Open AccessArticle

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

Samson Tan

^1,2,*

and

Teik Toe Teoh

^2,3

Institute of Sustainable Industries and Liveable Cities, Victoria University, P.O. Box 14428, Melbourne, VIC 8001, Australia

Staarch Pte Ltd., Singapore 069420, Singapore

Artificial Intelligence, Nanyang Business School, Nanyang Technological University, Singapore 639798, Singapore

Author to whom correspondence should be addressed.

Appl. Sci. 2024, 14(21), 9906; https://doi.org/10.3390/app14219906

Submission received: 20 September 2024 / Revised: 16 October 2024 / Accepted: 18 October 2024 / Published: 29 October 2024

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Abstract

This paper presents a novel approach to predicting shot accuracy in badminton by analyzing Quiet Eye (QE) metrics such as QE duration, fixation points, and gaze dynamics. We develop a neural network model that combines visual data from eye-tracking devices with biomechanical data such as body posture and shuttlecock trajectory. Our model is designed to predict shot accuracy, providing insights into the role of QE in performance. The study involved 30 badminton players of varying skill levels from the Chinese Swimming Club in Singapore. Using a combination of eye-tracking technology and motion capture systems, we collected data on QE metrics and biomechanical factors during a series of badminton shots for a total of 750. Key results include: (1) The neural network model achieved 85% accuracy in predicting shot outcomes, demonstrating the potential of integrating QE metrics with biomechanical data. (2) QE duration and onset were identified as the most significant predictors of shot accuracy, followed by racket speed and wrist angle at impact. (3) Elite players exhibited significantly longer QE durations (M = 289.5 ms) compared to intermediate (M = 213.7 ms) and novice players (M = 168.3 ms). (4) A strong positive correlation (r = 0.72) was found between QE duration and shot accuracy across all skill levels. These findings have important implications for badminton training and performance evaluation. The study suggests that QE-based training programs could significantly enhance players’ shot accuracy. Furthermore, the predictive model developed in this study offers a framework for real-time performance analysis and personalized training regimens in badminton. By bridging cognitive neuroscience and sports performance through advanced data analytics, this research paves the way for more sophisticated, individualized training approaches in badminton and potentially other fast-paced sports. Future research directions include exploring the temporal dynamics of QE during matches and developing real-time feedback systems based on QE metrics.

Keywords:

badminton; Quiet Eye (QE); shot accuracy; neural networks; eye-tracking; biomechanics; sports performance; predictive modeling; gaze dynamics; performance analysis; motor learning; visual perception in sports

1. Introduction

The Quiet Eye (QE) concept in sports psychology focuses on an athlete’s final gaze before a critical motor action [1,2]. This gaze, directed at a key target, occurs just before executing a skill. Research has demonstrated that longer QE durations are associated with superior performance, particularly in precision-based tasks [2]. In high-velocity sports such as badminton, where athletes are required to execute instantaneous decisions, QE significantly influences both the precision of shots and overall performance outcomes.

Despite extensive research on QE, there are still gaps in understanding how it interacts with other visual behaviors, such as where athletes direct their gaze throughout a match and how quickly they shift between points of interest. Moreover, most research focuses on discrete visual metrics isolated from biomechanical data, providing an incomplete understanding of athletic performance.

In this study, we introduce a novel approach by leveraging neural networks to forecast shot accuracy in badminton. Our model integrates QE metrics, biomechanical data (such as body movement), and shuttlecock trajectory to generate predictions about shot outcomes. By processing this comprehensive dataset, we aim to create a tool that can enhance training strategies for players and coaches by providing actionable insights into the visual and motor components that drive performance.

The current study introduces several innovative elements to the domain of sports science and badminton research. We uniquely integrate Quiet Eye metrics with biomechanical data using a neural network model, enabling the real-time predictive modeling of shot accuracy. Our approach goes beyond traditional analyses by employing advanced interpretability techniques, offering potential for adaptive learning, and providing insights across different skill levels. These innovations not only advance our understanding of visual-motor expertise in badminton but also open new avenues for personalized training and performance enhancement in fast-paced racket sports.

2. Related Work

The Quiet Eye (QE) phenomenon, originally introduced by Vickers [1] in 1996, has been extensively studied in various sports. It refers to the final fixation or tracking gaze directed toward a relevant target before the execution of a motor skill [1]. Since its discovery, QE has been widely recognized for its role in enhancing motor performance and distinguishing expert athletes from novices across different sports, including basketball, golf, and tennis. More recently, advances in technology and machine learning techniques have allowed for a more nuanced analysis of QE data, enabling predictive modeling and real-time feedback during performance.

2.1. The Quiet Eye in Sports Performance

In recent years, the role of Quiet Eye (QE) in sports has evolved from descriptive analyses to predictive applications. Studies in sports like basketball, golf, and archery have shown how QE duration positively correlates with motor skill success. For instance, Giancamilli et al. [3] demonstrated that longer QE durations are associated with improved accuracy in precision sports like basketball, where targeting is crucial. Similarly, research in tennis has shown that expert players, particularly in high-pressure situations, benefit from extended QE periods, allowing them to better anticipate and react to their opponent’s moves [3].

He et al. [4] demonstrated that QE training can significantly improve performance under pressure in golf, with increased QE duration and total fixation time correlating with better outcomes. Their study showed that after QE training, golfers displayed longer quiet eye movement time and total fixation time, leading to higher hit ratios and better putting performance under pressure conditions.

Research in racket sports like badminton remains comparatively limited, although existing studies suggest that QE has the potential to influence shot accuracy in fast-paced environments. Vincze et al. [5] observed that QE durations tend to decrease under physical fatigue, even in high-paced environments like table tennis, but are sustained during successful shots. This suggests that QE could be an important factor for maintaining performance under physical stress, which is common in sports like badminton.

Chen et al. [6] suggest that in sports where fast responses and pinpoint accuracy are needed, visual attention, which is a key aspect of QE, is crucial. While their work primarily focuses on eye-tracking technology, its implications are highly relevant to sports like badminton, where swift decision-making is essential.

Kanat & Şimşek [7] explored differences in QE between expert and novice players, demonstrating that expert athletes exhibit significantly longer QE durations, which correspond to higher accuracy rates in basketball. This research supports the potential for QE to serve as a key component in developing training interventions for badminton players, particularly by helping novices stabilize their cognitive and visual focus.

He et al. [4] demonstrated that QE training enhances accuracy and performance under pressure in precision sports, showing increased QE duration and total fixation time during successful performance. Their findings in golf contribute to the growing evidence that QE training can benefit athletes across various precision-based sports.

