🔬 sMAPE (Symmetric Mean Absolute Percentage Error)

sMAPE (Symmetric Mean Absolute Percentage Error)#

A symmetric percentage error bounded between 0 and 200%.

Important

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What it is#

Symmetric Mean Absolute Percentage Error fixes MAPE’s asymmetry by putting the average of actual and forecast in the denominator:

\[\text{sMAPE} = \frac{1}{n}\sum_{i=1}^{n} \frac{|y_i - \hat{y}_i|}{(|y_i| + |\hat{y}_i|)/2}.\]

In its common form it is bounded between 0% and 200%.

What it fixes (and doesn’t)#

Plain MAPE penalizes over-forecasts more than under-forecasts and explodes as actuals approach zero; sMAPE is more balanced and bounded, which is why it served as the official metric of the M-competitions. But it is not perfectly symmetric, and it still misbehaves when both actual and forecast are near zero (the error jumps toward 100–200%).

When to use it#

Reach for sMAPE when you want a bounded, roughly symmetric percentage error for comparing across series — but avoid it on intermittent or zero-heavy demand, where MASE is the safer scale-free choice.

Theme: Model Evaluation & Uncertainty · All terminology

Hint

Mind map — connected ideas

MASE (Mean Absolute Scaled Error) · WMAPE (Weighted Mean Absolute Percentage Error) · Mean Absolute Percentage Error (MAPE) · Root Mean Squared Error (RMSE) · Forecasting Competitions · Mean Absolute Error (MAE)

Hint

More in Model Evaluation & Uncertainty

Average Absolute Error (AAE) · Baseline Heuristics · Bootstrap · Bootstrap Confidence Intervals (CIs) · Coverage · Cramér’s V · DeLong’s Test · KS Statistic (Kolmogorov–Smirnov Statistic) · Likelihood Ratio (LR) · Mann–Whitney U Test (also called the Wilcoxon rank-sum test) · MASE (Mean Absolute Scaled Error) · Mean Absolute Error (MAE) · Mean Absolute Percentage Error (MAPE) · Mean Squared Error (MSE)