## 2 Materials and Methods
### Statistical Analyses
#### 2.5.6. Prognostic Validity of the Analyses  
Prognostic validity can be determined by the theoretical accuracy (sensitivity and specificity) of the performance forecasts of the various prediction methods. For all calculations of the parameters of the analysis methods, only the classification results of the corresponding hold-outs were used. Table 2 represents a typical example of a 2 \(\times\) 2 classification table. Variable A corresponds to true-positive predictions, B to false-positive predictions, C to false-negative predictions, and D to true-negative predictions. Sensitivity (recall; Formula (2)) indicates how many top performers (A = true positives) from the observed group (A + C = 16) were correctly predicted. For example, if twelve top performers were correctly identified/classified as top performers, the sensitivity is 75%. The specificity (Formula (3)) represents the percentage of correctly predicted low performers (D = true negatives) in the group of low performers (B + D). \[\text{Sensitivity}=\frac{\text{A}}{\text{A}+\text{C}} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & \multicolumn{3}{c}{**Predicted/Recommended**} \\ \cline{3-5}  & & **Low** & **Top** & \\  & & **Performer** & **Performer** & \(\Sigma\) \\ \hline \multirow{2}{*}{Observed/Existing} & Top Performer & C & A & A + C \\  & Low Performer & D & B & B + D \\ \hline \multirow{2}{*}{Observed/Existing} & \(\sum\) & C + D & A + B & A + B + C + D \\ \cline{2-5}  & & & & \\ \end{tabular}
\end{table} 
Table 2: Example for sensitivity and specificity calculation. Figure 1: Example of a Neural Network (Multilayer Perceptron). \[\text{Specificity}=\frac{\text{D}}{\text{B}+\text{D}} \tag{3}\]  
Furthermore, the positive and negative predictive values (Formulas (4) and (5)) of the predictions were determined (positive predictive value = precision). These two parameters indicate the probability of actually living out a corresponding forecast. It therefore corresponds to the percentage of predictions that actually occurred. \[\text{Positive Predictive Value}=\frac{\text{A}}{\text{A}+\text{B}} \tag{4}\]  
\[\text{Negativ Predictive Value}=\frac{\text{D}}{\text{C}+\text{D}} \tag{5}\]  
In general, the hit rate is the percentage of correctly predicted recommendations. Accordingly, the true-positive predictions (A) and the true-negative predictions (B) are added together and divided by the total sample size (Formula (6)). To calculate the random hit rate (Formula (8)), the selection rate (S) is needed. The selection rate is the percentage of top performer recommendations among all recommendations (Formula (7)). It is determined in advance or via the analysis types. Using the selection rate, the random hit rate (Formula (8)) can now be determined. For this purpose, the selection rate (S) is multiplied by the number of existing top performers (A + C). This calculates the number of correct top performer recommendations in a random draw from the group of top performers. In addition, the number of correct low performer recommendations in a random draw from the group of low performers (B + D) is also determined. This is done using the counter-probability of the selection probability (1 - S). Both values are then summed and divided by the total sample size to obtain the random hit rate. The maximum hit rate can  
The calculated value varies, usually in the range \(0<x_{RIOC}\leq 1\), but it can also have negative values. With a value of \(x_{RIOC}=0.33\), the classification is considered good. Above 0.66 is considered very good [53]. Using this calculation scheme, the four methods can be directly compared and evaluated independent of their actual selection rates. The real selection rate for talent diagnostics and, thus, also the maximum hit rate, always depends on the talent campaigns and support programs of the participating countries, and therefore, this selection rate can vary considerably in practice. The Youden Index \(J\) (also _Youden's_ J) was determined as a further comparative value (Formula (11)).