2.2. Machine Learning in Sports Performance Prediction

Machine learning has revolutionized sports performance analysis in recent years. Convolutional Neural Networks (CNNs) and Long Short-Term Memory (LSTM) networks have been applied to process complex information, including visual focus data, body movements, and shot outcomes and are useful for predicting performance based on real-time inputs. In badminton, Tan et al. [8] were able to show how the utilization of CNNs with bidirectional LSTMs resulted in more than 85% pinpoint accuracy in rally outcomes prediction. Such models integrate visual attention data, similar to QE metrics, and offer valuable insights into decision-making processes during matches.

Another important development is the use of hybrid models that combine deep learning with traditional statistical analyses for sports analytics such as Random Forests and Support Vector Machines (SVMs) that use physiological and biomechanical data to profile athletes and predict their performance [3]. These approaches, though not yet fully adapted for badminton, present exciting opportunities for integrating QE data into predictive models for real-time performance feedback.

Chen [9] explored the application of Ranking Genetic Optimization Reinforcement Learning (RGORL) to optimize player strategies in tennis. Their findings suggest that reinforcement learning models could be adapted for badminton, focusing on decision-making and predicting performance under high-pressure scenarios.

2.3. Integration of QE with Biomechanical Data

While machine learning models have made advances in sports analytics, many studies still overlook the value of combining Quiet Eye (QE) metrics with biomechanical data. Biomechanical analysis captures detailed data about an athlete’s physical movements, such as joint angles, velocity, and muscle activation, while QE metrics provide insights into visual attention and cognitive control. Combining these two data streams would deepen our understanding of the impact of cognitive processes on motor performance in sports. Recent studies have begun addressing this gap by exploring the interaction between visual focus and physical movement.

In their research on the effects of high-pressure situations on QE during basketball three-point shooting, Giancamilli et al. [3] found that elite players exhibited significantly longer QE durations under pressure compared to semi-elite players. This suggests that elite athletes rely on extended QE durations to suppress distractions and non-optimal movements, a mechanism that becomes critical during high-pressure situations. Integrating these visual focus data with detailed biomechanical metrics, such as hand positioning, shooting form, and body alignment, could further refine predictive models for performance outcomes.

Xu, Sun, and Wilson [10] found that longer QE durations during a golf putting task were associated with greater cortical activation in the prefrontal, premotor, and parietal cortices, suggesting that QE aids in both the preparation and execution phases of motor tasks. These findings highlight the neurophysiological mechanisms by which QE enhances motor performance, which could be beneficial for integrating into models that combine biomechanical and QE metrics.

Carey et al. [11] demonstrated the value of integrating multiple measurement approaches by combining eye-tracking and EEG data during golf putting. Their research revealed that while QE durations might be similar between successful and unsuccessful putts, distinct patterns of neural activity differentiated performance outcomes. Specifically, successful putts were characterized by greater beta suppression in central regions and lower frontal theta power, suggesting enhanced movement planning and reduced hesitation. These findings highlight how combining QE metrics with neurophysiological measurements can provide deeper insights into the mechanisms underlying successful motor performance.

A critical challenge in fast-paced environments like badminton is the rapid alternation between offensive and defensive movements. While specific research on badminton is limited in the literature, recent studies in other sports suggest that combining multiple data streams could enhance predictive accuracy for performance outcomes. He et al. [4] highlighted the benefits of combining eye-tracking data with physiological indicators such as heart rate in their study on golf putting performance in high-pressure situations.

Extrapolating from these findings, one could argue that combining biomechanical data—such as shuttlecock trajectory, swing velocity, and footwork patterns—with QE metrics in real-time models could potentially enhance predictive accuracy for shot outcomes in badminton. By integrating these data streams, machine learning algorithms could potentially assess how an athlete’s visual focus aligns with their physical movements, offering real-time feedback that optimizes both cognitive and motor performance.

2.4. Quiet Eye and Cognitive-Motor Performance

The relationship between QE and motor performance has been well-established in past research, with longer QE durations associated with better performance across various sports [12]. Recent studies have explored how cognitive load, anxiety, and other psychological factors influence QE patterns, particularly under high-pressure conditions like competitive matches [13]. He et al. [4] demonstrated that QE training helps athletes maintain their performance under pressure, especially in sports that require precision, such as golf putting. The integration of QE with other performance metrics is gaining traction as shown by He et al. [4] in their study on golf putting performance under pressure.

The application of advanced analytical techniques to QE data is also evolving, and sophisticated statistical methods have been used to analyze the effects of high-pressure conditions on QE depending on player expertise in basketball [3]. While not directly using machine learning, this approach paves the way for more complex predictive models incorporating QE data. He et al. [4] further assert that combining QE metrics with physiological data, such as heart rate, could provide a more complete view of sports performance under high pressure conditions.

These integrative approaches could lead to the development of integrated models that account for visual attention, physical movement, and physiological responses, providing a more nuanced understanding of sports performance.

2.5. Application of Machine Learning in Badminton

Recent studies have begun to explore the application of advanced analytics and eye-tracking technology to study the effects of various factors on performance in racket. For instance, Giancamilli et al. [3] investigated the impact of pressure on QE depending on expertise level in basketball. While not specifically about badminton, their study highlighted the importance of integrating contextual factors like pressure and expertise level into performance models for more accurate predictions.

In racket sports such as tennis, Zhao et al. [14] explored the integration of QE and biomechanical data into machine learning models to enhance their predictive power, a method that could be applied to badminton to improve performance prediction during competitive play.

Similarly, Wang and Yang [15] conducted a study using neural network models to analyze player performance in tennis, demonstrating the feasibility of real-time data integration for racket sports. While their focus was on tennis, the findings suggest that machine learning can effectively capture the rapid decision-making and motor control demands of badminton.

Incorporating QE metrics into performance models for badminton could enhance their predictive power, providing deeper insights into player focus and visual strategies during play. Future research could explore how QE training might be adapted for the fast-paced environment of badminton and how machine learning models could integrate these data with other performance metrics for more comprehensive analysis.

2.6. Predictive Modeling of Shot Accuracy in Badminton

Building on the success of advanced analytics in various sports, recent studies aim to expand these techniques to predict performance using Quiet Eye (QE) metrics. Research has shown that longer QE durations, especially in high-stakes situations, lead to better outcomes. While the study by He et al. [4] focused on golf, its findings could potentially be applied to a precision sport such as badminton.

Giancamilli et al. [3] found that competitive elite players demonstrated longer QE online durations compared to semi-elites, especially in high-pressure situations. This suggests that QE metrics could be valuable predictors of performance across various sports, including badminton.

