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

Abstract

The root-mean-squared error (RMSE) and mean absolute error (MAE) 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 which is more relevant. In a recent reprise to the 200-year debate over their use, Willmott and Matsuura (2005) and Chai and Draxler (2014) give arguments for favoring one metric or the other. However, this comparison can present a false dichotomy. Neither metric is inherently better: RMSE is optimal for normal (Gaussian) errors, and MAE is optimal for Laplacian errors. When errors deviate from these distributions, other metrics are superior.