1) Definition
WAPE is a regression / forecasting error metric that measures the total absolute error relative to the total actual values.
It is often called a “volume-weighted MAPE” because it weights errors by the scale of the actuals.
Formula:
$\text{WAPE} = \frac{\sum_{i=1}^{n} |y_i – \hat{y}_i|}{\sum_{i=1}^{n} |y_i|} \times 100\%$
- $y_i$: actual value
- $\hat{y}_i$: predicted value
- $n$: number of observations
2) Intuition
- Unlike MAPE, which averages percentage errors for each observation, WAPE uses total errors divided by total demand (or total actuals).
- This avoids MAPE’s issue of overweighting very small denominators (tiny $y_i$ values).
- Interpretation: “On average, across the whole dataset, the model’s predictions are off by X% of the actual demand.”
3) Example
Suppose actual vs predicted demand for three products:
| Item | Actual ($y$) | Predicted ($\hat{y}$) | Error $|y-\hat{y}|$ |
|---|---|---|---|
| A | 100 | 90 | 10 |
| B | 200 | 220 | 20 |
| C | 700 | 650 | 50 |
- Total Absolute Error = 10 + 20 + 50 = 80
- Total Actual = 100 + 200 + 700 = 1000
- WAPE = $\frac{80}{1000} \times 100 = 8\%$
Interpretation: Overall, predictions are off by 8% of total demand.
4) Comparison with Other Metrics
- MAE (Mean Absolute Error): Average error in units, not scale-free.
- MAPE (Mean Absolute Percentage Error): Scale-free but unstable when $y_i$ is small or zero.
- WAPE: Scale-free like MAPE but more robust (because it aggregates before dividing).
Rule of thumb:
- Use WAPE when data has many small values or zeros (common in retail forecasting).
- Use MAPE when you need interpretability per observation, but watch out for zeros.
5) Practical Use Cases
- Demand forecasting in retail or supply chain (how far predictions deviate from total sales).
- Inventory management: Helps estimate aggregate forecast error relative to stock levels.
- Finance: Aggregate error in predicting revenues, costs, or expenses.
6) Limitations
- Insensitive to distribution: Two models can have the same WAPE, but one may perform poorly on critical high-value items.
- Aggregate view only: Doesn’t tell you where the errors occur (small vs large items).
- Weighted by actual, not by business importance: If profit margin varies, WAPE may not reflect true cost impact.
Summary:
- WAPE = total absolute error ÷ total actuals.
- It’s a robust, scale-free error metric, often preferred over MAPE in real-world forecasting, especially when actual values vary widely or include zeros.
- Interpretation: “On average, predictions are off by X% of the total actual value.”