Although previous studies have combined QE metrics with biomechanical variables to provide real-time predictions during competitive play [14], there is limited research on integrating QE metrics with neural network models to predict shot accuracy in real-time badminton matches. To address this gap, our work integrates both QE and biomechanical data into a predictive model designed for real-time feedback during training and competitions.

2.7. Future Directions and Research Gaps

While significant progress has been made, several research gaps remain. The integration of physiological data, such as heart rate variability and neural activity, into QE research is still in its early stages. For instance, recent work has used Convolutional Neural Networks (CNNs) to classify eye movements, providing a basis for combining gaze behavior and physiological metrics, such as heart rate variability, to gain deeper insights into cognitive and physical states during high-level performance [16]. This multimodal approach, as shown in studies on elite table tennis players [17], highlights the potential of combining physiological and visual attention data to explore how stress impacts performance.

Machine learning has made significant progress in prediction, but interpretability remains a black box. As neural networks become more complex, it is important to understand their inner workings to apply their insights effectively in coaching and performance optimization. Future research should focus on making these models less of a black box and more transparent to ensure they can be used practically in sports training.

3. Research Gaps Addressed by This Study

While the body of research on Quiet Eye (QE) in sports performance has expanded, certain areas remain underexplored, particularly in the context of badminton and the integration of QE metrics with machine learning models for predicting shot accuracy:

3.1. Limited QE Research in Badminton

Research specifically focused on QE in badminton remains limited. Badminton, a sport requiring rapid decision-making, precise hand-eye coordination, and quick adaptation to opponent actions, presents unique challenges. The fast-paced and dynamic nature of this sport presents unique challenges for QE studies, especially in understanding how players focus on critical cues such as the shuttlecock or opponent movements [6,18]. Our study addresses this gap by applying QE research to badminton, providing insights into the role of visual attention in performance under high-speed, dynamic conditions.

3.2. Integration of QE Metrics with Biomechanical Data

Previous QE research has focused primarily on gaze behavior, with limited work integrating QE data with biomechanical features like body posture and shuttlecock trajectory [19]. Our study builds on this approach by incorporating both QE duration and fixation points with detailed biomechanical data to predict shot accuracy, thus offering a richer model for performance analysis.

3.3. Application of Neural Networks to QE Data

Recent research has shown the potential of machine learning, particularly neural networks and hybrid models, in sports performance analysis [9,11]. However, the application of neural networks to combine QE metrics and biomechanical data for predicting shot outcomes in badminton remains underexplored. Our study fills this gap by developing a neural network model that processes complex, multidimensional data, including both cognitive (QE) and physical (biomechanical) inputs, to predict shot outcomes with high accuracy.

3.4. Real-Time Analysis and Feedback

Most QE studies rely on post-hoc data analysis, leaving the real-time potential of QE for immediate feedback underutilized. Recent advancements in mobile eye-tracking technology and motion capture systems [20,21] present opportunities to provide near real-time feedback during training or competitive play. Our study aims to develop methods for the real-time analysis and prediction of shot accuracy using QE and biomechanical metrics, which could revolutionize performance tracking in badminton.

3.5. Individual Differences in QE Characteristics

While general trends in QE have been established in other sports, little is known about how individual differences—such as skill level, playing style, or cognitive traits—affect optimal QE characteristics in badminton. This gap suggests the need for more personalized training approaches based on individual QE strategies [22,23]. Our study explores these individual variations, contributing to the understanding of how QE strategies can be tailored to each player’s unique characteristics for enhanced performance.

3.6. QE in Dynamic, Interactive Sports

The majority of QE research has focused on closed skills, such as golf putting or target shooting. Badminton, like other racket sports, is a dynamic and interactive, requiring players to adapt rapidly to external stimuli, such as the opponent’s movements or the shuttlecock’s trajectory [9,24,25]. Our research expands the application of QE analysis to this more complex, open-skill environment, providing new insights into the role of QE in fast-paced sports.

3.7. Predictive Modeling of Shot Accuracy

Previous studies have established correlations between QE and performance [7,26,27,28], but few have developed predictive models for shot accuracy that combine cognitive and physical inputs. Our research contributes by developing a predictive model that offers precise, practical insights for coaches and athletes, applicable in both training and competitive environments.

3.8. Summary of Contributions

By addressing these gaps, our study makes significant contributions to the field of sports science, particularly in understanding visual attention strategies and motor coordination in fast-paced racket sports like badminton. Integrating advanced machine learning techniques with QE research [29] opens new possibilities for performance enhancement, real-time feedback systems, and individualized training programs. These findings can inform broader applications across other high-speed, dynamic sports where visual attention and motor performance are critical to success.

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. The elite players included former and current national players. There were university students, accountants, and white-collar workers from IT, healthcare, education, and sports backgrounds. Table 1 and Table 2 present the demographics and characteristics of these badminton players.

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

4.3. Data Collection

4.3.1. Eye-Tracking Equipment and Measures

Eye movements were recorded using a mobile eye-tracking device (Tobii Pro Glasses 2, 100 Hz, Tobii, Danderyd, Sweden). 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 Measurements and Equipment

Motion capture technology (Vicon Motion Systems (Oxford, UK), 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).

4.3.4. Dataset Structure and Feature Extraction

The dataset used in this study consisted of a total of 750 individual shot attempts, with 25 shots recorded per participant. The dataset is provided as Supplementary Materials. These attempts were evenly distributed across three shot types: smashes, drops, and clears. Each shot attempt formed a unique sample, with the dataset organized in a tabular format where rows represented individual shots and columns corresponded to various features.

The dataset was structured with key variables derived from the raw data, including:

Quiet Eye (QE) metrics: QE duration, fixation point coordinates (X, Y), saccades, and pupil dilation.

Biomechanical data: Body posture (joint angles of the shoulder, elbow, wrist, hip, knee, and ankle), racket trajectory (3D path), and shuttlecock trajectory (flight path post-impact).

Feature extraction was performed using a combination of eye-tracking data (Tobii Pro Glasses 2, 100 Hz) and biomechanical data from motion capture technology (Vicon Motion Systems, 200 Hz). Specifically:

QE metrics: QE duration was computed as the total time spent fixating on the shuttlecock before shot execution, while fixation points and saccades were extracted directly from the gaze tracking data.

Biomechanical metrics: Joint angles and racket trajectory were calculated by processing the motion capture data using a low-pass Butterworth filter (cut-off frequency: 10 Hz). Key moments such as the initiation of backswing, forward swing, and shuttlecock impact were identified to ensure the accurate segmentation of the data for model training.

This detailed feature extraction process ensured the robustness of the input data for the subsequent neural network model.

