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    $\begingroup$ Very nice, +1. If we use probabilistic class membership predictions $0\leq \hat{y}\leq 1$, then calculate $R^2$ straightforwardly, then it's the ratio between the Brier scores of the focal model and an "overall average" model. $\endgroup$ Commented Feb 15, 2023 at 7:21
  • $\begingroup$ @StephanKolassa The UCLA page mentions that one as Efron’s $R^2$. // It turns out that my $R^2_{accuracy}$ was hiding in plain sight this whole time as UCLA’s adjusted count! $\endgroup$ Commented Feb 18, 2023 at 15:21
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    $\begingroup$ +1. I'm very sure you can derive this identity starting from likelihood ratios of Dirac deltas, one for the model being investigated, another for a constant model. In the case of the Dirac likelihood, the constant parameter that minimizes the loss is the majority class. $\endgroup$ Commented Sep 7, 2023 at 11:46