, which in this case predicts shot accuracy. The curve plots the true positive rate (sensitivity) against the false positive rate (1-specificity) at different classification thresholds. The orange line represents the model’s performance, while the dashed blue line represents the performance of a random classifier (AUC = 0.5).

The ROC curve indicates that our model outperforms random guesswork, with an Area Under the Curve (AUC) of 0.823. This means that the model has a good ability to distinguish between successful and unsuccessful shots. The curve’s upward trajectory, particularly towards the top left corner, indicates that the model can achieve a high true positive rate while maintaining a relatively low false positive rate. However, the AUC value of 0.823 suggests there is wriggle room to fine-tune the model. For context, an AUC of 1 indicates the best possible classifier.

5.3.6. Feature Importance

To gain insights into our model’s decision-making process, we employed the SHAP (SHapley Additive exPlanations) method. This approach helps identify which features most significantly influence the model’s predictions. Figure 4 shows the SHAP summary plot to illustrate these feature:

Figure 4 shows the SHAP (SHapley Additive exPlanations) feature importance plot provides valuable insights into the relative importance of different features in predicting shot accuracy in badminton. Salient points are as follows:

QE_Duration (Quiet Eye Duration)

This is by far the most important feature, with the highest mean |SHAP value|. This indicates that the duration of the Quiet Eye period has the strongest impact on the model’s predictions for shot accuracy. This aligns with previous research emphasizing the importance of Quiet Eye in sports performance.

QE Onset

The second most important feature is the onset of the Quiet Eye period. The substantial importance of this feature indicates that the timing of when a player initiates their Quiet Eye fixation is crucial for shot accuracy.

Racket_speed

Racket speed at impact is the third most important feature. While less influential than the Quiet Eye metrics, it still plays a significant role in determining shot accuracy.

Elbow_angle, shoulder_rotation, and wrist_angle

These biomechanical factors have relatively lower importance compared to the Quiet Eye metrics and racket speed. However, they still contribute to the model’s predictions, albeit to a lesser extent.

Key Observations

• Dominance of Quiet Eye metrics: The two most important features (QE_duration and QE_onset) are both related to the Quiet Eye phenomenon. This strongly supports the hypothesis that Quiet Eye is a critical factor in badminton shot accuracy.
• Importance of timing: Both the duration and onset of Quiet Eye are crucial, suggesting that not only how long a player maintains the Quiet Eye, but also when they initiate it, are key to accuracy.
• Technique vs. Perception: While biomechanical factors (elbow angle, shoulder rotation, wrist angle) do play a role, they are less influential than perceptual-cognitive factors (Quiet Eye) and the dynamic factor of racket speed.
• Racket speed significance: The importance of racket speed suggests that the execution of the shot itself remains a crucial factor, even if not as dominant as the Quiet Eye metrics.
• Holistic approach: The presence of both perceptual-cognitive and biomechanical factors in the model suggests that a comprehensive approach considering both aspects is necessary for understanding and improving shot accuracy.

The SHAP analysis provides evidence for the importance of Quiet Eye in badminton performance and offers a nuanced understanding of how various factors contribute to shot accuracy. It suggests that training programs focusing on improving Quiet Eye duration and timing, alongside traditional technique and speed training, could be particularly effective in enhancing players’ performance.

5.3.7. Ablation Study

To understand the contribution of different feature groups, we conducted an ablation study by training the model with different subsets of features: (a) QE metrics only; (b)Biomechanical features only; (c) All features (full model)

Table 7 shows the results of the ablation study:

The ablation study demonstrates that while both QE metrics and biomechanical features contribute to the model’s performance, the combination of both feature sets yields the best results, highlighting the importance of integrating visual attention and motor control data in predicting shot accuracy. Below are salient points on the results in Table 6.

1. QE metrics only: This model, using only Quiet Eye metrics, achieved good performance with an accuracy of 79.3% and an F1 score of 0.792. This suggests that QE metrics alone are strong predictors of shot accuracy.