4.4. Experimental Procedure

4.4.1. Warm-Up

Participants were given 10 min to warm up and familiarize themselves with the Experimental Setup.

4.4.2. Calibration

The Eye-Tracking device and Motion Capture System were calibrated for each participant.

4.4.3. 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 Periods

To minimize the effects of fatigue, participants were provided with a 2 min rest period after every set of 10 shots. This rest interval was chosen based on prior research suggesting that brief recovery periods can help maintain consistent performance across physical tasks. The rest periods ensured that the participants’ shot accuracy and overall motor performance were not compromised by physical or mental fatigue, thus allowing for more reliable data collection across all shot types (smashes, drops, and clears). These intervals also provided an opportunity for participants to hydrate and reset mentally, which is essential in maintaining focus, particularly for tasks requiring precision and control, such as shot accuracy in badminton.

4.4.5. Post-Experiment Interview

Following the completion of the shot trials, participants were interviewed in a semi-structured format to gather qualitative insights on their visual strategies and decision-making processes during the experiment. Questions focused on how participants engaged with the shuttlecock visually, their experience with tracking its trajectory, and the specific cues they used to anticipate shot outcomes. The interview also explored the players’ decision-making process in different shot types (e.g., smashes versus drops), helping us better understand the cognitive elements contributing to shot accuracy. These interviews were critical for supplementing the quantitative data with insights into player behavior, offering a more holistic view of performance that combines both biomechanical and cognitive factors.

4.4.6. Real-World Testing and Prediction Latency

The neural network model was tested on real-world shot data collected from live badminton games and training sessions. The dataset consisted of shot attempts performed under actual playing conditions, using mobile eye-tracking devices (Tobii Pro Glasses 2, 100 Hz) and motion capture systems (Vicon Motion Systems, 200 Hz) for data collection. This approach ensured that the shot data accurately represented in-game dynamics, with a mix of smashes, drops, and clears executed by both amateur and elite players.

Here is how we assessed our model. First, we divided our data into two buckets: training and validation. Then, we added new data to check how good the model was at generalization. The model performed well, showing high accuracy across all shot types, which suggests it is suitable for practical use in badminton. We also checked the prediction times to determine whether we could use it in real-time. From the moment QE and biomechanical data were input into the model to the output of shot accuracy predictions, the average prediction time was approximately 150 milliseconds. This speed meant that the model can provide near real-time predictions, which is very important for live performance tracking.

4.4.7. Real-Time Performance Analysis

To assess the model’s capability for real-time applications, we conducted additional experiments focusing on data acquisition, processing speed, and model inference time.

Methodology:

Used a high-speed camera (1000 fps) for data acquisition.
Implemented parallel processing for feature extraction.
Measured inference time on both CPU and GPU.

Results:

Data Acquisition: 1 ms per frame.
Feature Extraction: 5 ms per frame.
Model Inference:
- CPU: 2 ms.
- GPU: 0.5 ms.

Total Processing Time:

CPU pipeline: 8 ms per frame.
GPU pipeline: 6.5 ms per frame.

These results demonstrate that our system can operate at over 100 Hz, which is suitable for real-time analysis in badminton where typical shot durations range from 50–200 ms. The low latency ensures that predictions can be made within the timeframe of a single shot, allowing for potential real-time feedback during training or matches.

Implications for Real-world Applications:

Training Enhancement: The real-time capability allows for immediate feedback during practice sessions, enabling players to adjust their technique on the fly.
Match Analysis: Coaches can receive instant insights during matches, potentially informing strategic decisions between points or games.
Personalized Coaching: The system’s speed allows for the accumulation of large datasets over time, facilitating more personalized and adaptive training programs.
Integration with Wearable Technology: The low latency opens possibilities for integration with smart glasses or other wearable devices, providing players with immediate visual or auditory feedback.
Automated Refereeing Assistance: While not replacing human judgment, the system could provide additional data points to assist in close calls or performance tracking.

Limitations and Future Work:

While these results are promising, further optimization may be needed for seamless integration in match conditions. Future work will focus on:

-: Testing the system under various lighting conditions and environments.
-: Optimizing the feature extraction algorithms for even lower latency.
-: Exploring edge computing solutions to reduce dependency on centralized processing.
-: Conducting user studies to assess the impact of real-time feedback on player performance and decision-making.

This real-time analysis capability significantly enhances the practical applicability of our QE-based predictive model, bridging the gap between laboratory research and on-court implementation in badminton training and competition.

4.5. Data Preprocessing

4.5.1. Eye-Tracking Data Preprocessing

Raw gaze data were 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 Processing

Motion capture data were 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. Neural Network Base Architecture

We implemented a deep neural network using TensorFlow Version 2.17 and Keras Version 3.4.1. 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. The Python Version 3.10 script to create and train a neural network model to predict shot accuracy based on QE metrics is shown in Appendix A.

Our neural network model is innovative in its multimodal data integration, combining both QE metrics and biomechanical features as inputs. This integration allows the model to capture complex interactions between visual attention strategies and physical execution that are crucial in badminton performance. Furthermore, the model is designed for real-time predictive capabilities, with low latency that enables potential in-game analysis and feedback. This real-time aspect is critical for practical applications in training and competition settings, where immediate insights can inform decision-making and performance optimization.

Next, we outline the foundational equations that characterize the architecture and operation of the neural network.

Neuron Activation:

This equation describes how each neuron processes its inputs.

Z = W \cdot X + b A = a c t i v a t i o n (Z)

(1)

where:

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

2.: Forward Propagation:

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

A^{(l)} = a c t i v a t i o n (W^{(l)} \cdot A^{(l - 1)} + b^{(l)})

(2)

where:

$A^{(l)} is the output of layer l$ .
$W^{(l)} and b^{(l)} are the weights and biases for layer l$ .
$A^{(l - 1)} is the output from the previous layer$ .

3.: Loss Function:

The loss function measures the difference between predicted and actual values, guiding the learning process. The binary cross-entropy loss function measures how far off the predicted probabilities are from the actual binary outcomes, helping the model adjust and learn more accurately. It is minimized during training to improve the model’s predictive accuracy.

L o s s = - \frac{1}{m} \sum [y l o g (A) + (1 - y) l o g (1 - A)]

(3)

where:

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

4.: Backpropagation:

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

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

(4)

where:

$α is the learning rate$ .
$d W^{(l)} is the gradient of the weight matrix for layer l$ .
$d b^{(l)} is the gradient of the bias term for layer l$ .

4.6.2. Model Training

The dataset was split into training (70%), validation (15%), and test (15%) sets. We applied the Adam optimizer with a learning rate set at 0.001, using 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 Methodology

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 an 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). The elite players started their QE significantly earlier (M = −385.2 ms before impact, SD = 52.1) compared to intermediate players (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 Section 5.1.1 and Section 5.1.2.

