  The key point to prove the optimal $C^{1,\frac12}$ regularity of the thin
obstacle problem is that the frequency at a point of the free boundary
$x_0\in\Gamma(u)$, say $N^{x_0}(0^+,u)$, satisfies the lower bound
$N^{x_0}(0^+,u)\ge\frac32$.
  In this paper we show an alternative method to prove this estimate, using an
epiperimetric inequality for negative energies $W_\frac32$. It allows to say
that there are not $\lambda-$homogeneous global solutions with $\lambda\in
(1,\frac32)$, and by this frequancy gap, we obtain the desired lower bound,
thus a new self contained proof of the optimal regularity.