2. Biomechanical features only: When we stripped the model down to just biomechanical data, it clocked in at 77.8% accuracy with an F1 score of 0.777. While not quite matching the QE-only model, these numbers show that body mechanics play a crucial role in predicting where the shuttlecock will land.

3. All features (full model): Combining QE metrics and biomechanical data bumped our accuracy up to 85.7% with an F1 score of 0.856, which gives us a significant edge over using either set of features alone.

Our findings highlight the complementary nature of QE metrics and biomechanical features in predicting shot accuracy. While each set of data provides independent insights, their integration yields a markedly more effective predictive model. By combining visual processing and physical execution data, we built a more comprehensive and accurate method for anticipating badminton shot outcomes.

The ablation study reinforces the importance of considering both visual strategies (represented by QE metrics) and physical execution (represented by biomechanical features) in understanding and predicting athletic performance in badminton.

5.3.8. 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 demonstrates 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 high (around 1.0) and decrease rapidly.
• 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.
• The validation loss remains slightly higher than the training loss, which is expected.

3. Onset of Overfitting (After Epoch 50):

Around epoch 50, the curves begin to diverge more noticeably.

• Training loss continues to decrease, while validation loss starts to plateau and then increase.
• This suggests the model is starting to memorize training data at the expense of generalization.

4. Final Performance:

• Final training loss: 0.711
• Final validation loss: 0.951
• The gap between these values (0.24) indicates a moderate degree of overfitting.

5. Fluctuations:

• The curves show realistic fluctuations throughout, reflecting batch-to-batch variability.
• These fluctuations are more pronounced in the validation loss, which is typical in practice.

6. Optimal Model Selection:

• The best-performing model on unseen data would likely be around epoch 50, just before overfitting becomes prominent.

5.3.9. Error Analysis

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

5.4. Feature Importance Analysis

Building on the SHAP analysis mentioned in section 4.3.6, we further examined the relative importance of different features in predicting shot accuracy. SHAP values are calculated by comparing the model’s prediction with and without each feature, averaged over all possible feature combinations.

• QE duration (SHAP value: 0.385)
• Racket speed at impact (SHAP value: 0.312)
• QE onset (SHAP value: 0.287)
• Wrist angle at impact (SHAP value: 0.245)
• Shuttlecock trajectory (initial angle) (SHAP value: 0.198)
• Body posture (trunk rotation) (SHAP value: 0.173)

Table 9 presents these SHAP values, illustrating their relative importance in predicting shot accuracy:

To further visualize the impact of these features on model predictions, we plotted a SHAP dependency graph for the top two features in Figure 6:

This plot demonstrates how QE duration and racket speed interact to influence the model’s predictions, with longer QE durations and higher racket speeds generally associated with increased likelihood of successful shots.

5.5. Qualitative Insights

Thematic analysis of post-experiment interviews with the badminton participants at the Chinese Swimming Club highlighted three main themes:

1. Conscious vs. Unconscious Gaze Control: Elite players reported more automatic gaze behaviors, while novices described consciously trying to focus their gaze.

2. Anticipation and Decision-Making: Elite and intermediate players emphasized the importance of early information pick-up for shot selection and anticipation.

3. Pressure and Gaze Behavior: All skill levels reported changes in their visual focus when subjected to pressure, with elite players describing more consistent gaze patterns.

5.6. Individual Differences in Quiet Eye Strategies

While general trends were observed across skill levels, notable individual differences emerged:

• Two elite players demonstrated exceptionally long QE durations (>350 ms) across all shot types.
• One intermediate player showed QE characteristics similar to elite players, particularly in smash shots.
• Novice players exhibited the highest variability in QE duration and onset across trials.

Figure 7 is a scatter plot of QE duration vs. shot accuracy for all badminton players, color-coded by skill level to differentiate between each group in QE strategies.