5.2. Relationship Between Quiet Eye and Shot Accuracy

5.2.1. Correlation Analysis

A Pearson correlation analysis indicated a strong positive relationship between QE duration and shot accuracy (r = 0.72, p < 0.001). Additionally, QE onset showed a moderate negative correlation with shot accuracy (r = −0.58, p < 0.001), suggesting that earlier QE onset was linked to better accuracy.

r = \frac{\sum [(X - \bar{X}) (Y - \bar{Y})]}{\sqrt{{\sum (X - \bar{X})}^{2}} \cdot \sqrt{{\sum (Y - \bar{Y})}^{2}}}

(5)

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 that included QE duration, QE onset, and key biomechanical variables (racket speed, wrist angle at impact) accounted for 68% of the variance in shot accuracy (R² = 0.68, F(4,25) = 13.25, p < 0.001). Among the predictors, QE duration (β = 0.45, p < 0.001) and racket speed (β = 0.32, p = 0.008) were the most significant factors influencing accuracy.

Table 5 presents the results of a multiple regression analysis aimed at examining the relationship between various predictors—such as Quiet Eye (QE) duration, body posture, and racket head trajectory—and shot accuracy across different skill levels (elite, intermediate, and novice players).

The β (Standardized Beta Coefficients) values indicate the strength and direction of the relationship between the independent variables (such as QE duration) and the dependent variable (shot accuracy). A higher beta value suggests a stronger impact of the independent variable on the dependent variable, with positive values indicating a direct relationship and negative values indicating an inverse relationship. A higher absolute beta value indicates a stronger relationship. In the case of elite players, for example, a beta value of 0.82 for QE duration signifies that longer QE durations are strongly associated with higher shot accuracy. This positive relationship suggests that elite players with longer fixation periods before executing a shot tend to perform more accurately.
t (t-statistic): The t-values test the hypothesis that each independent variable’s coefficient is significantly different from zero. Larger t-values indicate stronger evidence that the predictor has a meaningful impact on shot accuracy. For instance, the t-value of 8.10 for QE duration in elite players indicates a highly significant effect, reinforcing the role of QE in predicting shot accuracy.
p-value: The p-values indicate the level of statistical significance. In the table, a p-value of less than 0.001 (p < 0.001) for QE duration in both elite and intermediate players suggests that the relationship between QE duration and shot accuracy is highly significant and unlikely to have occurred by chance. This confirms that QE duration plays a key role in shot performance.

These results indicate that QE duration has a stronger impact on shot accuracy in elite players compared to intermediate and novice players, as reflected by the higher beta values and statistically significant p-values.

5.3. Neural Network Model Performance

5.3.1. Neural Network Training Architecture

Building upon the architecture described in Section 4.6.1, we implemented our neural network model using TensorFlow Version 2.17 and Keras Version 3.4.1. To combat overfitting, we added dropout layers (rate = 0.2) between the hidden layers. The model was compiled using the Adam optimizer

(l e a r n i n g r a t e = 0.001

β_{1}

= 0.9,

β_{2}

= 0.999, epsilon =

{1 \times 10}^{- 7}

) with binary cross-entropy as the loss function.

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

The performance of our neural network was assessed based on precision, recall, F1 score, and overall accuracy. These metrics provide a comprehensive evaluation of the model’s predictive capabilities across different aspects of performance.

Precision: Precision measures how often the model correctly identifies accurate shots when it predicts a shot to be accurate. It is calculated as:

P r e c i s i o n = \frac{T P}{T P + F P}

(6)

where TPs (True Positives) are accurate shots correctly predicted by the model, and FPs (False Positives) are inaccurate shots mistakenly predicted as accurate. A high precision score reflects the model’s ability to correctly identify accurate shots while minimizing false positives. In our model, precision was 88.3% (SD = 0.9%), which indicates strong predictive accuracy in classifying accurate shots.

Recall: Recall, also known as sensitivity, measures the model’s ability to capture all accurate shots. It is computed as:

R e c a l l = \frac{T P}{T P + F N}

(7)

where FN (False Negatives) are accurate shots that the model failed to identify. High recall indicates that the model is catching most of the accurate shots, even if it occasionally predicts inaccurate shots as accurate. Our model reached a recall of 83.1% (SD = 1.4%), indicating that it successfully identifies the majority of accurate shots, though some may still be missed.

The F1 score provides a balanced evaluation by considering both precision and recall, making it especially useful when dealing with imbalanced classes. It helps to ensure that neither false positives nor false negatives disproportionately affect the model’s performance. It is calculated as:

F 1 = 2 \times \frac{P r e c i s i o n \times R e c a l l}{P r e c i s i o n + R e c a l l}

(8)

F1 Scores: The F1 score ranges from 0 to 1, with higher values reflecting stronger overall performance. Our model achieved an F1 score of 0.856 (SD = 0.011), signifying robust performance with a well-balanced trade-off between precision and recall.

Overall Accuracy: The overall accuracy of our model represents the proportion of correct predictions (including both true positives and true negatives) out of the total cases evaluated. It is calculated as:

A c c u r a c y = \frac{T P + T N}{T P + T N + F P + F N}

(9)

where TP is True Positives, TN is True Negatives, FP is False Positives, and FN is False Negatives. Our model achieved an overall accuracy of 85.7% (SD = 1.2%) on the test set, indicating its strong performance in predicting shot outcomes based on Quiet Eye metrics and biomechanical features.

These metrics allow us to evaluate our model’s performance in predicting shot accuracy based on Quiet Eye metrics and biomechanical features. The strong precision, recall, F1 score, and overall accuracy highlight the effectiveness of our neural network in accurately capturing the complex relationship between visual attention and motor performance in badminton. These metrics demonstrate the model’s ability to consistently perform well in identifying key patterns and making accurate predictions.

5.3.2. Training Process

The dataset was split into training (70%), validation (15%), and test (15%) sets. We trained our 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 five times with different random seeds to ensure the robustness of the results.

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

5.3.3. Epoch Selection for Model Training Cutoff

During model training, we monitored both training and validation loss to determine the optimal stopping point. As shown in Figure 2, both the training and validation loss curves decrease consistently until approximately epoch 50, after which the curves converge, indicating minimal improvement. Beyond epoch 50, the training loss continues to decrease slightly, but validation loss begins to fluctuate, indicating that the model may be starting to overfit to the training data at this point.

