WAPE (Weighted Absolute Percentage Error)

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

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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.”

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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.

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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.

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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.

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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.

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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.”