## 5 In the Search for a Missing Link
### Outcome Predictions
#### 5.3.6 Scenario #6: Selected Number of Chasers, Cash Builder Result, and Time Advantage  
In the last scenario we report in this paper, we decided to combine the previous two scenarios and use the selected number of chasers, the cash builder result, and the chasers' time in the selected offer for game's outcome prediction. The previous two scenarios showed promising results, which led us to investigate how these three features would work when combined but without any other information.  
Table 17 gives an overview of the results. As many as six different models reached an F1-score of higher than 72%, while the voting classifier and neural network exceeded an F1-score of 82%. The neural network had higher precision, but the voting classifier had higher accuracy, recall, and a slightly higher F1-score. It used three _hard_ voting models: (1) a kNN model (\(k=1\), \(p=1\)), (2) an RF (27 estimators), and (3) an MNB classifier. The same parameters were used for the independently trained and tested kNN and RF, which results are also reported in Table 17. For XGBoost, we used 73 estimators and \(lr=1.0\). The neural network's architecture remained the same as that in the previous scenario, but we used a batch size of 16 in this case. The optimal performance was reached after 104 epochs. It is important to note that all the mentioned methods (the voting classifier, kNN model, RF, and neural network), alongside the GNB classifier, had a high precision score. As can be seen in the table, pruning the DT (\(ccp\_alpha=0.003\)) did not lead to any performance degradation, but in contrast to the full DT, it performed better in the oversampled dataset.  
In this scenario, the DT, pruned DT, and RF ranked the cash builder result as the most important feature, followed by the chasers' time in the selected offer, and, ultimately, the selected number of chasers. The model with the highest performance after the voting classifier (the neural network) identified the selected number of chasers as the most important feature, and the cash builder result as the least important one. As in the previous scenarios,  
Figure 11: Features’ impacts on the neural network model’s outputs for the outcome prediction based on the selected number of chasers and the chasers’ time in the selected offer.  
for all models except for the neural network, a higher cash builder result decreased the model's output, while a lower one increased it. As seen in Figure 12, in the case of the neural network, mid-range values for the cash builder result pushed the model toward a positive prediction, while high and low values shifted the model toward predicting the negative outcome for the contestant, just as in scenario #4. A lower selected number of chasers increased the outputs of all the tested models. Although, in the majority of the models, a higher value for the chasers' time in the selected offer led to a decrease in the output, in the neural network, a higher value for this feature favored the contestants by increasing the model's output.  
Observing the results, we can conclude that introducing the cash builder result to the combination of the selected number of chasers and the chasers' time in the selected offer led to an overall improvement in the model's results. Although the best-performing option remained the neural network that predicted the outcome based on the selected number of chasers and their time, the information about the cash builder results boosted the performance of the other tested methods. On average, the best results were obtained when using these three features.