Blog · Forecast and pipeline · Supply chain
Probabilistic demand forecasting describes possible demand outcomes and their likelihood. Compare supplied forecast intervals with actual demand, measure coverage and width, and check whether uncertainty assumptions support business decisions.
Probabilistic demand forecasting describes the likelihood of different demand outcomes, rather than presenting one quantity as certain. To evaluate a supplied forecast, compare its intervals with actual demand at the same product, location, period and lead time. Check how often the intervals contain demand and how wide they are.
A distribution can support a purchasing or capacity discussion without becoming an automatic ordering rule. The forecast describes uncertainty; the business still supplies service requirements, shortage costs, storage limits and decision authority. The broader demand forecasting overview covers the planning purpose; this page focuses on whether supplied uncertainty estimates hold up.
A point forecast is a single summary, such as a mean or median. A forecast distribution assigns probabilities across possible outcomes. Quantiles mark positions within that distribution, while a prediction interval joins two boundaries.
For example, an equal-tailed interval labeled 80% commonly runs from the 10th to the 90th percentile. Demand can fall outside it without making that individual forecast invalid. The question is whether repeated outcomes match the stated probabilities over a suitable evaluation period. Forecasting: Principles and Practice explains prediction intervals and their probability interpretation.
Ask the forecast owner which summary each column contains. A column labeled “expected demand” might mean the average, a median or a purchasing target. Those are different quantities. Ask whether the distribution covers demand during one calendar period or the entire replenishment lead time, and whether uncertainty includes changes in assumptions.
For low-volume products, boundaries must respect whole units and the possibility of zero demand. See intermittent demand forecasting when long gaps between transactions make a continuous-looking range hard to interpret.
Bring the forecast snapshot issued before each demand period, not a revised file saved after actual demand became known. Each comparable row needs product, site, forecast issue date, demand period, forecast horizon, interval level, lower boundary, upper boundary and observed demand. Keep a supplied point forecast as a separate field.
An evaluation row is eligible only when the actual demand period is complete and the matching forecast exists. Missing actuals are missing, not zero demand. Retain stock availability flags so that shipment limits are visible rather than mistaken for a successful forecast of unconstrained demand.
Interval coverage = Rows with lower boundary ≤ actual demand ≤ upper boundary / Eligible rows
Interval width = Upper boundary − Lower boundary
Use a consistent boundary convention and record it. Inclusive boundaries are appropriate for the count example below. Compute average width across the same eligible rows used for coverage. Otherwise a forecast can appear narrower simply because its hardest periods were excluded.
Keep evaluation horizons separate. A forecast made shortly before delivery and one made before a supplier commitment have different information available. The demand forecasting process explains the handoffs that establish those snapshots.
A US distributor receives two supplied weekly forecasts for one product at one site. Both have a point forecast of 100 units each week and an interval labeled 80%. Forecast A supplies boundaries of 80 and 120; forecast B supplies 60 and 140. These are illustrative supplied values, not distributions fitted from the evaluation rows.
| Week | Actual demand (units) | A interval | Inside A? | B interval | Inside B? |
|---|---|---|---|---|---|
| 1 | 90 | 80–120 | Yes | 60–140 | Yes |
| 2 | 110 | 80–120 | Yes | 60–140 | Yes |
| 3 | 80 | 80–120 | Yes | 60–140 | Yes |
| 4 | 130 | 80–120 | No | 60–140 | Yes |
| 5 | 100 | 80–120 | Yes | 60–140 | Yes |
| 6 | 120 | 80–120 | Yes | 60–140 | Yes |
| 7 | 70 | 80–120 | No | 60–140 | Yes |
| 8 | 100 | 80–120 | Yes | 60–140 | Yes |
| Total | 800 | 6 inside | 8 inside |
Forecast A has coverage of 6 / 8 = 75% and width of 120 − 80 = 40 units. Forecast B has coverage of 8 / 8 = 100% and width of 140 − 60 = 80 units. Its range is twice as wide, so its higher coverage alone does not establish better uncertainty estimates.
Both point-forecast totals are 8 × 100 = 800 units, exactly matching the actual total. That reconciliation proves the total quantities agree; it says nothing about the quality of the intervals. The forecast bias check by SKU and site addresses directional errors separately.
An interval score combines width with a penalty when demand falls outside the range. The Winkler score in Forecasting: Principles and Practice uses the interval's excluded probability to set that penalty. Lower scores are better when comparing the same interval level on the same observations.
Interval score = Width + (2 / α) × Distance outside the interval
Here α = 1 − 0.80 = 0.20, so the multiplier is 10. Distance is zero for an observation inside the interval.
| Forecast | Inside-row scores | Outside-row scores | Total score | Mean score |
|---|---|---|---|---|
| A | 6 × 40 = 240 | 2 × (40 + 10 × 10) = 280 | 520 | 65 |
| B | 8 × 80 = 640 | No outside rows | 640 | 80 |
A misses once above and once below, each by 10 units. Its mean score is 520 / 8 = 65, against B's 640 / 8 = 80. A scores better on this small set despite having lower coverage. Keep the unrounded calculations; the displayed scores here are exact.
Eight weeks cannot establish long-run calibration. Extend the review across comparable periods, inspect seasonal segments and preserve the same eligible rows when comparing suppliers. If only interval boundaries were supplied, describe the result as an interval evaluation, not validation of the entire distribution.
Demand planning owns the forecast definitions and snapshots. Operations checks capacity and replenishment implications. Procurement checks supplier commitments, while finance reviews the cash and margin consequences of alternative demand outcomes. Assign an owner to every exception before the next planning cycle.
The main traps are:
Upload a forecast export and matching actual-demand file or Google Sheet with the supplied interval boundaries, dates and product identifiers. Covirage maps the columns; its tools compute and check the comparisons, and the external AI model explains the results with every figure traced to its rows. Create a free Covirage account, which takes about a minute, and bring a sample of your own data.
See Covirage for supply chain teams for the surrounding workflow.
A point forecast gives one central estimate for a future period. A probabilistic forecast also describes uncertainty around that estimate. Two forecasts can have the same center but very different chances of high or low demand, which matters when reviewing capacity, purchasing and service commitments.
No. The percentage describes the intended long-run coverage under the forecast assumptions. A short evaluation can contain more or fewer outcomes. For discrete demand counts, attainable coverage may also differ from the label because interval boundaries must include whole quantities.
Coverage alone rewards intervals that are unnecessarily wide. Compare coverage with width and an interval score on the same observations. Also inspect misses above and below the interval separately, because those outcomes can have different operational consequences.