When can MAPE be misleading?

MAPE can be misleading when actual target values are zero or very small, or when percentage errors do not reflect the real cost of prediction mistakes.

MAPE divides each absolute error by the magnitude of the actual value:

MAPE = (100 / n) × Σ |(actual - predicted) / actual|

That denominator creates several important limitations.

1. Actual values equal to zero

When the actual value is 0, the percentage error requires division by zero and is undefined.

This is common in intermittent-demand forecasting, such as products with days of zero sales.

2. Actual values close to zero

A small absolute mistake can become an enormous percentage error.

For example:

• Actual 1, predicted 3 → absolute error 2, percentage error 200%.
• Actual 100, predicted 110 → absolute error 10, percentage error 10%.

MAPE gives the first error much greater weight even though its absolute difference is smaller.

3. Large and small targets receive uneven emphasis

Because each error is divided by its own actual value, observations with smaller actual values can dominate the average. A low MAPE does not necessarily mean the model avoids the most financially costly errors.

4. Negative actual values make interpretation difficult

The absolute-value formula can be calculated for nonzero negative actuals, but percentage errors relative to negative quantities may be hard to interpret meaningfully in the application.

5. MAPE can favor particular forecasting behavior

Percentage-error measures are not symmetric when actual values change. Predicting 120 for an actual value of 100 gives 20%, whereas predicting 100 for an actual value of 120 gives approximately 16.7%.

This asymmetry can influence which forecasts perform best under MAPE.

What should you use instead?

• MAE: when you want average error in the target's original units.
• RMSE: when larger absolute errors should receive more penalty.
• A domain-specific metric: when errors have different business costs or the target contains many zeros.

No replacement metric is universally best; choose one based on the target distribution and the cost of mistakes.

In short, MAPE is easiest to interpret for positive actual values comfortably away from zero. It can be undefined, exaggerated, or misleading when the target contains zeros, near-zero values, or highly uneven scales.