@e-pet commented on different PRs & issues some interesting fact. I take the opportunity to consolidate some of those comments here.

First, we use the term "chance" that is ambiguous depending of the displays. The term "baseline" would probably be better. In addition, I checked and I think we should make an extra effort on the definition of the baseline for each of the type of plot: for ROC curve, the baseline is "a random classifier assigning the positive class with probability p and the negative class with probability 1 − p" [1] while for the PR curve, the baseline is derived from the "always-positive classifier" where any recall or precision under π should be discarded [1].

It leads to a second where in the PR curve, we plot the horizontal line derived from the always-positive classifier but we don't discard when recall < π. In this case, as mentioned by @e-pet, it might make sense to show the hyperbolic line of the always-positive classifier instead (cf. Fig. 2 in [1]).

@e-pet feel free to add any other points that you wanted to discuss. Here, I wanted to focus on the one that looks critical and could be addressed.

[1] Flach, P., & Kull, M. (2015). Precision-recall-gain curves: PR analysis done right. Advances in neural information processing systems, 28.