Computing Forecast Error: Should I divide by forecast or demand?

I often get the following question from my clients and trainees:

To express the forecast error as a percentage, should we divide the forecast error by the demand or the forecast?

To be or not to be? Credit

Basically, we can compute the forecast error percentage by dividing the absolute error by the demand; or by the forecast.

Or

Both approaches will usually result in slightly different numbers; but in some cases, the difference can be massive. As we will discuss, using the forecast as the denominator is an open door to metric-hacking.

For example in the figure below, the forecast error is 75% if computed based on demand, and 88% if computed based on forecast.

MAE% computed with demand as the denomiator = 75%. MAE% with forecast as denominator = 88%.

PS: remember never to use MAPE to track forecast errors. This is a bad practice. I guess you know this already — if not, see my article below for a detailed explanations.

Forecast KPI: RMSE, MAE, MAPE & Bias

Demand Forecasting

When discussing demand forecasting in general and forecasting KPIs in particular, I like to keep a few statements in mind:

• Our objective is to forecast demand. In other words, (unconstrainted) demand is what we aim for when forecasting.
• The objective of a forecasting KPI is not to be easy to maximize/minimize but to promote useful forecasts.
  For example: let’s imagine that KPI1 is aligned with your supply chain objectives…