Let $(X_i, Y_i)_{i=1}^n$ be i.i.d. training data with $\mathbb{E}[Y_i^2] < \infty$, and let $\hat{T}_D : \mathbb{R}^p \to \mathbb{R}$ denote the regression tree fitted to data $D = (X_i, Y_i)_{i=1}^n$. Define $\bar{T}(x) := \mathbb{E}[\hat{T}_D(x)]$, where the expectation is over the randomness in the training data $D$, and let $R(f) := \mathbb{E}[(Y - f(X))^2]$ denote the risk of a predictor $f$. Then
\begin{align*}
\mathbb{E}[R(\hat{T}_D)] = \underbrace{\mathbb{E}[(\mathbb{E}[Y \mid X] - \bar{T}(X))^2]}_{\text{squared bias}} + \underbrace{\mathbb{E}[\operatorname{Var}(\hat{T}_D(X) \mid X)]}_{\text{variance}} + \underbrace{\mathbb{E}[\operatorname{Var}(Y \mid X)]}_{\text{irreducible}}.
\end{align*}