Self-assembled monolayers are predicated on thermodynamic equilibrium; hence, their properties project accessible relaxation pathways. Herein, we demonstrate that charge tunneling correlates with conformational degrees of freedom(s). Results from open chain and cyclic head groups show that, as expected, distribution in tunneling data correlates with the orientation of the head group, akin to the odd-even effect and more importantly the degree of conformational freedom, but fluctuates with applied bias. Trends in nature of distributions in current density illuminate the need for higher statistical moments in understanding these rather dynamic systems. We employ skewness, kurtosis, and estimation plots to show that the conformational degree of freedom in the head group significantly amplifies the odd-even effect and may lead to enhanced or perturbed tunneling based on whether the head group is on an odd- or even-parity spacer.