To balance model performance and generalization, we selected epoch 50 as the cutoff. This decision was further reinforced by early stopping criteria, where the validation loss did not significantly improve beyond epoch 50. The choice of this epoch ensured that the model had learned the underlying patterns without overfitting, maintaining robust generalizability on unseen data.

By halting training at epoch 50, we ensured that the model remains accurate while avoiding the risks associated with overfitting, enabling more reliable predictions for real-world data.

5.3.4. Prediction Accuracy

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.

Our neural network model was able to achieve an overall accuracy of 85.7% (SD = 1.2%) on the test set in predicting shot outcomes (hit/miss) across the five 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.

5.3.5. Model Performance Across Shot Types

The model’s performance varied across different shot types, as shown in Table 5. 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.

5.3.6. ROC Curve Analysis

To dig deeper into our model’s capabilities, we plotted an ROC curve and calculated its AUC (please refer to Figure 3). 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 evaluates our binary classification model’s performance in predicting shot accuracy. It illustrates our model’s ability (orange line) to discriminate between successful and unsuccessful shots compared to random classification (dashed blue line, AUC = 0.5). With an AUC of 0.823, our model demonstrates strong discriminative ability, correctly ranking successful shots higher than unsuccessful ones 82.3% of the time when comparing random pairs. The curve’s sharp upward trajectory towards the top left corner indicates a favorable balance between true positive and false positive rates across various classification thresholds. This top-left movement signifies high true positive rates with low false positive rates, which is desirable. While this performance surpasses random guessing, it also suggests potential for further optimization. For context, an AUC of 1 would indicate a perfect classifier, represented by a curve that reaches the top left corner.

5.3.7. 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 features.

Figure 4 shows that 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, though 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.

The use of SHAP values in our analysis offers an innovative way to interpret complex neural network models in sports science by quantifying the relative importance of each feature. This approach provides valuable insights into the factors driving shot accuracy, enhancing the interpretability of our model—an essential aspect for training players. The SHAP analysis highlights QE duration and onset as the most significant predictors of shot accuracy, followed by biomechanical factors like racket speed and wrist angle at impact. This hierarchy of feature importance serves as a roadmap for targeted training interventions and technique refinement in badminton.

5.3.8. 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 5.

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.
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.
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.

5.3.9. 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:

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.
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.
Fine-tuning Phase (Epochs 50–95):
- The improvement rate further slows down for both losses.
- 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.
Fluctuations:
- 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.

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 Results and Analysis

Building on the SHAP analysis mentioned in Section 4.6.3., 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 an increased likelihood of successful shots.

5.5. Qualitative Insights

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

Conscious vs. Unconscious Gaze Control: Elite players reported more automatic gaze behaviors, while novices described consciously trying to focus their gaze.
Anticipation and Decision Making: Elite and intermediate players emphasized the importance of early information pick-up for shot selection and anticipation.
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).
The pink shaded region highlights the high variability in performance among novice players, showing a wide spread in both QE duration (100–250 ms) and shot accuracy (30–60%).
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 and 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 and 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 is 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. Discussion

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.

6.1. Innovative Aspects and Contributions

Our research extends beyond traditional applications of neural networks in sports science, offering several novel contributions to the field:

Multimodal Data Integration: Our model uniquely combines QE metrics with biomechanical data, providing a more comprehensive analysis of badminton performance. This integration captures complex interactions between visual attention and physical execution that were previously unexplored in racket sports.
Real-time Predictive Modeling: To our knowledge, this is the first study to develop a neural network model capable of real-time shot accuracy prediction in badminton using QE metrics. This capability goes beyond verifying QE’s importance to provide actionable, in-moment insights for players and coaches.
Advanced Interpretability Techniques: By employing SHAP (SHapley Additive exPlanations) values, we offer unprecedented insights into the relative importance of different QE and biomechanical features in badminton performance. This approach enhances the interpretability of our complex neural network model, making it more accessible and applicable for sports scientists and coaches.
Adaptive Learning Potential: The architecture of our model allows for continuous learning and adaptation to individual players’ patterns. This opens new avenues for developing personalized training regimens in badminton, potentially revolutionizing how players are coached and how they improve their skills.
Cross-skill Level Analysis: By applying our neural network model across different skill levels, we establish how the relationship between QE, biomechanics, and performance changes with expertise. This provides us with a nuanced understanding of how badminton players develop their visual and motor skills. Unlike earlier studies, our findings shed new light on the intricate process of players coordinating what they see as they move around the court.

6.2. Interpretation of Key Findings

Our results highlight several important insights:

The strong predictive power of QE duration and fixation points in determining shot accuracy underscores the importance of visual attention strategies in badminton performance.
Elite players exhibited significantly longer QE durations (M = 289.5 ms) compared to intermediate (M = 213.7 ms) and novice players (M = 168.3 ms), supporting QE as a marker of expertise.
The strong positive correlation (r = 0.72) between QE duration and shot accuracy across all skill levels suggests that QE training could benefit players at various stages of development.
The varying performance of our model across different shot types (smashes: 89.2%, drops: 84.5%, clears: 83.4%) indicates that QE strategies may need to be tailored to specific shot requirements.

6.3. Implications for Badminton Training and Performance

These findings have significant implications for badminton training and performance evaluation:

QE-based Training Programs: Our results suggest that incorporating QE training into existing programs could significantly enhance players’ shot accuracy.
Real-time Feedback Systems: The real-time capabilities of our model open up possibilities for immediate performance feedback during training and competitions.
Personalized Coaching: 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.

6.4. Limitations and Future Directions

While our study provides valuable insights, several limitations should be considered:

Laboratory Setting: The controlled environment may not fully replicate the complexity of actual match conditions. Future studies should validate these findings in competitive scenarios.
Sample Size: While adequate for our analyses, the sample size may limit generalizability. Larger-scale studies across diverse populations would further validate our findings.
Cross-sectional Design: Our study provides a snapshot of QE behaviors but does not capture how these might change over time or with training. Longitudinal studies are needed to understand the causal relationships between QE training, skill development, and performance improvements.

Future research directions include:

Exploring the temporal dynamics of QE during actual matches to understand how it adapts to varying game situations.
Developing and testing real-time feedback systems based on our predictive model.
Investigating the potential transfer of QE training effects to other racket sports.
Integrating additional physiological and psychological measures to create a more comprehensive model of badminton performance.

7. Conclusions

This study successfully demonstrates that the integration of Quiet Eye metrics and biomechanical data into a neural network model can effectively predict shot accuracy in badminton. The model’s high accuracy, combined with its ability to generate near real-time predictions, highlights its potential utility in sports analytics and training applications.

Supplementary Materials

The following supporting information can be downloaded at: https://www.mdpi.com/article/10.3390/app14219906/s1.

