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Forecast Error Metrics Reference: MAPE, WMAPE, sMAPE, RMSE, MASE

Forecast accuracy numbers are only comparable when everyone uses the same definition. This reference lists the metrics demand planners meet most, with the formula, the unit, how to read the result and where each one breaks down.

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Metric	Formula	Unit	How to read it	Main weakness	Best used for
Error (E)	Actual - Forecast	Units	Positive means under-forecast, negative means over-forecast	Positive and negative errors cancel when summed	Building block for every other metric
Percentage error (PE)	(Actual - Forecast) / Actual	Percent	Signed error relative to demand	Undefined when actual is zero	Single item, single period review
Absolute error (AE)	\|Actual - Forecast\|	Units	Size of the miss, direction ignored	Not comparable across items of different volume	Input to MAE and WMAPE
MAE (mean absolute error)	Sum of \|A - F\| / n	Units	Average miss per period in units	Scale dependent, cannot compare SKUs	One item over time, safety stock inputs
MAPE	Sum of (\|A - F\| / A) / n x 100	Percent	Average percent miss, lower is better	Fails on zeros, overweights low volume periods, penalises over-forecast less than under-forecast	Stable, high volume items
WMAPE (weighted MAPE)	Sum of \|A - F\| / Sum of A x 100	Percent	Total absolute error as a share of total demand	Dominated by high volume items in a mixed portfolio	Family or portfolio accuracy reporting
Forecast accuracy	100% - WMAPE (floored at 0)	Percent	Headline accuracy figure used in S&OP packs	Definition varies by company, always state it	Executive reporting
sMAPE	Sum of (\|A - F\| / ((A + F) / 2)) / n x 100	Percent	Percent error scaled by average of actual and forecast	Several definitions exist, still unstable near zero	Comparing models across items with a zero-safe variant
MSE	Sum of (A - F)^2 / n	Units squared	Penalises large misses heavily	Units are hard to interpret	Model fitting and selection
RMSE	Square root of MSE	Units	Typical miss in units with large misses weighted up	Sensitive to outliers	Safety stock sigma when errors are roughly normal
MASE	MAE of forecast / MAE of naive forecast	Ratio	Below 1 beats the naive forecast, above 1 is worse	Needs a clean in-sample history	Comparing accuracy across different SKUs fairly
Bias (mean error)	Sum of (F - A) / n	Units	Positive means consistent over-forecast	Hides large offsetting errors	Spotting systematic optimism or sandbagging
Percent bias	Sum of (F - A) / Sum of A x 100	Percent	Net over or under forecast as a share of demand	Sign convention differs between companies	Bias reporting by family or region
MPE (mean percentage error)	Sum of ((A - F) / A) / n x 100	Percent	Average signed percent error	Undefined at zero actual	Bias on stable items
Tracking signal	Running sum of errors / MAD	Ratio	Beyond about plus or minus 4 suggests persistent bias	Threshold is a rule of thumb, not a law	Automatic bias alerts per SKU
MAD (mean absolute deviation)	Sum of \|A - F\| / n	Units	Same as MAE in forecasting use	Name is used for other statistics in other fields	Tracking signal denominator
Forecast value add (FVA)	Error of baseline - Error of step	Percentage points	Positive means the step improved accuracy	Needs a stored baseline forecast	Judging manual overrides against the statistical forecast
Coefficient of variation	Standard deviation / mean demand	Ratio	How volatile demand is before any forecast	Unstable on intermittent items	Setting realistic accuracy targets by segment

Always state the forecast lag and the aggregation level when you quote a metric. The same data gives very different MAPE at SKU-week and at family-month.

Metrics from your ERP data

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How to use this reference

Search by metric name or by the problem you have, for example zero demand or bias. Each row gives the formula in plain text so you can reproduce it in Excel, SQL or your planning tool. Export the table to Excel and add it to your KPI definition document so finance, sales and operations quote the same measure. Agree one headline accuracy metric, one bias metric and one fairness metric such as MASE, rather than reporting everything.

Choosing between MAPE and WMAPE

MAPE averages percent errors, so a miss on a ten unit month counts as much as a miss on a ten thousand unit month. WMAPE divides total absolute error by total demand, so volume sets the weight. For a portfolio view WMAPE usually reflects business impact better. For judging a model on one stable item MAPE is fine. If any actuals are zero, avoid plain MAPE.

Use WMAPE for family and company level
Use MAPE only when actuals are rarely zero
Use MASE to compare across items
Report bias beside accuracy, never instead of it

Worked example

Three months of actuals are 100, 120 and 80 against forecasts of 110, 100 and 90. Absolute errors are 10, 20 and 10, so MAE is 13.3 units. WMAPE is 40 divided by 300, which is 13.3%. Bias is (110 + 100 + 90) minus 300, which is zero, so the forecast looks unbiased even though each month missed. That is why you need both an absolute and a signed measure.

Common mistakes

Teams compute accuracy against the latest forecast instead of the frozen one that supply used. Others average SKU-level MAPE and call it the company number. A third error is flooring accuracy at zero in one report but not another. Document the definition, the lag, the level and the treatment of zeros next to the figure every time.

Frequently Asked Questions

Which forecast accuracy metric is the best?

There is no single best one. WMAPE suits portfolio reporting, RMSE suits safety stock, MASE suits comparing items, and bias or tracking signal suits detecting systematic error. Most teams track one accuracy metric and one bias metric.

Why is MAPE a problem when demand is zero?

MAPE divides by actual demand. A zero actual makes the percent error undefined or infinite, and tiny actuals produce huge percentages. Use WMAPE, MASE or a zero-safe sMAPE variant for intermittent items.

Is forecast accuracy just 100 minus MAPE?

Many companies define it as 100 minus MAPE or WMAPE, floored at zero, but this is a convention. Always write the definition beside the number, because a competitor or another plant may define it differently.

What is a good WMAPE?

It depends on demand variability and aggregation. Family level monthly figures are usually far better than SKU-week figures. Set targets by segment using volatility, and judge improvement against a naive baseline rather than a universal number.

If you compute these metrics by hand each cycle, Netray can build them from your ERP shipment and forecast history and show the query behind every number.

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