Summary: Let \((X, d)\) be a compact metric space and \(f : X \to X\), if \( X^{r}\) is the product of \(r\)-copies of \(X, r \geq 1\), and \(\Phi : {X}^{r} \to \mathbb R\) then the multifractal decomposition for \(V\)-statistics is given by \[ E_\Phi (\alpha)=\left\{x:\lim\limits_{n\to\infty}\frac{1}{n^r} \sum\limits_{0\leq i_1\leq\dots\leq i_r \leq n-1} \Phi (f^{i_1}(x), \dots, f^{i_r}(x))=\alpha \right\}. \] The irregular part, or historic set, of the spectrum is the set points \(x \in X\), for which the limit does not exist.{ }In this article we prove that for dynamical systems with specification, the irregular part of the \(V\) statistics spectrum has topological entropy equal to that of the whole space \( X\).