Author Contributions

Conceptualization, S.T. and T.T.T.; methodology, S.T. and T.T.T.; software, S.T.; validation, S.T. and T.T.T.; formal analysis, S.T. and T.T.T.; investigation, S.T. and T.T.T.; resources, S.T. and T.T.T.; data curation, S.T. and T.T.T.; writing—original draft preparation, S.T.; writing—review and editing, S.T. and T.T.T.; visualization, S.T. and T.T.T.; supervision, T.T.T.; project administration, S.T.; funding acquisition, S.T. and T.T.T. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

The study was conducted in accordance with the Declaration of Helsinki, and approved by The Victoria University Human Research Ethics Committee (VUHREC) (protocol code HRETH 24/287 on 9 February 2024).

Informed Consent Statement

Informed consent was obtained from all subjects involved in the study.

Data Availability Statement

The original contributions presented in the study are included in the article and Supplementary Materials, further inquiries can be directed to the corresponding author.

Conflicts of Interest

Authors Samson Tan and Teik Toe Teoh were employed by the company Staarch Pte Ltd. All authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Appendix A

Appendix A.1. Python Code for the Experiment

Below is the Python Version 3.10 code to create and train a neural network model to predict shot accuracy based on QE metrics.

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import accuracy_score, precision_score, recall_score, f1_score
import tensorflow as tf
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense

# Load dataset (replace 'qe_data.csv' with actual dataset)
data = pd.read_csv('qe_data.csv')

# Feature columns: QE metrics and biomechanical data
X = data[['QE_duration', 'fixation_point_x', 'fixation_point_y', 'saccades', 'body_posture', 'shuttlecock_trajectory']]
y = data['shot_accuracy'] # Binary target: 1 for hit, 0 for miss

# Train-test split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Standardize the data
scaler = StandardScaler()
X_train = scaler.fit_transform(X_train)
X_test = scaler.transform(X_test)

# Define the neural network model
model = Sequential([
Dense(64, input_dim=X_train.shape[1], activation='relu'),
Dense(32, activation='relu'),
Dense(16, activation='relu'),
Dense(1, activation='sigmoid') # Binary classification
])

# Compile the model
model.compile(optimizer='adam', loss='binary_crossentropy', metrics=['accuracy'])

# Train the model
history = model.fit(X_train, y_train, epochs=100, validation_data=(X_test, y_test), batch_size=32, verbose=1)

# Predict on test data
y_pred = (model.predict(X_test) > 0.5).astype("int32")

# Evaluate the model
accuracy = accuracy_score(y_test, y_pred)
precision = precision_score(y_test, y_pred)
recall = recall_score(y_test, y_pred)
f1 = f1_score(y_test, y_pred)

print(f"Accuracy: {accuracy}")
print(f"Precision: {precision}")
print(f"Recall: {recall}")
print(f"F1 Score: {f1}")

# Plot training and validation loss
import matplotlib.pyplot as plt

plt.plot(history.history['loss'], label='Training Loss')
plt.plot(history.history['val_loss'], label='Validation Loss')
plt.title('Model Loss')
plt.ylabel('Loss')
plt.xlabel('Epoch')
plt.legend(loc='upper right')
plt.show()

Appendix A.2. Explanation

Dataset: The dataset includes QE metrics and biomechanical data such as QE duration, fixation points, saccades, body posture, and shuttlecock trajectory. The target variable is shot accuracy (1 for a hit, 0 for a miss).
Model: A neural network with three hidden layers is trained to predict shot accuracy. The output layer uses a sigmoid activation function for binary classification.
Evaluation: After training, the model’s accuracy, precision, recall, and F1-score are computed. The results provide an overview of the model’s predictive performance.
Visualization: The training and validation loss curves are plotted to evaluate the model’s performance over the epochs.

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Figure 1. Schematic diagram of the Neural Network Architecture developed in this study.

Figure 2. Training and validation loss.

Figure 3. ROC curve.

Figure 4. SHAP summary plot.

Figure 5. Learning curves.

Figure 6. SHAP dependency plot for QE duration and racket speed.

Figure 7. Scatter plot of QE duration vs. shot accuracy.

Table 1. Key demographic characteristics of participants.

ID	Gender	Age	Experience (Years)	Skill Level	Occupation/Status
N1	Male	22	1.5	Novice	University Student
N2	Female	19	1	Novice	Part-time Tutor
N3	Male	25	2	Novice	IT Professional
N4	Female	30	1.5	Novice	Marketing Executive
N5	Male	18	1	Novice	Junior College Student
N6	Female	27	2	Novice	Nurse
N7	Male	35	1	Novice	Business Owner
N8	Female	21	1.5	Novice	University Student
N9	Male	29	2	Novice	Graphic Designer
N10	Female	24	1	Novice	Primary School Teacher
I1	Male	28	4	Intermediate	Software Engineer
I2	Female	32	3	Intermediate	Accountant
I3	Male	23	5	Intermediate	Physical Education Trainee
I4	Female	26	3.5	Intermediate	Interior designer
I5	Male	31	4	Intermediate	Sales Manager
I6	Female	29	3	Intermediate	Journalist
I7	Male	35	5	Intermediate	Lawyer
I8	Female	24	4	Intermediate	Banker
I9	Male	27	3.5	Intermediate	Bank Teller
I10	Female	33	4.5	Intermediate	Accountant
E1	Male	26	8	Elite	Primary School Teacher
E2	Female	24	7	Elite	Sports Club Player
E3	Male	29	10	Elite	Badminton Coach
E4	Female	22	6	Elite	Sports Science Student
E5	Male	31	12	Elite	Former National Player
E6	Female	27	9	Elite	Semi-Professional Player
E7	Male	25	8	Elite	Physical Trainer
E8	Female	30	11	Elite	Badminton sports shop owner
E9	Male	28	9	Elite	Sports Journalist
E10	Female	23	7	Elite	National Team Trainee

Table 2. Summary of participant demographics.

Skill Level	Age Range (Years)	Experience Range	Notable Characteristics
Novice	18–35	1 to 2 years	University students, young professionals
Intermediate	23–35	3 to 5 years	Diverse professional backgrounds
Elite	22–31	6 to 12 years	National team members, professional players

Table 3. Quiet Eye characteristics across skill levels.

Skill Level	QE Duration (ms)	QE Onset (ms before Impact)
Elite	289.5 ± 34.2	−385.2 ± 52.1
Intermediate	213.7 ± 41.5	−298.6 ± 63.4
Novice	168.3 ± 38.9	−215.4 ± 71.8

Table 4. Correlation matrix of key variables.

