Reading a Probability
By the end of this module
- Separate calibration from accuracy, and say which one a threshold needs
- Read a reliability chart and judge whether a model is calibrated
- Name the three situations where a well-calibrated number is still not enough to act on
Definition
The previous module ended on a number and a warning: a calibrated 0.90 is a claim about a population of decisions, not about the one in front of you. This module is about what you can and cannot do with that.
Two properties get confused, and they are independent. Accuracy is how often the model is right. Calibration is whether its stated confidence matches how often it is right. A model can have one without the other, and the one a threshold depends on is calibration.
Calibration and Accuracy
| Model | What it looks like | Can you threshold it |
|---|---|---|
| Calibrated and accurate | Right most of the time, and its confidence tracks how often. | Yes, and the threshold means what it says. |
| Calibrated, less accurate | Often unsure, and honest about it. Says 0.6 and is right about 60% of the time. | Yes. Fewer cases clear a high bar, but the ones that do are trustworthy. |
| Accurate, not calibrated | Right 95% of the time and says 0.99 on everything, including what it gets wrong. | No. There is no cut that separates the wrong answers from the right ones. |
The third row is the one worth sitting with. A model that is right 95% of the time but says 0.99 every time is useless for routing, because there is no number you can set a threshold at that separates the cases it will get wrong from the cases it will get right. Accuracy without calibration gives you a good average and no way to act on an individual case.
Reading the Bands
Below are 100 past decisions on whether a refund request was within policy, grouped by the confidence the model stated at the time, with what actually turned out to be true. Compare the pairs of bars before touching the slider.
Everything is accepted, including the least confident band. 19 of 100 went through wrong, and nobody saw them.
In each band the two bars are close. That is the whole claim: among the decisions where it said 0.90 or more, it was right 94% of the time. Nothing here says the model understood a single request, and nothing here tells you whether the next one will be right. It tells you the rate you are buying.
Choosing a Threshold
Now move the slider. Every position is a position on one trade, and the panel reports both sides of it rather than the flattering one.
Accept everything and 19 wrong decisions go through with nobody looking. Accept only the top band and the wrong ones drop to 2, but 66 decisions now need a person, most of which the model would have got right. There is no setting that reduces both. Picking one is a judgement about which error is more expensive, and that judgement belongs to whoever owns the consequences, not to whoever owns the model.
Where the Number Stops Helping
Three situations defeat a well-calibrated probability. None of them is a defect in the model.
| Situation | Why the number is not enough |
|---|---|
| A rare and costly case | If serious fraud is one request in ten thousand, a threshold tuned on the other 9,999 will wave it through at high confidence. Rarity, not the model, is what beats you, and the fix is a separate check rather than a higher number. |
| Asymmetric cost | A 5% error rate is fine when the wrong answer is a mildly annoyed customer and unacceptable when it is a payment that cannot be recalled. The same number supports opposite decisions, which is why the threshold is a business choice. |
| Input unlike the fitted data | Calibration is fitted on a distribution. A new product, a new market or an upgraded model moves the inputs, and confidence stays confident while becoming wrong. Nothing in the output signals this, so it has to be rechecked on a schedule. |
A model is right 95% of the time and returns a confidence between 0.97 and 0.99 on every case, correct or not. You want to auto-approve the easy ones. What do you have?
Discussion
Take the decision the room picked at the end of the last module. Ask which error costs more: letting a wrong one through, or sending a right one to a person. Then ask who in the organisation would have to agree to the answer before a threshold could be set.