  The aim of this paper is to provide new perspectives on relative finite
element accuracy which is usually based on the asymptotic speed of convergence
comparison when the mesh size $h$ goes to zero. Starting from a geometrical
reading of the error estimate due to Bramble-Hilbert lemma, we derive two
probability distributions that estimate the relative accuracy, considered as a
random variable, between two Lagrange finite elements $P_k$ and $P_m$, ($k <
m$). We establish mathematical properties of these probabilistic distributions
and we get new insights which, among others, show that $P_k$ or $P_m$ is more
likely accurate than the other, depending on the value of the mesh size $h$.
