## 3 Handling Our Dataset
### Feature Summary and Correlations  
In summary, this section presents a comprehensive overview of the features included in our dataset, which were collected using the three methods discussed above. Table 2 shows a comprehensive summary of all features included in the analysis, detailing both descriptions and their correlation coefficients represent the average of the two target variables, \(xGg\) and \(aGg\). The table highlights the various features and their correlations, demonstrating their influence on the model's predictions. Features 1 to 14 were collected using a heatmap, with their respective correlation values directly related to this method. For instance, the _goals_ feature shows a strong correlation of 0.85, indicating its significant impact on evaluating player performance. Similarly, \(xG\)has a high correlation of 0.91, underscoring its essential role in outcome prediction. Other notable features from this group include _shots_ with a correlation of 0.80, playing a crucial role in the model. Conversely, the remaining features, from 15 to 27, were developed through feature engineering, and their correlation values with the target variable are also included in the table. For example, _gpm_ (goals per minute) and _sbm_ (shots per minute) have correlations of 0.54 and 0.53, respectively, offering valuable context by capturing different aspects of gameplay. Additionally, _league_weight_ and _position_weight_ exhibit moderate correlations of 0.55 each. While these features may have lower individual importance, they enhance the model by providing supplementary insights that, when combined with other metrics, improve overall predictive accuracy. This table categorizes the model's variables into input and input and target features. Input features reflect a player's past performance, capturing historical data as foundational information. Input and target features, however, combine historical data with predictive relevance, directly contributing to the model's target outcomes. Metrics like \(aGg\) and \(xGg\) not only summarize past achievements but also enhance predictions, making them essential for performance evaluation and forecasting. Moreover, Table 3 illustrates the feature importance for both \(xGg\) and \(aGg\). This table provides a detailed comparison of how different features contribute to the predictions of \(xGg\) (expected goals per game) and \(aGg\) (actual goals per game). To determine feature importance, we employed SHAP (SHapley Additive exPlanations) values, which provide an in-depth understanding of how different features influence the model's predictions. In the context of \(xGg\), the most influential features include \(aGg\) (goals per game) and _gpm_ (goals per minute), which contribute 33.82% and 33.31% to the model, respectively. Other significant features are _shpg_ (shots per game) with 6.43%, and _apg_ (assists per game) with 4.91%. These features indicate that scoring efficiency and shooting metrics are critical for predicting expected goals per game. Conversely, for \(aGg\), the most impactful feature is \(xGg\) (expected goals per game), which has a dominant importance of 60.61%. This suggests that the expected goals metric is highly predictive of the actual goals scored. Other important features for \(aGg\) include _gpm_ (goals per minute) with 10.90%, and _sbm_ (shots per minute) with 10.46%. These contributions highlight the relevance of shooting metrics and goals efficiency in predicting actual goals per game. While some features, such as \(xG\)_chainind_\(xG\)_Buildup_ show relatively low importance percentages (below 1% for \(xGg\) and below 0.5% for \(aGg\)), they still play a role in the overall model. For instance, features like \(xG\)_chain_ and \(xG\)_Buildup_ capture aspects of play that, despite their smaller individual impact, can affect the prediction accuracy when combined with other features. Table 4 presents a comprehensive overview of player performance metrics, offering valuable insights into the intricate dynamics of soccer.