Quantities calculated from molecular simulations are often subject to initial bias due to unrepresentative starting configurations. The resultant systematic error can be reduced by truncating data from the start of the simulation and calculating the quantity of interest using the remaining data. However, discarding too many data unnecessarily increases random error. It is common practice to select a fixed truncation point, which is unlikely to be optimal across many simulations, or to select by visually inspecting the data, which is only feasible for a few simulations. Robust automated truncation point selection methods are required to minimise errors in calculated quantities while facilitating automation. Here we address the selection of an optimal truncation point given some data, and not the much harder problem of detecting when sufficient data have been collected (so that enough representative configurations of the equilibrium distribution have been sampled). Therefore, we refer to "truncation point selection" and not "equilibration detection", which might be expected to refer to the latter problem. We define the optimal truncation point to be that minimising the root mean square error (RMSE) compared to the value which would be obtained with infinite sampling.