## 5 In the Search for a Missing Link
### Outcome Predictions
#### 5.3.3 Scenario #3: Cash Builder Result and Offers  
After looking into the features' importances for the tree-based methods in Table 13, we decided to investigate whether it is possible to successfully predict the game's outcome based solely on the cash builder result, all the received offers, the selected offer, and the chasers who participated in the second phase. Table 14 shows the different models' performances after excluding the information about the contestant. We can notice that the models reacted differently to the absence of the contestant's profile information. Both the SVM (\(C=10\), \(gamma=1\)) and the voting classifier model underwent drops in their capabilities to predict the game's outcome successfully. The voting classifier (_soft_ voting) consisted of (1) a kNN model (\(k=3\), \(p=3\)), (2) XGBoost (77 estimators, \(lr=0.5\)), and (3) a GNB classifier. When used alone, the kNN method's (\(k=3\), \(p=1\)) F1-score slightly deteriorated, but its accuracy, precision, and recall improved by around 5%. The performances of the pruned DT (maximum tree depth = 2) and XGBoost (77 estimators, \(lr=0.5\)) methods remained unchanged. The models which performance increased were the LR, RF (162 estimators), and neural network. Like in the previously considered setup, the neural network was the most successful approach, predicting the game's outcome with an accuracy of 80.8%, a precision of 79.4%, a recall of 80.8%, and an F1-score of 79.9%. The only change in the network's architecture from those in the previous two cases was increasing the number of nodes in the first hidden layer from 32 to 64. The network reached the optimal performance in the validation dataset after only 12 epochs.  
When looking into the features' importances, the models with higher performances, such as the neural network, pruned DT, and RF, highlighted the prize money and chasers' time in the selected offer, alongside the participation of Chaser #4, as the most relevant features. Again, both the longer time and more prize money in the selected offer and the participation of Chaser #4 led the model toward predicting the negative outcome for the contestant. Simpler models (LR, SVM, and kNN) considered the cash builder result as one of the most important features, with lower values pushing the prediction in favor of the contestant.  
These results showed that the game's outcome was influenced more by the game-specific information than by the contestant's profile. The cash builder result, the chasers' time in the selected offer, and the selected number of chasers were the most relevant features for predicting the game's outcome. Nevertheless, these features were also indirectly influenced by the contestant. First, the cash builder results reflect some information about the contestants' quizzing abilities. Second, different contestants did not receive identical offers independently of their potentially equal performances in the cash builder.  
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Method** & **SMOTE** & **Accuracy** & **Precision** & **Recall** & **F1-Score** \\ \hline Logistic Regression & - & 0.71429 & 0.70238 & 0.71429 & 0.65306 \\ Support Vector & + & 0.62857 & 0.57767 & 0.62857 & 0.59147 \\ Machine & - & 0.71429 & 0.70238 & 0.71429 & 0.65306 \\
**Neural Network** & + & **0.80769** & **0.79371** & **0.80769** & **0.79924** \\ Pruned Decision Tree & + & 0.74286 & 0.72976 & 0.74286 & 0.73012 \\ Voting Classifier & - & 0.74286 & 0.72972 & 0.74286 & 0.71717 \\ Random Forest & + & 0.74286 & 0.72976 & 0.74286 & 0.73012 \\ XGBoost & - & 0.71429 & 0.69143 & 0.71429 & 0.67659 \\ \hline \hline \end{tabular}
\end{table}
Table 14: Outcome predictions based on the cash builder result, all the offers, and specific chasers within the selected offer.  
This suggests that the offers may have been tailored for a specific contestant, potentially influencing their selection.