# Analysis of Bullet Impact Locations in the 10 m Air Pistol Men's Competition Based on Covariance
## 5 Discussion
### Rankings and Feature Indicator Correlation  
The correlation between the x-variance, representing the distribution in the left-right direction, and the ranking showed a weak positive trend with an R-squared value of 0.1549. This indicates that as the ranking decreases, the shot patterns in the left-right direction tend to widen, suggesting a decrease in stability. It also implies that improving the aiming precision in the left-right direction becomes crucial as the ranking decreases. We found that the accuracy of shooting athletes is mainly affected by the sway in the anterior-posterior direction. Thus, reducing the sway in the anterior-posterior direction is essential for improving shooting accuracy [22]. The correlation between the y-variance, representing the distribution in the up-down direction, and the ranking showed a weak positive trend with an R-squared value of 0.1866. This indicates that athletes with lower rankings may exhibit wider shot patterns in the up-down direction, suggesting a need for improving the accuracy of up-down aiming, particularly for athletes with lower rankings. In shooting, there is a tendency for aiming in the horizontal and vertical directions to change together or in opposite directions. This interaction can be assessed through covariance, and in this study, the covariance between the horizontal direction (x) and the vertical direction (y) was analyzed to examine its correlation with rankings. When covariance is positive, it indicates a tendency for aiming in both horizontal and vertical directions to increase or decrease together. This suggests that the aiming in both directions interacts with each other and influences the shooting pattern. In cases where this tendency is observed, focusing on maintaining balance between aiming in both directions is necessary to enhance aiming stability. On the other hand, when the covariance is negative, it indicates that when the horizontal direction increases, the vertical direction decreases, or vice versa. This suggests that aiming in both directions may interact in opposite directions, leading to a higher possibilityof aiming instability. Players exhibiting such patterns may require training and strategies to enhance the consistency of their aiming. Examining the correlation between covariance and ranking, the R-squared value of 0.0178 was observed for the absolute value of covariance. This indicates a weak positive trend, suggesting that the interaction between horizontal and vertical aiming may have a slight influence on ranking. It implies that maintaining a balance between aiming in both directions can positively impact shooting performance. Analysis of the average position in the horizontal direction provides insight into the accuracy and consistency of horizontal aiming. The average position indicates how far the shots deviate from the horizontal center of the target. The correlation between ranking and the average position in the horizontal direction showed an R-squared value of 0.0048, indicating no significant correlation. This suggests that the average position in the horizontal direction does not directly influence ranking. Analysis of the average position in the vertical direction allows understanding of the accuracy and consistency of vertical aiming. The average position indicates how far the shots deviate from the vertical center of the target. The correlation between ranking and the average position in the vertical direction showed an R-squared value of 0.0809, indicating a weak positive trend. This implies that players with lower rankings tend to deviate more from the vertical center. The precision of the bullet impact locations can be determined through the root mean square error (RMSE). The RMSE represents the distance between the bullet impact locations and the center position, with smaller values indicating a more precise shooting pattern. The correlation between ranking and RMSE showed an R-squared value of 0.0808, indicating a weak positive trend.