Forecast accuracy is often reduced to a single number: MAPE.

It is easy to understand, expressed as a percentage and widely used in demand planning reports. A statement such as “our forecast error was 12%” sounds clear and useful.

The problem is that MAPE can become highly misleading when demand is low, intermittent or occasionally zero. This is common when forecasting individual SKUs, customer orders or store-level sales.

Suppose actual demand is 2 units and the forecast is 5 units. The absolute error is only 3 units, but MAPE reports an error of 150%. Whether that is a serious forecasting failure depends entirely on the business context.

This is why forecast accuracy should not be judged using MAPE alone. A more reliable assessment normally combines several metrics, with each answering a different question:

  • How many units are we normally wrong by?
  • Are there occasional large forecasting failures?
  • How accurate is the forecast across the full product portfolio?
  • Is the percentage error being distorted by low-volume demand?

This article compares five commonly used measures: MAPE, MAE, RMSE, WAPE and sMAPE. It also explains how to use MAPE when zero-demand periods are present.

Why the choice of metric matters

Most forecast error metrics begin with the same calculation:

$$e_t = A_t - F_t$$

where:

  • $A_t$ is actual demand
  • $F_t$ is forecast demand
  • $e_t$ is the forecast error

The difference lies in how those individual errors are combined.

Some metrics report errors in units. Others convert them into percentages. Some give additional weight to large misses, while others give equal importance to every observation.

As a result, two metrics can produce very different conclusions about the same forecast.

A model may appear poor under MAPE because a few low-volume periods produce extremely large percentage errors. The same model may perform reasonably well under MAE because the actual number of units missed is small.

The metric must therefore match both the demand pattern and the business decision.

MAPE: Mean Absolute Percentage Error

MAPE measures the average absolute error as a percentage of actual demand:

$$MAPE=\frac{1}{n}\sum_{t=1}^{n}\left|\frac{A_t-F_t}{A_t}\right|\times100$$

If MAPE is 12%, the usual interpretation is that the forecast differs from actual demand by 12% on average.

MAPE has several practical advantages:

  • It is expressed as a percentage and is easy to communicate.
  • It can compare series measured on different scales.
  • It is widely recognised by planners, managers and analysts.
  • It works reasonably well for stable, high-volume demand.

For example, MAE values cannot be compared directly between a product selling 10 units per week and another selling 10,000. MAPE appears to solve this by putting both errors on a percentage scale.

Where MAPE fails

The denominator in the formula is actual demand. When actual demand is small, even a modest forecasting error can produce a very large percentage.

Actual Forecast Absolute error Absolute percentage error
2 5 3 150%
200 203 3 1.5%
2,000 2,003 3 0.15%

The operational error is 3 units in every case, but MAPE treats the first observation as dramatically worse.

MAPE also has several other limitations:

  • It is undefined when actual demand is zero.
  • A few near-zero observations can dominate the average.
  • It penalises over-forecasting and under-forecasting differently.
  • Different software may handle zero actuals differently, making results difficult to compare.
  • It performs poorly on slow-moving and intermittent-demand items.

MAPE is most useful for relatively stable, positive and reasonably high-volume demand. It should not be the only measure used for store–SKU, spare-parts or other intermittent series.

MAE: Mean Absolute Error

MAE measures the average size of the forecasting error in the original unit:

$$MAE=\frac{1}{n}\sum_{t=1}^{n}|A_t-F_t|$$

If the MAE is 4 units, the forecast is wrong by 4 units per period on average, regardless of whether the error is positive or negative.

Why MAE is useful

MAE is one of the easiest forecast metrics to interpret operationally.

If a planner is forecasting weekly demand for a fastener and MAE is 20 boxes, that result can be related directly to inventory, order quantities, warehouse capacity and safety stock.

Its main advantages are:

  • It is expressed in meaningful business units.
  • It works when actual demand is zero.
  • It is not inflated by dividing errors by small actual values.
  • Every unit of error receives the same weight.