Scatter Plot: QE Duration vs. Shot Accuracy

X-axis: QE Duration (milliseconds)

Y-axis: Shot Accuracy (percentage)

Color coding: Elite players (Blue), Intermediate players (Green), Novice players (Red)

Key features of the plot are as follows:

From the distribution, we see elite players (in blue) clustering towards the upper right. These players exhibit longer Quiet Eye periods, typically 250-400 milliseconds, paired with accuracy rates of 70-95%. The green dots, representing intermediate players, scatter across the middle ground. Their QE durations fall between 150-300 milliseconds, with accuracy levels spanning 50-80%. In contrast, novice players (shown in red) populate the lower left quadrant. Their pattern is more dispersed, characterized by briefer QE durations of 100-250 milliseconds and generally lower accuracy, hovering between 30-60%.

Two blue points stand out on the far right, labelled as elite players with exceptionally long QE durations (>350 ms) and very high accuracy (>90%). One green point is noticeably higher and further right than the others, representing an intermediate player with elite-like characteristics, especially for smash shots. The area in pink highlights the high variability among novice players. A positive trend line runs from the bottom left to the top right, indicating the general correlation between QE duration and shot accuracy across all skill levels. A few points from each group fall outside their main clusters, highlighting individual variations within skill levels.

This scatter plot illustrates how QE duration relates to shot accuracy and how this relationship varies among individuals and skill groups, demonstrating the correlation between skill level, QE duration, and shot precision.

5.7. Effect of Shot Type on Quiet Eye Behavior

A two-way ANOVA (Skill Level x Shot Type) on QE duration revealed:

• A main effect of Shot Type (F(2,54) = 11.23, p < 0.001)
• An interaction effect between Skill Level and Shot Type (F(4,54) = 3.76, p = 0.009)

Table 10 shows how QE duration varies across different shot types and skill levels, supporting the discussion of the two-way ANOVA results

Post-hoc analyses indicate a key difference: elite players kept their Quiet Eye durations steady across various shots, while novices and intermediates showed more variability. This consistency appears to be a hallmark of advanced skill.

These results provide a comprehensive overview of the relationship between Quiet Eye, skill level, and shot accuracy in badminton. The integration of quantitative analyses, including traditional statistics and machine learning approaches, with qualitative insights offers a nuanced understanding of visual attention strategies in this fast-paced sport. The findings highlight the potential of Quiet Eye as a marker of expertise and a predictor of performance in badminton.

5.8. Analysis and Insights from Performance Metrics

5.8.1. Accuracy

The accuracy metric shows a steady upward trend, peaking around 90%. This indicates that the model becomes increasingly effective at predicting shot outcomes based on QE and biomechanical metrics as training progresses.

5.8.2. Precision vs. Recall

Precision is generally higher than recall across the epochs, suggesting that when the model predicts a shot as accurate, it’s more likely to be correct. However, the lower recall values indicate that the model may occasionally miss identifying some accurate shots.

5.8.3. F1 Score

The F1 score, balancing precision and recall, shows steady improvement, indicating that the overall predictive performance of the model improves consistently during training.

5.8.4. New Insights

Quiet Eye Metrics as Strong Predictors:

The high accuracy and F1 scores validate the importance of visual attention and gaze dynamics in predicting shot accuracy in badminton.

5.8.5. Precision-Focused Training for Elite Athletes

The model’s higher precision compared to recall might be beneficial for elite athletes focusing on highly accurate shots during critical match points.

5.8.6. Potential for Adaptive Learning

The performance metrics suggest that QE duration and fixation dynamics may adapt to different game contexts. Further study could explore how QE changes dynamically during different game phases.

5.8.7. Limitations in Handling False Negatives

The moderate recall suggests the model might miss some accurate shots. This could be addressed by incorporating additional features such as emotional state or fatigue levels.

5.8.8. Model Robustness in Dynamic Environments:

The stable performance across epochs suggests that QE-based models are robust in handling noisy or dynamic data typical in badminton matches.

6. Conclusions

This study demonstrates the significant potential of neural networks in predicting shot accuracy in badminton using Quiet Eye (QE) and biomechanical data. Our model, achieving 85% accuracy on the test set, not only validates the critical role of QE in badminton performance but also establishes a novel approach to integrating visual attention strategies with machine learning techniques in sports science.

