Ranking well is not the same as being right
Most classification models output a number between zero and one, and everyone treats it as a probability. Often it is not. It is a score that ranks cases correctly while being systematically too high or too low in absolute terms.
For ranking-only uses - call the top 200 leads - that is fine. The moment the number is multiplied by anything, it stops being fine.
Where uncalibrated scores cost money
Any expected-value calculation uses the probability directly. Expected value equals probability times value, so an error in the probability flows straight into the decision.
- Deciding whether to chase an invoice based on recovery probability times amount
- Setting a credit limit from default probability
- Choosing whether to send an engineer based on failure probability times downtime cost
- Pricing anything where risk is a component
- Deciding whether a human should review a case
Illustrative arithmetic: if a model says 30% but the true rate among such cases is 10%, every expected value built on it is roughly three times too high, and the decisions that follow are wrong in a consistent direction.
Checking calibration
The check is straightforward. Group predictions into bands, and for each band compare the average predicted probability against the actual observed rate.
| Predicted band | Average prediction | Actual rate | Reading |
|---|---|---|---|
| 0-20% | 0.10 | 0.09 | Well calibrated |
| 20-40% | 0.30 | 0.18 | Over-confident |
| 40-60% | 0.50 | 0.35 | Over-confident |
| 60-80% | 0.70 | 0.52 | Badly over-confident |
Plotted, this is a reliability diagram, and a perfectly calibrated model sits on the diagonal. Deviations show where the numbers cannot be taken at face value.
Fixing it
Calibration is corrected by fitting a simple adjustment from raw score to true probability, learned on data the model did not train on. It does not change the ranking, so nothing about the model's discrimination is lost - only the scale is corrected.
Some model families are better calibrated out of the box than others. Ensembles of trees are often over-confident at the extremes; models trained with heavy class rebalancing are almost always miscalibrated, because the training distribution no longer matches reality.
That last case is worth remembering. If you rebalanced your data to handle rare events, your probabilities need correcting back before they mean anything.
Say what the number means
Where a score is shown to staff, state plainly whether it is a probability or a rank. People reasonably assume 80% means eighty per cent, and will make decisions accordingly.
If it is only a ranking, present it as a band - high, medium, low - rather than a number that invites arithmetic nobody should be doing.
If a number is going to be multiplied by money, it had better be a real probability.