MAPE & WMAPE

Definition

MAPE (mean absolute percentage error) measures the average gap between forecast and actual, in percent. WMAPE is its volume-weighted version: each reference counts for what it truly represents in the business. The first is universal and misleading; the second, less known and far more reliable.

Why it matters

The most widespread indicator, and the most misused.

MAPE is everywhere: it is the number shown in committee when accuracy is discussed. Its strength is disarming simplicity, one percentage readable by all, comparable over time. Its weakness is hidden in its very mechanics: it treats every reference with strict equality, whether it weighs one unit a month or ten thousand.

The concrete result: a handful of erratic, inconsequential small references can sink the global MAPE below the presentable line, even as the products that make the revenue are perfectly forecast. The forecast is then believed poor, useless improvement projects are launched, and the place where error truly costs money is entirely missed. WMAPE fixes exactly this flaw of perspective.

Business impact

The choice of metric is no statistician's fancy: it drives inventory decisions. A target service level is computed from forecast uncertainty. If that uncertainty is measured by a MAPE artificially inflated by small references, the safety stock of the WHOLE portfolio is oversized.

Plainly: a bad metric is not just bad reporting, it is cash needlessly tied up. Moving from MAPE to WMAPE, or better, steering both side by side, often has a direct, measurable effect on working capital.

The mechanism

Why MAPE explodes on small values.

On a reference selling one unit, missing by a single unit is 100% error. On a reference at a thousand, the same one-unit gap is 0.1%. MAPE averages these percentages with no weighting whatsoever.

On the chart, each bar is the percentage error of a reference, sorted from smallest to largest volume. On the left, small references show huge errors, purely mechanical and operationally meaningless. On the right, high volumes are well forecast. MAPE, a plain arithmetic mean, is pulled up by that handful of left-side values.

The black horizontal line is WMAPE: by weighting each error by the reference's volume, it tracks the reality of the big sellers and ignores the statistical noise of small references. It is rigorously the same underlying gap between forecast and actual, but read two diametrically opposite ways, leading to two contrary diagnostics.

1210502008003k volume de la reference (unites/periode) →
Inflated MAPE (small volumes)Controlled errorWeighted WMAPE

Figure 1. Percentage error per reference, smallest to largest volume. MAPE is inflated by small references; WMAPE, weighted, follows the volumes that matter. Illustrative schematic.

WMAPE = Σt | Dt − Ft |Σt Dt
WMAPE (weighted MAPE) sums the absolute gaps then divides by total demand: each reference counts for its real volume. Compare with the classic MAPE, MAPE = mean( |Dt − Ft| / Dt ), which divides BEFORE averaging and so gives a 1-unit reference the same weight as a 10,000-unit one. That early division is what makes MAPE explode on small volumes. WMAPE, dividing at the end, stays stable and representative.

The traps

Three handling errors.

MAPE mostly fools those who grant it blind, unweighted trust.

01

Applying it to small volumes

On a slow mover or intermittent demand, MAPE becomes huge, unstable, even mathematically undefined when actual demand hits zero. It is simply not designed for these cases, where other metrics take over.

02

Comparing MAPEs across products

A 20% MAPE on a big seller and a 20% MAPE on a small niche reference describe neither the same forecast quality nor the same stakes. Without volume weighting, the comparison has no decision value whatsoever.

03

Forgetting the division by zero

On zero-sale periods, the MAPE formula divides by zero and yields infinity or an error. These periods must be explicitly handled apart, or the whole aggregate calculation skews or breaks.

Computing it

Three steps, from MAPE to WMAPE.

The calculation fits in an ordinary spreadsheet. What changes everything is not technical difficulty, it is the decision to move to the weighted version.

Compute the error per period

For each reference and period, the absolute gap between actual and forecast: |D − F|. It is the elementary brick common to both metrics.

Turn it into MAPE

Divide each gap by the period's actual, then average the whole: MAPE = mean( |D − F| / D ). Reserve strictly for references with sufficient, non-zero volume.

Move to WMAPE

First sum all absolute gaps, then divide by the sum of all actual demands (see formula above). This is the measure to favor for a heterogeneous portfolio: robust, representative, decision-grade.

Neighboring concepts

Read next.

Error measurement sharpens against bias and the value added by the process.

From knowledge to action

Do your forecast indicators tell the truth?

Choosing the right measure concretely changes stock decisions and tied-up cash. Our Planning, Forecasting & S&OP file squares your indicators.