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This is an theorical question, so, I am looking for the point in a ROC Curve. And I got the idea, that different curves has different best point. So, I try to identify those points.

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For the yellow one, the best point of a 'receiver operating characteristic' (ROC) curve is: Top left corner. (0,1)

For the bright purple one, the best point of a 'receiver operating characteristic' (ROC) curve is: The best point is (0.3; 0.8)

For the blue one, the best point of a 'receiver operating characteristic' (ROC) curve is: (0.5;0.5)

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  • $\begingroup$ Your suggested points aren't necessarily the best, it depends on the value/cost of TP/FP/TN/FN. towardsdatascience.com/… $\endgroup$
    – Ben Reiniger
    Nov 17, 2021 at 17:01

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A ROC curve is not really suitable for choosing a "best point", on the contrary it's meant to show the performance independently from any particular threshold.

Additionally this raises the question of how does one formally define what is a "best point". If the goal is to maximize both precision and recall, then it makes more sense to pick the threshold which gives the maximum F1-score.

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    $\begingroup$ Or to be more flexible you can introduce some business reasons and find an $F_\beta$ for whatever $\beta$ makes sense. $\endgroup$
    – rapaio
    Nov 17, 2021 at 17:14

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