Bayes Risk under 0–1 Loss

Let $\eta(x) = \mathbb{P}(Y = 1 \mid X = x) \in [0, 1]$, with labels in $\{-1, +1\}$ and the 0–1 loss. Let $f^\star$ be the Bayes classifier.

Which expression equals the Bayes risk $L^\star = L(f^\star)$?