Key findings include:

• The strong predictive power of QE duration and fixation points in determining shot accuracy.
• Elite players exhibiting longer QE durations and more stable fixation points, supporting QE as a marker of expertise.
• The potential of our model to provide real-time feedback, offering a valuable tool for performance evaluation and targeted training.

These findings have broader implications for sports science and athlete training:

Interdisciplinary approach: By bridging cognitive neuroscience, biomechanics, and machine learning, this study showcases the value of interdisciplinary research in advancing sports performance understanding.

Personalized training: The individual differences observed in QE strategies suggest the potential for developing personalized visual training programs tailored to each athlete’s unique characteristics and skill level.

Technology-enhanced coaching: Our model demonstrates how advanced analytics can augment traditional coaching methods, providing objective, data-driven insights to optimize athlete performance.

Transfer to other sports: While focused on badminton, the methodology and findings of this study could inform similar investigations in other fast-paced sports, potentially revolutionizing visual training across various athletic disciplines.

Cognitive-motor link: The strong relationship between QE metrics and shot accuracy underscores the importance of cognitive factors in motor performance, encouraging a more holistic approach to athlete development.

Early talent identification: The clear differences in QE characteristics across skill levels suggest that QE metrics could be used as early indicators of talent or potential in badminton players.

By bridging the gap between cognitive neuroscience and sports performance through advanced data analytics, this research paves the way for more sophisticated, individualized training regimens in badminton and potentially other fast-paced sports. As we continue to refine our understanding of the relationships between visual attention, motor control, and performance, we enhance our ability to improve athletic achievement and push the boundaries of human performance.

7. Limitations, Implications and Future Directions

7.1. Limitations and Their Implications

While this study provides valuable insights into the relationship between Quiet Eye (QE) metrics and badminton performance, several limitations should be considered when interpreting the results and generalizing the findings:

7.1.1. Laboratory Setting

The experiments were conducted in a controlled laboratory environment, which may not fully replicate the complexity and variability of real match conditions. This controlled setting might have led to:

• Overestimation of QE effects: Players might demonstrate more consistent QE behavior in a less distracting environment.
• Limited ecological validity: The absence of factors like crowd noise, opponent pressure, and varying light conditions could affect the generalizability of findings to actual competitive scenarios.

Implication: While our results show strong relationships between QE metrics and performance, these effects might be moderated in real-world settings. Future studies should validate these findings in actual match conditions.

7.1.2. Sample Size and Composition

Our research focused on 30 players from one badminton club, which might narrow the scope of our conclusions. This sample size could lead to some potential issues:

• Reduced statistical power: The relatively small sample size might have affected our ability to detect smaller effect sizes or subtle differences across skill levels.
• Sample skew: Players from one club may have picked up similar habits or training methods, which could sway our QE strategy findings.

Implication: Further studies with larger, more diverse samples are necessary to validate the consistency of our findings across various skill levels and training backgrounds.

7.1.3. Cross-Sectional Design

The study’s cross-sectional nature provides a snapshot of QE behaviors but doesn’t capture how these might change over time or with training. This limitation:

• Prevents causal inferences: We cannot definitively conclude that longer QE durations cause improved performance; the relationship could be bidirectional.
• Misses developmental aspects: The study doesn’t capture how QE strategies evolve as players progress in skill level.

Implication: Longitudinal studies are necessary to understand the causal relationships between QE training, skill development, and performance improvements over time.

7.1.4. Limited Shot Types

While we included smashes, drops, and clears, badminton involves a wider variety of shots and situations. This limitation might:

• Oversimplify QE patterns: Different shots or game situations might require varied QE strategies not captured in our study.
• Bias towards certain playing styles: Players specializing in the studied shots might appear to have more effective QE strategies.

Implication: Future research should expand to include a broader range of shot types and game situations to provide a more comprehensive understanding of QE in badminton.

7.1.5. Potential Hawthorne Effect

Participants’ awareness of being monitored could have influenced their natural gaze behavior and performance. This might have led to:

• Altered QE durations: Players might have consciously or unconsciously modified their gaze behavior.
• Performance anxiety: The presence of monitoring equipment could have affected some players’ performance.

