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

“Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not” (2022), by Timothy Hodson. Earth and Planetary Sciences research paper. Original abstract below, unchanged. A free PDF is available.

- Authors: Timothy Hodson
- Published: July 19, 2022
- Field: Earth and Planetary Sciences
- DOI: https://doi.org/10.5194/gmd-15-5481-2022
- Free PDF: https://gmd.copernicus.org/articles/15/5481/2022/gmd-15-5481-2022.pdf

## 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.

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