## Why Measure?

Failing to learn from your forecasting mistakes makes you a lot less likely to become a better sales forecaster. Measuring accuracy should be a positive thing (and definitely not a stick for beating sales forecasters with).

However, calculating accuracy data over hundreds, possibly thousands of items can be a real challenge – especially finding a balanced ‘single number’ measure for accuracy. Here, we explain the different alternatives of calculating accuracy available in Prophecy, Data Perceptions sales forecasting software solution. They are mostly well-known methods for getting to a single, summary number that describes the overall accuracy of a group of many separate forecasts.

## Exceptions Analysis

Before we get to exceptions analysis, let’s remember that summary measurement is useful for tracking accuracy over time. Exceptions analysis – identifying and explaining the reasons for the biggest / most expensive forecast errors – arguably has a bigger payoff. It provides the valuable opportunity to learn from mistakes and apply the lessons of experience to current and future forecasts.

Therefore, step 1 in accuracy analysis should be a process for rapidly identifying the exceptions – the big deviations that caused the most problems. Prophecy’s Accuracy Analysis control dialog lets you specify an exception percent and only items exceeding this limit are listed in the resulting detail report:

Step 1 is to review these exceptions and try to explain them. Could the reasons have been anticipated? Forecasting is constrained to skillfully playing the hand the forecaster was dealt at the time the forecast was made. What’s to learn from reviewing the exceptions? Clearly, if better information or interpretation was available at the time the forecast was made there is a lesson to apply to future forecasts.

Moving on to obtaining a single number to describe forecast accuracy, there are several common measures and a couple of deviated ones. Prophecy’s Accuracy module calculates them ‘for free’ – Excel forecasters will need a little more work but they are mathematically simple.

The important thing to bear in mind when looking at all these measures is that they measure what they measure – i.e. simple maths. They DO NOT measure the real impact on your company’s supply chain or sales, revenue and profit.

## Weighted Average % Error

This statistic calculates a percentage deviation by dividing the sum of the absolute, unit deviations by the sum of the actuals, as illustrated in the following example:

The ‘simple’ % error, 15%, shown in the ‘TOTAL’ line does not allow for a mix of over and under-forecasts. They cancel each other out and are therefore misleading.

The weighted average method effectively weights the absolute variance by the size of the actual. This gives a more appropriate indication of overall forecast accuracy relative to volume, but assumes a product selling twice as much has twice as much impact. This is not necessarily the case. For example, where one item has a very high price and the other a very low price. In that case, consider measuring accuracy using revenue instead of quantity.

However, if you’re trying to measure supply chain impact, both quantity and revenue can be misleading. Sku-1 could have a long lead time, Sku-2 a short lead time. If they sell the same and are the same price, how can accuracy measures measure supply chain impact?

## Alternate Weighted Average % Error

This calculation is similar to the Weighted Average % Error. However, instead of dividing by the sum of the actuals as shown in the example above, it divides by the sum of the forecast or actual for each line, whichever is greater.

This means that *actual=0/forecast=100* has the same weight as *actual=100/forecast=0*. For two items with these forecasts and actuals, the weighted percent is 200% (misleadingly high?) whereas the Alternate Weighted percent is 100% (perhaps closer to ‘correct’ because both items were effectively 100% out?).

The Alternate Weighted Average % approach was suggested by a Prophecy customer and is thought to be non-standard. Nevertheless, it has the stated advantages over the more usual calculation.

## Mean Absolute Percent Error (MAPE)

This is a commonly used measure in sales forecasting. It is the mathematical average of the individual percent errors, ignoring their signs, as shown in the cell outlined in red here:

It is a moot point whether to divide by 3 or 4 in the example shown, where Sku-4 has no actual. If you divide by 4 you are rewarded with a lower MAPE than dividing by 3, but if you divide by 3 you are effectively ignoring Sku-4!

In addition, this method gives equal weight to a percent deviation, irrespective of the relative size of the forecast or actual. An item that sells a million has the same weight as one that sells 10.

## Mean Average Deviation (MAD)

This measure definitely has the most appropriate acronym! It is calculated from the mathematical average of the individual unit deviations, regardless of their sign:

The advantage of MAD over MAPE is that instances like Sku-4, where there is no actual, are included in the measure. The same percentage error on a high volume item has a much bigger effect on the result. This may or may not be desirable where, for example, the high seller is low value and the low seller is high value.

In addition, unlike a percent measure, it can be hard to know if the MAD is good or bad – it is just a number.

## Conclusions

As with so many areas of sales forecasting, there is no right answer or single ‘best’ measure that can be used to describe sales forecasting accuracy.

The first and most beneficial purpose of accuracy analysis is to learn from your mistakes. In that sense, exceptions analysis has the highest return. The summary measures are helpful for tracking cumulative improvement over time and are control barometers.

Our next post on this subject will reflect on comparability. You have two forecasters. One has a lower MAPE or Weighted Error than another. Does that mean forecaster one is a better forecaster, or just has easier products or customers to forecast?

Author: Peter Boulton, Data Perceptions.