# Application of Machine Learning Models for Baseball Outcome Prediction
## 3 Result
### Feature Importance Analysis  
Figure 3 displays the feature importance rankings derived from the XGBoost model, with corresponding values presented in the accompanying table (Table 4). The most influential predictor is wRC+ (Weighted Runs Created Plus), with an importance value of 0.21, demonstrating its critical role in evaluating offensive contributions. The PLOB% (percentage of left-on-base runners) and wRAA (Weighted Runs Above Average) rank among the top features, reflecting their importance in measuring team efficiency in run production and prevention. Pitching metrics constitute several high-ranking features, including the WHIP (walks + hits per inning pitched), FIP (fielding independent pitching), H9 (hits per nine innings), and P_HR (percentage of home runs allowed). These results underscore the significance of limiting baserunners, hits, and home runs for game success. Traditional batting statistics--OPS (on-base plus slugging), OBP (on-base percentage), and AVG (batting average)--also demonstrate a considerable influence on predictions, confirming their continued relevance in modern baseball analytics. Lower-ranked features such as Strike Percentage (5%), K9 (strikeouts per nine innings), and B_H (total hits by  
Figure 2: AUC in different models. batters) showed a relatively minimal impact on model predictions. The analysis reveals that game outcomes are primarily driven by offensive efficiency metrics and pitching control variables, highlighting the fundamental importance of run creation and prevention in determining baseball game results. Figure 4 presents the SHAP summary plot, visualizing feature contributions to XGBoost model predictions for game outcomes. Each dot represents an individual game instance, with the color indicating the feature magnitude (red for higher values, blue for lower values). The \(x\)-axis displays SHAP values, quantifying each feature's contribution to predictions, where positive values increase the win probability and negative values decrease it. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rank** & **Feature** & **Importance** & **Rank** & **Feature** & **Importance** \\ \hline
1 & wRC+ & 0.21 & 20 & B BB & 0.01 \\
2 & PLOB\% & 0.11 & 21 & N\(\overline{\text{P}}\)/IP & 0.01 \\
3 & wRAA & 0.10 & 22 & BABIP & 0.01 \\
4 & WHIP & 0.06 & 23 & P\_BB & 0.01 \\
5 & wOBA & 0.05 & 24 & P\(\overline{\text{A}}\) & 0.01 \\
6 & H\(\bar{\text{p}}\) & 0.05 & 25 & B9 & 0.01 \\
7 & OPS & 0.05 & 26 & P\_H & 0.01 \\
8 & FIP & 0.04 & 27 & P\(\overline{\text{G}}\)/F & 0.01 \\
9 & P\_HR & 0.03 & 28 & SH & 0.01 \\
10 & OBP & 0.02 & 29 & IsoP & 0.01 \\
11 & AVG & 0.02 & 30 & G/F & 0.01 \\
12 & SF & 0.02 & 31 & AB & 0.01 \\
13 & B\_SO & 0.02 & 32 & 3B & 0.01 \\
14 & SLG & 0.02 & 33 & S\% & 0.01 \\
15 & P\_SO & 0.01 & 34 & Strike & 0.01 \\
16 & \(\overline{\text{B}}\) & 0.01 & 35 & K9 & 0.01 \\
17 & B\_HR & 0.01 & 36 & 2B & 0.00 \\
18 & BF & 0.01 & 37 & B\_H & 0.00 \\
19 & NP & 0.01 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Feature importance table. Figure 3: Feature importance analysis of XGBoost model. The PLOB% (left on base percentage) demonstrates the strongest influence, with higher values (red dots) generally producing positive SHAP contributions. The WHIP (walks and hits per inning pitched) and wRAA show substantial predictive significance, with a clear separation between high and low values driving predictions in opposite directions. The traditional metrics AVG and wRC+ emerge as influential predictors, where a superior performance typically generates positive SHAP values, confirming their positive impact on game outcomes. Conversely, features such as the B_BB (batting walks) and G/F (ground ball to fly ball ratio) exhibit minimal contributions, with SHAP values clustering near zero. This analysis confirms the relative importance of key performance metrics in determining game outcomes, providing quantitative insights into the statistical factors that drive model predictions.