Choosing the Right Denominator: Understanding the Importance of Actual Sales and Forecast in MAPE Calculation

When calculating the Mean Absolute Percentage Error (MAPE), the denominator represents the scale of measurement or the "size" of the forecasted or actual values. Depending on the purpose of the analysis, actual sales or forecasts are used in the denominator.

Use Actual Sales in the denominator

If we use actual sales in the denominator, we are measuring forecast accuracy relative to the actual sales demand. This is useful when we want to evaluate how well our forecasts are capturing the true demand of our products or services. However, this approach may not be appropriate when we are comparing the forecast accuracy of different products or services with varying sales volumes.

Pros of using actual sales in the denominator for measuring forecast accuracy:

• Provides an accurate evaluation of how well our forecasts are capturing the true demand of our products or services.
• Allows us to make data-driven decisions based on the actual sales demand

Cons of using actual sales in the denominator for measuring forecast accuracy:

• It may not be appropriate when comparing the forecast accuracy of different products or services with varying sales volumes.
• This may not reflect the accuracy of the Forecast itself but rather the accuracy of the demand data used in the forecast.

Use Forecast in the denominator:

On the other hand, if we use Forecast in the denominator, we are measuring forecast accuracy relative to the forecasted demand. This is useful when we want to compare the forecast accuracy of different products or services with varying sales volumes. However, this approach may not be appropriate when we evaluate how well our forecasts capture the true demand of our products or services.

Pros of using forecast accuracy measurement relative to forecasted demand:

• It allows us to compare the forecast accuracy of different products or services with varying sales volumes.

Cons of using forecast accuracy measurement relative to forecasted demand:

• It may not accurately reflect how well our forecasts are capturing the true demand of our products or services.
• It may not be suitable for evaluating the overall accuracy of our forecasting process, as it only measures accuracy relative to the forecasted demand.

Example

Let's say we have a shoe manufacturer and two products: Product A and Product B.

• For Product A, the forecasted demand is 1000 units, and it ends up selling 900 units.
• For Product B, the forecasted demand is 1000 units, and it ends up selling 1100 units.

If we want to measure the forecast accuracy using the Mean Absolute Percentage Error (MAPE) formula with Sales in the denominator, we will get:

• For Product A: MAPE = [ABS(900 - 1000)/ 900] x 100 = 11.11%
• For Product B: MAPE = [ABS(1100 - 1000)/1100] x 100 = 9.09%

Now, If we want to measure the forecast accuracy using the MAPE formula with Forecast in the denominator, we would get:

• For Product A: MAPE = [ABS(900 - 1000)/1000] x 100 = 10%
• For Product B: MAPE = [ABS(1100 - 1000)/1000] x 100 = 10%

The computations presented above clearly compare the results obtained from both scenarios.

Therefore, it's important to choose the appropriate denominator based on the purpose of our analysis.

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