Ensemble averaging and mean squared error

In fields such as climate science, it is common to compile an ensemble of different simulators for the same underlying process. It is a striking observation that the ensemble mean often out-performs at least half of the ensemble members in mean squared error (measured with respect to observations). In fact, as demonstrated in the most recent IPCC report, the ensemble mean often out-performs all or almost all of the ensemble members across a range of climate variables. This paper shows that these could be mathematical results based on convexity and averaging, but with implications for the properties of the current generation of climate simulators.