The authors consider the almost Mathieu operator \[ (H_{\lambda,\alpha,\theta}u)(n)= u(n+1)+ u(n- 1)+2\lambda\cos 2\pi(\alpha n+\theta)u(n) \] by its action on \(u \in\ell^2(\mathbb{Z})\). Here \(\lambda\neq0\) is the coupling, \(\alpha\in\mathbb{R}\backslash\mathbb{Q}\) is the frequency, and \(\theta\in\mathbb{R}\) is the phase. They prove that for supercritical almost Mathieu operators with Diophantine frequencies the exponential decay rate in expectation is well defined and is equal to the Lyapunov exponent.