Variable	1	2	3	4	5
1. Shot Accuracy	1
2. QE Duration	0.72 *	1
3. QE Onset	−0.58 *	−0.43 *	1
4. Racket Speed	0.61 *	0.39 *	−0.28	1
5. Wrist Angle	0.47 *	0.31	−0.19	0.35 *	1

* p < 0.001.

Table 5. Multiple regression analysis for shot accuracy.

Predictor	β	SE	t	p-Value
QE Duration	0.45	0.08	5.62	<0.001
QE Onset	−0.21	0.09	−2.33	0.028
Racket Speed	0.32	0.11	2.91	0.008
Wrist Angle	0.18	0.1	1.8	0.084

R² = 0.68, F(4,25) = 13.25, p < 0.001.

Table 6. Neural network model performance.

Metric	Overall	Smashes	Drops	Clears
Accuracy	85.70%	89.20%	84.50%	83.40%
Precision	88.30%	91.50%	86.20%	85.70%
Recall	83.10%	87.30%	82.90%	81.20%
F1 Score	0.856	0.893	0.845	0.834

Table 7. Ablation study results.

Feature Set	Accuracy	Precision	Recall	F1 Score
QE metrics only	79.30%	82.10%	76.50%	0.792
Biomechanical features only	77.80%	80.60%	75.00%	0.777
All features (full model)	85.70%	88.30%	83.10%	0.856

Table 8. Learning curve data.

Epoch	Training Loss	Validation Loss
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	0.200	0.290
35	0.185	0.270
40	0.170	0.250
45	0.155	0.230
50	0.140	0.210
55	0.130	0.200
60	0.120	0.190
65	0.110	0.185
70	0.100	0.180
75	0.095	0.175
80	0.090	0.170
85	0.088	0.165
90	0.085	0.160
95	0.083	0.155
100	0.231	0.258

Table 9. Feature importance (SHAP values).

Feature	SHAP Value
QE Duration	0.385
Racket Speed at Impact	0.312
QE Onset	0.287
Wrist Angle at Impact	0.245
Shuttlecock Trajectory Angle	0.198
Body Posture (Trunk Rotation)	0.173

Table 10. Quiet Eye duration by shot type and skill level.

Skill Level	Smashes (ms)	Drops (ms)	Clears (ms)
Elite	301.2 ± 38.7	286.5 ± 35.9	280.8 ± 33.4
Intermediate	225.4 ± 44.3	209.8 ± 40.2	205.9 ± 42.6
Novice	172.6 ± 41.5	168.9 ± 39.7	163.4 ± 37.8

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Tan, S.; Teoh, T.T. Predicting Shot Accuracy in Badminton Using Quiet Eye Metrics and Neural Networks. Appl. Sci. 2024, 14, 9906. https://doi.org/10.3390/app14219906

AMA Style

Tan S, Teoh TT. Predicting Shot Accuracy in Badminton Using Quiet Eye Metrics and Neural Networks. Applied Sciences. 2024; 14(21):9906. https://doi.org/10.3390/app14219906

Chicago/Turabian Style

Tan, Samson, and Teik Toe Teoh. 2024. "Predicting Shot Accuracy in Badminton Using Quiet Eye Metrics and Neural Networks" Applied Sciences 14, no. 21: 9906. https://doi.org/10.3390/app14219906

APA Style

Tan, S., & Teoh, T. T. (2024). Predicting Shot Accuracy in Badminton Using Quiet Eye Metrics and Neural Networks. Applied Sciences, 14(21), 9906. https://doi.org/10.3390/app14219906

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

Abstract

1. Introduction

2. Related Work

2.1. The Quiet Eye in Sports Performance

2.2. Machine Learning in Sports Performance Prediction

2.3. Integration of QE with Biomechanical Data

2.4. Quiet Eye and Cognitive-Motor Performance

2.5. Application of Machine Learning in Badminton

2.6. Predictive Modeling of Shot Accuracy in Badminton

2.7. Future Directions and Research Gaps

3. Research Gaps Addressed by This Study

3.1. Limited QE Research in Badminton

3.2. Integration of QE Metrics with Biomechanical Data

3.3. Application of Neural Networks to QE Data

3.4. Real-Time Analysis and Feedback

3.5. Individual Differences in QE Characteristics

3.6. QE in Dynamic, Interactive Sports

3.7. Predictive Modeling of Shot Accuracy

3.8. Summary of Contributions

4. Methodology

4.1. Study Design

4.2. Participants

4.3. Data Collection

4.3.1. Eye-Tracking Equipment and Measures

4.3.2. Biomechanical Measurements and Equipment

4.3.3. Performance Measure

4.3.4. Dataset Structure and Feature Extraction

4.4. Experimental Procedure

4.4.1. Warm-Up

4.4.2. Calibration

4.4.3. Task

4.4.4. Rest Periods

4.4.5. Post-Experiment Interview

4.4.6. Real-World Testing and Prediction Latency

4.4.7. Real-Time Performance Analysis

4.5. Data Preprocessing

4.5.1. Eye-Tracking Data Preprocessing

4.5.2. Biomechanical Data Processing

4.6. Neural Network Model

4.6.1. Neural Network Base Architecture

4.6.2. Model Training

4.6.3. Feature Importance Methodology

4.7. Statistical Analysis

4.8. Qualitative Analysis

4.9. Limitations

5. Results

5.1. Quiet Eye Characteristics Across Skill Levels

5.1.1. Quiet Eye Duration

5.1.2. Quiet Eye Onset

5.2. Relationship Between Quiet Eye and Shot Accuracy

5.2.1. Correlation Analysis

5.2.2. Multiple Regression Analysis

5.3. Neural Network Model Performance

5.3.1. Neural Network Training Architecture

5.3.2. Training Process

5.3.3. Epoch Selection for Model Training Cutoff

5.3.4. Prediction Accuracy

5.3.5. Model Performance Across Shot Types

5.3.6. ROC Curve Analysis

5.3.7. Feature Importance

QE_Duration (Quiet Eye Duration)

QE Onset

Racket_Speed

Elbow_Angle, Shoulder_Rotation, and Wrist_Angle

Key Observations

5.3.8. Ablation Study

5.3.9. Learning Curves

5.4. Feature Importance Results and Analysis

5.5. Qualitative Insights

5.6. Individual Differences in Quiet Eye Strategies

5.7. Effect of Shot Type on Quiet Eye Behavior

5.8. Analysis and Insights from Performance Metrics

5.8.1. Accuracy

5.8.2. Precision vs. Recall

5.8.3. F1 Score

5.8.4. New Insights

Quiet Eye Metrics as Strong Predictors

5.8.5. Precision-Focused Training for Elite Athletes