MAE is particularly useful when evaluating one SKU or a group of products with similar volumes.

Limitations of MAE

Because MAE is scale-dependent, it cannot fairly compare products with very different sales volumes.

An MAE of 10 units may be excellent for a product selling 1,000 units per week but unacceptable for one selling 12.

MAE also does not distinguish strongly between several moderate errors and one very large error. If severe forecast misses create disproportionate business costs, RMSE may provide a better warning signal.

RMSE: Root Mean Squared Error

RMSE squares each error before averaging and then takes the square root:

$$RMSE=\sqrt{\frac{1}{n}\sum_{t=1}^{n}(A_t-F_t)^2}$$

Squaring the errors gives more weight to large misses.

Why RMSE is useful

Consider two models:

  • Model A is usually accurate but occasionally produces a very large error.
  • Model B has slightly larger routine errors but no major failures.

Their MAE values could be similar. RMSE will usually penalise Model A more heavily because of its occasional large misses.

This can be useful when major forecast errors have a disproportionate cost, such as:

  • stockouts on key products
  • excess purchases with long lead times
  • missed production capacity
  • inaccurate promotion forecasts
  • urgent airfreight or expediting costs

RMSE is also commonly used as a loss function when training statistical and machine-learning models.

Limitations of RMSE

RMSE is sensitive to outliers. This is helpful when large errors are genuine business risks, but misleading when the outliers are caused by data-quality problems or unusual events that the model could not reasonably predict.

Like MAE, RMSE is scale-dependent. It should not be used to compare unrelated products without some form of normalisation.

It is also less intuitive for non-technical stakeholders. Although RMSE is reported in the original units, it should not be described simply as the “average error.”

WAPE: Weighted Absolute Percentage Error

WAPE compares total absolute error with total actual demand:

$$WAPE=\frac{\sum_{t=1}^{n}|A_t-F_t|}{\sum_{t=1}^{n}|A_t|}\times100$$

It is sometimes called volume-weighted MAPE or MAD/Mean, although terminology varies between organisations.

The important difference is that WAPE adds the errors and actuals before calculating the percentage. MAPE calculates a separate percentage for every observation and then averages those percentages.

Why WAPE often works better for demand planning

Because WAPE uses total actual demand as its denominator, a single low-volume day cannot dominate the result in the way it can under MAPE.

Other advantages include:

  • It remains easy to communicate as a percentage.
  • It works well for portfolio and category reporting.
  • It naturally gives greater weight to high-volume products.
  • It can include individual periods with zero demand, provided total actual demand is greater than zero.
  • It is less unstable than MAPE when demand contains small values.

For operational reporting, WAPE is often a better headline metric than MAPE.

What WAPE can hide

WAPE is volume-weighted, which means high-volume products dominate the result.

A forecast may perform well on the top-selling items and poorly across the long tail. The overall WAPE may still look good because the slow-moving products contribute little to total volume.

This matters when low-volume items are commercially or operationally important—for example:

  • critical spare parts
  • contractual customer lines
  • high-margin products
  • long-lead-time components
  • items with strict service-level requirements

WAPE should therefore be reviewed by product class, demand segment or ABC–XYZ category rather than only at total-company level.

WAPE can also be undefined when total actual demand for the evaluation window is zero.

sMAPE: Symmetric Mean Absolute Percentage Error

sMAPE attempts to reduce MAPE’s imbalance between over-forecasting and under-forecasting:

$$sMAPE=\frac{1}{n}\sum_{t=1}^{n}\frac{|A_t-F_t|}{(|A_t|+|F_t|)/2}\times100$$

Using this definition, sMAPE is bounded between 0% and 200%.

Advantages of sMAPE

Compared with ordinary MAPE, sMAPE:

  • treats over- and under-forecasting more evenly
  • prevents individual percentage errors from becoming infinite
  • remains scale-free
  • provides another percentage-based measure for comparing models

It is frequently used in forecasting competitions and academic studies.

