Before revision:  For an observable with lattice errors of order \alpha and an integrated autocorrelation time that grows like \mathrm{int}\propto a^{-z}, multilevel Monte Carlo (MLMC) can reduce the cost from O(\text{stat}^{-2}\text{disc}^{-(1+z)/\alpha}) to O(\epsilon_{\text{stat}}^{-2}\vert\log \epsilon_{\text{disc}} \vert^2+\epsilon_{\text{disc}}^{-1/\alpha}) . Even higher performance(\epsilon_{\text{stat}}^{-2}+\epsilon_{\text{disc}}^{-1/\alpha}).
After revision:  For an observable with lattice errors of order \alpha and an integrated autocorrelation time that grows like \mathrm{int}\propto a^{-z}, multilevel Monte Carlo (MLMC) can reduce the cost from O(\text{stat}^{-2}\text{disc}^{-(1+z)/\alpha}) to O(\epsilon_{\text{stat}}^{-2}\vert\log \epsilon_{\text{disc}} \vert^2+\epsilon_{\text{disc}}^{-1/\alpha}) or \mathcal{O(\epsilon_{\text{stat}}^{-2}+\epsilon_{\text{disc}}^{-1/\alpha}).