It indicates signed cancellation on the chosen basis, but accuracy may still be poor.

Can MPE exceed one hundred percent in magnitude?

Yes; large overpredictions against small positive actuals can produce very large negative values under this convention.

Is MPE the same as percentage bias in totals?

Not generally; aggregation and weighting must be specified.

AI Glossary / Statistics and probability / Intermediate

Mean Percentage Error

Definition

Mean Percentage Error, or MPE, is the arithmetic average of signed forecast errors expressed as percentages of the corresponding actual values. Using error equals actual minus forecast, MPE is 100 times the average of (actual minus forecast) divided by actual. It describes average relative overprediction or underprediction; it does not measure the typical size of errors because opposite signs can cancel.

What it means

Suppose a demand forecast tends to fall below realized demand. When actual values are positive, the actual-minus-forecast convention produces positive percentage errors. A positive MPE therefore indicates average underprediction on this percentage basis. A negative MPE indicates average overprediction.
Always state the sign convention. Some systems calculate forecast minus actual, reversing this interpretation. Also distinguish a sample diagnostic from a population claim: a small observed MPE does not establish that a forecasting method is statistically unbiased in every relevant sense.

How it works

First align each forecast with the actual outcome for the same item, period, and forecast horizon. Evaluate predictions made before those outcomes were known. Mixing fitted historical values with genuine future forecasts can create an overly reassuring picture.
For each eligible observation, subtract the forecast from the actual and divide by that actual value. Multiply by one hundred to express the result in percent. Retain the sign, add the percentages, and divide by the number of included observations.
A zero actual makes this ordinary formula undefined. Values close to zero can generate extremely large contributions. Decide and disclose how these observations are handled; silently dropping them changes the population being evaluated.
Percentage interpretation also requires a meaningful zero. It is generally unsuitable for quantities such as Celsius temperature, where the choice of origin changes ratios. Negative actuals further complicate the intuitive underprediction interpretation.
Finally inspect the error distribution and subgroups. Average signed percentages can hide large individual mistakes and offsetting patterns across products, seasons, or customer groups.

Three practical examples

Demand planning: a distributor checks whether forecasts consistently fall below positive weekly demand, while separately measuring absolute errors and stockouts.
Service operations: a team compares signed percentage errors in predicted call volumes across forecast horizons to identify persistent planning imbalance.
Personal planning: someone reviews forecasts of positive monthly travel distance, recognizing that a month with almost no travel can dominate the percentage average.

Think of it this way

Think of MPE as averaging signed departures from several targets after scaling each departure by its own target. Departures to one side can cancel departures to the other. A balanced average therefore does not mean the individual departures were small, and smaller targets can magnify otherwise modest differences.

Worked example

Consider four positive actual values: 100, 200, 50, and 100. Corresponding forecasts are 90, 240, 40, and 110. Use actual minus forecast throughout.
The percentage errors are 100 × 10/100 = 10%; 100 × (-40)/200 = -20%; 100 × 10/50 = 20%; and 100 × (-10)/100 = -10%.
Their sum is zero, so MPE = (10 - 20 + 20 - 10)/4 = 0%. Nevertheless, every forecast is wrong. Taking absolute values instead gives MAPE = (10 + 20 + 20 + 10)/4 = 15%.
Actual totals equal 450 and forecast totals equal 480. The percentage error calculated from these totals is 100 × (450 - 480)/450 = -6.67%, approximately. That is a different aggregation: it weights individual relative errors by their actual volumes. Zero ordinary MPE therefore does not imply that total forecast volume equals total actual volume.

Illustrative case study

Fictional case: Juniper Supplies evaluates forecasts for several product families. Its overall MPE is close to zero, and a manager initially assumes that purchasing quantities are well balanced. A review shows underprediction among small-volume items and overprediction among larger-volume items.
The team keeps MPE as a directional diagnostic but adds absolute error, total volume discrepancy, and separate results by family. It also lists zero-demand periods rather than quietly excluding them. This fictional example illustrates why several views are needed; it does not claim measured commercial savings or demonstrate that one replacement model is superior.

Common misconceptions and mistakes

Do not confuse MPE with MAPE: removing the absolute-value operation changes the question from magnitude to signed balance. Do not interpret zero MPE as perfect forecasting, or negative MPE as inherently better than positive MPE.
Averaging percentages is not the same as taking a percentage of aggregate totals. An unweighted average gives each included observation equal influence before accounting for its denominator.
Do not replace zero actuals with an arbitrary tiny constant without reporting the altered metric. Do not treat one favorable historical score as evidence of future reliability or use MPE alone as an optimization objective: increasingly negative values can simply mean increasingly severe overprediction.

Business use

Use MPE to investigate directional planning tendencies when percentage errors are meaningful and actual values support stable denominators. Report the convention, inclusion rules, evaluation period, horizon, sample size, and relevant segments.
Pair it with a magnitude measure and the business costs of shortages and excess capacity. If zeros or small actuals are common, evaluate alternatives appropriate to the decision. An operational correction should address a demonstrated pattern, not merely force a pooled percentage average to zero.

Check your understanding

with positive actuals and actual-minus-forecast errors, what does a negative MPE suggest?

Answer: average relative overprediction. Question: two percentage errors are +30% and -30%.

What are MPE and MAPE?

Answer: zero percent and thirty percent, respectively.

can a zero actual be used directly in ordinary MPE?

Answer: no, because the calculation divides by that actual.

Related terms

Learn next

Next, compare signed relative error with absolute error and errors aggregated over total volume. Then examine time-based evaluation and how denominator choices affect conclusions for intermittent demand.

Absolute error

Sources

Hyndman and colleagues, Glossary of Forecasting Terms: https://robjhyndman.com/mwh3/FG4.pdf Fabletools, primary accuracy implementation: https://raw.githubusercontent.com/tidyverts/fabletools/master/R/accuracy.R Hyndman and Athanasopoulos, Forecasting: Principles and Practice, forecast accuracy: https://otexts.com/fpp3/accuracy.html

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