How mean absolute deviation measures forecast error
Mean absolute deviation (MAD) calculates the average distance between your forecast and actual demand, ignoring whether the forecast was too high or too low. If your forecast missed by +40 units one month and -60 units the next, the absolute deviations are 40 and 60, so the mean absolute deviation is 50 units. That single number tells you how much your forecast typically misses by.
MAD is the foundation of safety stock calculations for FBA sellers. The standard formula for safety stock uses mean absolute deviation directly: Safety Stock = z × MAD × √(Lead Time in periods), where z is the service level multiplier (1.65 for 95% service level). A higher MAD means you need more buffer inventory to maintain the same fill rate.
Unlike MAPE (percentage-based accuracy), mean absolute deviation is expressed in units. This makes it more actionable for reorder decisions because your purchase orders are in units, not percentages. A MAD of 80 units on a product selling 400/month tells you something very different than a MAD of 80 units on a product selling 5,000/month, even though the unit count is the same.
Mean absolute deviation formula
| Variable | Meaning |
|---|---|
|Actual − Forecast| | Absolute error for each period (ignore sign) |
n | Number of periods measured |
z | Service level multiplier (1.28 for 90%, 1.65 for 95%, 2.33 for 99%) |
Lead Time | Measured in the same periods as MAD (e.g., if MAD uses monthly data, lead time in months) |
Example: calculating MAD and safety stock
You sell a pack of reusable produce bags at $25 ASP with a 50-day lead time. Here are 6 months of forecast vs. actual data:
| Month | Forecast | Actual | |Error| |
|---|---|---|---|
| 1 | 600 | 550 | 50 |
| 2 | 580 | 620 | 40 |
| 3 | 590 | 510 | 80 |
| 4 | 570 | 630 | 60 |
| 5 | 600 | 560 | 40 |
| 6 | 580 | 650 | 70 |
MAD = (50 + 40 + 80 + 60 + 40 + 70) / 6 = 56.7 units.
Now calculate safety stock at a 95% service level (z = 1.65). Lead time is 50 days, and your MAD is based on monthly data (30-day periods), so lead time in periods = 50/30 = 1.67.
Safety Stock = 1.65 × 56.7 × √1.67 = 1.65 × 56.7 × 1.29 = 121 units.
At $25 ASP, that is $3,025 in buffer inventory. If your MAD were lower (say 30 units from better forecasting), safety stock would drop to 64 units ($1,600), freeing $1,425 in working capital.
FBA-specific considerations
For FBA sellers, mean absolute deviation is more actionable than percentage-based accuracy metrics because your purchase orders are denominated in units. A MAD of 80 units tells you exactly how much buffer to add for a 95% service level. A MAPE of 12% leaves you to do the conversion to units yourself, which is error-prone across SKUs with different volumes.
High-MAD SKUs need more storage capacity, which feeds back into your IPI score. If your MAD is high because of genuine demand volatility, you have two choices: carry larger safety stock and accept the storage cost, or improve forecast accuracy through better methods (seasonality adjustment, trend adjustment, or adaptive smoothing). The economics depend on your contribution margin per unit.
MAD also helps you identify which SKUs need a forecasting method change. If you have 200 SKUs and 20 of them have MAD values 3x higher than the median, those 20 are the ones to investigate. Maybe they need adaptive smoothing, or they need to be moved off automated forecasting entirely and managed with manual overrides.
Common mistakes
- Comparing MAD across SKUs with different volume levels. A MAD of 50 units on a product selling 100 units/month is terrible (50% relative error). The same MAD on a product selling 5,000 units/month is excellent (1% relative error). Use MAD for absolute reorder calculations, but use MAPE for cross-SKU comparisons.
- Not recalculating MAD as demand patterns change. A product that was steady all year may become volatile when a competitor enters. Old MAD values produce safety stock that is too low for the new reality. Recalculate MAD on a 6-month rolling window, not lifetime data.
- Confusing mean absolute deviation with standard deviation in safety stock formulas. Some formulas use standard deviation (σ) and some use MAD. The relationship is approximately σ ≈ 1.25 × MAD for normal distributions, but they are not interchangeable in formulas. Match the formula to the input metric, or convert correctly.