Root mean square error (RMSE) or mean absolute error (MAE): when to use them or not

Abstract. The mean absolute error (MAE) and root mean squared error (RMSE) are widely used metrics for evaluating models. Yet, there remains enduring confusion over their use, such that a standard practice is to present both, leaving it to the reader to decide. Some of this confusion arises from a recent debate between Willmott and Draxler (2005) and Chai and Draxler (2014), in which either side presents their arguments for one metric over the other. Neither side was completely correct; however, because neither metric is inherently better: MAE is optimal for Laplacian errors, and RMSE is optimal for normal (Gaussian) errors. When errors deviate from these distributions, other metrics are superior.

• UG
  U.S. Geological Survey