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It has been stated in many places that AUROC is an improper scoring rule.But I haven't seen anyone proving it. Does someone have a working example that shows that maximizing AUROC actually moves away probability estimates from actual probabilities.

J.doe
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    [Gneiting & Vogel (2018, arXiv:1809.04808)](https://arxiv.org/abs/1809.04808), in their footnote 4 note that AUC ignores calibration, referring to p. 346 in Wilks (2011), *Statistical Methods in the Atmospheric Sciences*. – Stephan Kolassa Sep 20 '19 at 20:27
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    Take a look at [Byrne (2016)](https://projecteuclid.org/euclid.ejs/1455715967), as cited in [this answer to the proposed duplicate](https://stats.stackexchange.com/a/339993/1352). – Stephan Kolassa Sep 20 '19 at 20:32

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