Root Mean Squared Error

Forecast error that punishes big misses more than small ones.

Also known as: RMSE, root mean squared error, root mean square error

RMSE is the square root of the average squared forecast error. Squaring before averaging means a single huge miss counts more than many small ones — an error of 10 contributes 100 times what an error of 1 does, before the root brings the units back to the original scale (“off by $4.2K on average, big misses weighted heavily”).

errors: 1, 2, 1, 10  →  mean |err| = 3.5,  RMSE = √(1+4+1+100)/4 ≈ 5.1
                              (the 10 dominates RMSE, barely moves the mean)

Use RMSE when big misses are disproportionately costly — stockouts, capacity breaches, cash shortfalls. Use a plain average error (MAPE) when all misses cost roughly in proportion. The choice encodes how much you fear the tail.

The classic mistakes:

RMSE on data with outliers you do not care about. One data glitch dominates the score and model selection chases it. Clean or winsorise first, then measure.
Comparing RMSE across different series. Its units are the series’ units — an RMSE of 50 is great for revenue in thousands and terrible for conversion rates. Compare models on the same series, or scale first.
Forgetting the root. Reporting MSE (squared units, “square-dollars”) to stakeholders is meaningless. Take the root so the number reads in real units.
No baseline. Like every accuracy number, RMSE needs the naive forecast’s value beside it to mean anything — see forecast accuracy.