Symmetric MAPE (sMAPE)
Also known as: sMAPE, SMAPE, symmetric MAPE
Symmetric Mean Absolute Percentage Error is a refinement of MAPE that addresses its asymmetry by using the average of actual and predicted values as the denominator. Proposed by J. Scott Armstrong and refined by Makridakis (1993) and Hyndman & Koehler (2006), sMAPE treats over- and under-predictions symmetrically.
Key highlights
- Scale-independent and symmetric, avoiding MAPE asymmetry
- Penalizes over- and under-predictions equally
- Interpretable as a percentage
- Better statistical properties than MAPE
Intuition
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How it works
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When to use it
Use sMAPE when you want a scale-independent metric with symmetric treatment of prediction errors. It is particularly valuable in contexts where over- and under-prediction have equal cost (e.g., inventory balancing, resource allocation). Like MAPE, sMAPE is undefined or poorly behaved when both actual and predicted are close to zero, so avoid using it with intermittent or zero-heavy data.
Strengths & limitations
- Scale-independent and symmetric, avoiding MAPE asymmetry
- Penalizes over- and under-predictions equally
- Interpretable as a percentage
- Better statistical properties than MAPE
- Still undefined or poorly behaved when both actual and predicted are near zero
- Denominator approaches zero when actual and predicted are both small, causing instability
- Less interpretable than standard MAPE for practitioners
- Bounded by 0-100% only under specific conditions
Common pitfalls
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Applications
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Frequently asked
How does sMAPE differ from MAPE?
MAPE divides error by actual value; sMAPE divides by the average of actual and predicted. This makes sMAPE symmetric (equal treatment of over- and under-predictions) while MAPE is asymmetric. They can rank models differently.
When does sMAPE fail?
When both actual and predicted are near zero, the denominator becomes small, causing the metric to become unstable or undefined. For example, if actual = 0.1 and predicted = 0.2, sMAPE = 67%, which may not reflect true error magnitude.
Why is sMAPE bounded by 0-100%?
sMAPE is only strictly bounded by 0-100% when both actual and predicted are positive. With mixed signs or zeros, it can exceed 100% in some formulations. Check your specific implementation.
Is sMAPE better than MAPE?
Not universally. sMAPE addresses MAPE's asymmetry but introduces new instability issues with zero or near-zero values. Choose based on your data characteristics and cost structure: MAPE for directional bias, sMAPE for symmetry.
Can I use sMAPE as a loss function?
Technically yes, but it is not smooth near the zero denominator, making optimization difficult. In practice, other metrics like MAE, RMSE, or MASE are more suitable for loss functions.
Sources
- 1.Armstrong, J. S. (1985). Long-range forecasting: from crystal ball to computer (2nd ed.). New York: John Wiley & Sons.ISBN 978-0471082010
- 2.Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679-688.
- 3.Makridakis, S. (1993). Accuracy measures for a robust comparison of forecasting methods. International Journal of Forecasting, 9(4), 679-688.
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Cite this page
ScholarGate. (2026, June 3). Symmetric MAPE. ScholarGate. https://scholargate.app/model-evaluation/symmetric-mape