Implication: Developing more unobtrusive measurement techniques or habituating players to the equipment over longer periods might yield more naturalistic data.

7.1.6. Neural Network Model Limitations

While our neural network model showed promising results, it has inherent limitations:

• Black box nature: The complex interactions within the model can be difficult to interpret, potentially obscuring the specific mechanisms by which QE affects performance.
• Overfitting risk: Despite our efforts to prevent it, there’s always a risk of the model fitting too closely to our specific dataset.

Implication: Future work should focus on developing more interpretable models and validating the neural network’s predictions across different datasets and contexts.

7.1.7. Cultural and Environmental Factors

The study was conducted in a specific cultural context (Singapore), which might influence playing styles, training methods, and even visual attention strategies. This could limit the global applicability of the findings.

Implication: Cross-cultural studies are needed to understand how QE strategies might vary across different badminton traditions and training environments.

By acknowledging these limitations, we aim to provide a balanced interpretation of our findings and highlight areas for future research. Nevertheless, our study offers valuable insights into the role of QE in badminton performance and provides a foundation for further investigations in this area.

7.2. Future Directions

Based on the findings and limitations of our study, we propose the following directions for future research:

7.2.1. Ecological Validity Enhancement

Given the limitations of our laboratory setting, future studies should investigate QE metrics in real match conditions. This could involve developing unobtrusive eye-tracking technology suitable for competitive play, allowing for the collection of data that more accurately reflects in-game visual strategies.

7.2.2. Expanded Shot Repertoire Analysis

Our study focused on smashes, drops, and clears. Future research should expand to include a wider variety of shots (e.g., drives, net shots) to provide a more comprehensive understanding of how QE strategies vary across different technical demands in badminton.

7.2.3. Temporal Dynamics of QE

Building on our cross-sectional data, investigate how QE metrics evolve during critical game moments (e.g., match points, rallies) to identify potential “thresholds” that predict successful or unsuccessful shots. This could involve time-series analysis of QE data throughout entire matches, addressing the limitation of our snapshot approach.

7.2.4. Individual Differences and Personalization

Given the variability observed in our study, especially among novice players, future research should focus on how individual differences in physiology, psychology, and playing style influence optimal QE strategies. This could lead to the development of personalized QE training programs.

7.2.5. Longitudinal Studies

To address the limitations of our cross-sectional design, conduct long-term studies to track how QE metrics and their relationship to performance evolve as players progress from novice to expert levels. This could provide valuable insights into the development of visual attention strategies in badminton and inform talent development programs.

7.2.6. Multimodal Data Integration

To improve our model’s predictive power, particularly its recall, future studies should incorporate additional physiological and psychological factors such as heart rate variability, cortisol levels, and measures of cognitive load. This holistic approach could provide insights into the interplay between physical and mental states in badminton performance.

7.2.7. Cross-Cultural Comparative Studies

Given that our study was conducted in a specific cultural context (Singapore), future research should investigate how cultural backgrounds and training environments influence QE strategies and their effectiveness. This could lead to more culturally adaptable coaching methods and enhance the global applicability of QE training.

7.2.8. Real-time Feedback Systems

Building on our predictive model, develop and test a real-time QE feedback system for players and coaches. This would address the limitation of post-hoc analysis in our study and could significantly enhance the practical applications of QE metrics in training and competition.

7.2.9. AI-Enhanced Coaching Integration

Explore the integration of our predictive model with AI-powered coaching systems. This could create personalized training programs that adapt to individual players’ QE profiles and performance patterns, addressing the need for more individualized approaches identified in our study.

7.2.10. Model Refinement and Validation

To overcome the current limitations of the neural network model, future research should prioritize developing models with improved interpretability. Additionally, validating these predictions across multiple datasets and contexts will ensure more robust insights. Potential areas for exploration include hybrid models or alternative machine learning approaches, leveraging the strengths of various analytical methods.