Accuracy & evaluation
Prediction intervals: reading p10, p50, and p90
A prediction interval is a range the future value is expected to fall in, not a promise. p50 is the middle path; p10–p90 is a band for planning stock, staff, and cash without pretending the future is a single line.
Updated Aug 14, 2026·8 min read
Not a confidence interval
A confidence interval is about a mean. A prediction interval is about a new observation. Next Tuesday’s orders are a new observation. Warehouses do not stock means. They stock milk.
People collapse the two because both have bands. Then they are surprised when actuals sit outside a 95% interval more than 5% of the time. That is a calibration problem, or a mix-up of which interval they were looking at.
p10 · p50 · p90
p10, p50, p90
p50 is the middle path — a median, not a promise. p10 is a low plan. p90 is a high one. If the model is calibrated, about 10% of similar days fall below p10 and 10% above p90. Teams use p90 as “don’t stock out” and p10 as “don’t drown.” That is the product.
Quantile forecasts can be trained with pinball loss, or read off samples. The serving contract is what matters: can you get the percentiles out of the API, or only a center line someone screenshot?
How ops actually uses the band
- Inventory: p50 for the buy, p90 for a promo weekend.
- Staffing: median for the roster, p90 for the on-call list.
- Energy: high quantiles for reserve, not the average load.
The band should widen as the horizon grows. Uncertainty compounds. A skinny fan at week 12 is swagger. Ask to see coverage: do 80% of actuals land in the 80% band? If 99% do, you are too wide to plan. If 40% do, you are decorating.
Is the band honest?
Plot coverage by horizon and by volume. Models often look calibrated in the middle and wild on the A items. Recalibrate if you must — conformal methods exist — but first check whether the world moved and the champion did not.
FAQ
- What is a prediction interval in forecasting?
- It is a range attached to a future point: 'we expect Tuesday's orders between 820 and 1,140, with 900 as the middle.' It describes uncertainty about a new observation, not uncertainty about a model's average.
- What do p10 and p90 mean?
- Roughly: 10% of similar days should fall below p10, 10% above p90, if the model is calibrated. p50 is the median path. Teams use p90 as a 'don't stock out' plan and p10 as a 'don't drown in inventory' plan.
- Why is the band so wide at the far horizon?
- Because uncertainty compounds. A calibrated model gets less sure as it looks further out. A skinny band at week 12 is often a model that has not been told it can be wrong.
Keep going
Guide
Anomaly detection for business metrics
A fixed threshold treats every Tuesday like every Saturday. A forecast band asks whether today is weird given what the series usually does at this clock. That is the difference between an on-call fire drill and a useful alert.
Guide
What-if analysis for forecasts
A what-if is a second forecast under a change you control — price up 8%, a promo pulled, a plant offline. You compare paths, not opinions. The point is not a perfect simulation; it is catching the decision that only looks cheap this week.
Guide
Choosing a forecast horizon
The horizon is how far ahead the forecast looks; the grain is how finely it ticks. Pick both from the decision they serve — lead time, planning cycle, and how fast the world can change — not from what the model can print.
Use case
Inventory and replenishment forecasting
See future stock positions, shortage risk, and excess inventory across products and locations.
Use case
Energy load forecasting
Forecast demand by interval, feeder, zone, and customer class with weather-driven uncertainty.