Limitations of sMAPE

Despite its name, sMAPE is not perfectly intuitive or fully symmetric in every practical situation.

It can still produce large percentage errors when actual demand and forecast demand are both small. If both are zero, the denominator is also zero and the implementation must define how that observation is handled.

There are also several published versions of the formula. Some produce a range of 0% to 100%, while others produce 0% to 200%. The exact formula should always be stated when results are reported.

sMAPE is best treated as a supplementary measure rather than the only headline KPI.

MAPE calculated only on positive actuals

A common workaround is to calculate MAPE only when actual demand is greater than zero:

$$MAPE_{A>0}=\frac{1}{n_+}\sum_{t>0}\left|\frac{A_t-F_t}{A_t}\right|\times100$$

This prevents division by zero and allows an organisation to continue reporting a familiar metric.

However, it does not solve MAPE’s main weakness. Actual demand of 1 or 2 units can still create extremely large percentage errors.

More importantly, excluding zero-demand periods removes part of the forecasting problem.

Suppose a slow-moving product has demand in only 40% of weeks. Calculating MAPE only for those weeks ignores the remaining 60%, including any false-positive forecasts made when actual demand was zero.

Whenever this adjusted MAPE is reported, the report should also show:

  • the percentage of observations excluded
  • the number of zero-demand periods
  • a metric such as MAE or WAPE covering the complete test period

Without that disclosure, positive-actual MAPE can make a model appear more reliable than it really is.

A practical comparison

Metric Result format Best use Main weakness
MAPE Percentage Stable, positive, higher-volume demand Unstable around zero
MAE Original units Operational error for one series or similar products Cannot compare different scales
RMSE Original units Detecting and penalising large misses Sensitive to outliers
WAPE Percentage Portfolio, category and business-level reporting Can hide poor long-tail performance
sMAPE Percentage Supplementary scale-free model comparison Still behaves awkwardly near zero
MAPE on positive actuals Percentage Continuity with existing MAPE reporting Excludes part of the demand history

Which metrics should a demand planner use?

There is no single best forecast metric for every situation. A practical scorecard should normally contain more than one measure.

For a single SKU or a group of similar products, use:

  • MAE to show the typical error in units
  • RMSE when large misses create additional cost or risk
  • forecast bias to determine whether the forecast is consistently too high or too low

For a product portfolio, use:

  • WAPE as the main percentage accuracy measure
  • MAE or RMSE by segment to retain operational meaning
  • MAPE or sMAPE only as a supporting measure where appropriate

For intermittent or low-volume demand, give greater weight to:

  • MAE
  • WAPE across a sufficiently broad group
  • bias
  • service-level and stockout measures
  • metrics specifically designed for intermittent demand, where required

Plain MAPE should be treated cautiously.

Always compare against a baseline

A forecast metric is not meaningful in isolation.

A model with 15% WAPE might appear strong, but not if a simple seasonal-naïve forecast achieves 12%. Before accepting a SARIMA, machine-learning or foundation model, compare it with a straightforward baseline using the same test period.

For weekly seasonal demand, a common baseline is:

$$\hat{Y}_t = Y_{t-7}$$

This simply forecasts that demand will match the same day of the previous week.

The advanced model adds value only if it produces a meaningful and repeatable improvement over that baseline.

Final takeaway

“The model has a high forecast error” and “the selected metric is unsuitable for the data” are two different diagnoses.

MAPE remains useful when demand is stable, positive and reasonably high. It becomes unreliable when the series contains zeros, near-zero values or intermittent demand.

For most practical demand-planning work, a stronger approach is to use:

  • WAPE for the portfolio-level percentage
  • MAE for the operational error in units
  • RMSE to expose costly large misses
  • bias to show the direction of the error
  • MAPE or sMAPE only as supporting indicators

Forecast accuracy cannot be understood from one number. The right metric should reflect the demand pattern, the level of aggregation and the business cost of being wrong.