Table 1 Numerical approximation of some landmark values of \((\text {TNR},\text {TPR})\) yielded by a high ROC AUC of 0.785, that approximates \(\pi /4\). For example, if TNR is 0.35, then TPR must be greater or equal to 0.670. Due to the symmetric nature of the necessary condition Eq. 9, the relation between the two rates \(\text {TNR}\) and \(\text {TPR}\) holds when swapped. \(TNR \ge 0.00\) means that TNR can have any value in the [0; 1] range and \(TPR \ge 0.00\) means that TPR can have any value [0; 1] range. Please notice that the half semicircle ROC represented by the blue line in Fig. 3b has AUC \(= \pi /4 \simeq 0.785\), but there are several other ROC curves with the same AUC

From: The Matthews correlation coefficient (MCC) should replace the ROC AUC as the standard metric for assessing binary classification