The mean Huber score is defined by:
$$S(\textbf{\textit{x}}, \textbf{\textit{y}}, a) := (1/n)
\sum_{i = 1}^{n} L(x_i, y_i, a)$$
where
$$\textbf{\textit{x}} = (x_1, ..., x_n)^\mathsf{T}$$
$$\textbf{\textit{y}} = (y_1, ..., y_n)^\mathsf{T}$$
and
$$
L(x, y, a) := \left\{
\begin{array}{ll}
\dfrac{1}{2} (x - y)^2, & |x - y| \leq a\\
a |x - y| - \dfrac{1}{2} a^2, & |x - y| > a
\end{array}
\right.
$$
Domain of function:
$$\textbf{\textit{x}} \in \mathbb{R}^n$$
$$\textbf{\textit{y}} \in \mathbb{R}^n$$
$$a > 0$$
Range of function:
$$S(\textbf{\textit{x}}, \textbf{\textit{y}}, a) \geq 0,
\forall \textbf{\textit{x}}, \textbf{\textit{y}} \in \mathbb{R}^n, a > 0$$