A system described as 90 percent accurate sounds reassuring. Whether its warnings deserve confidence depends on what that percentage measures and how common the underlying event is.
The starting frequency is called a base rate. It is easy to overlook when a vivid story or a strong-looking signal captures attention. Tversky and Kahneman’s research examined how judgments based on resemblance can neglect the prior frequency of possible outcomes. [1]
Begin with a population you can count
Consider an entirely hypothetical quality-control system examining 10,000 components. Exactly 1 percent, or 100 components, are defective. Suppose the system correctly flags 90 percent of defective components and mistakenly flags 10 percent of good ones.
It flags 90 genuinely defective components. But there are 9,900 good components, so the 10 percent false-positive rate produces 990 false alarms. The system issues 1,080 warnings in total. Only 90 are correct, making approximately 8.3 percent of flagged items genuinely defective.
The arithmetic does not contradict the stated detection rate. The two percentages have different denominators. Detecting 90 percent of defective items is not the same as having 90 percent of warnings identify defects correctly.
Name the metric before relying on it
In classification, recall measures the share of actual positives detected; precision measures the share of positive predictions that are correct. Google’s technical guidance explains why overall accuracy can be misleading when one class is much less common than the other. [2]
In the example, the system has found most defects, but it has also created substantial inspection work. Whether that tradeoff is acceptable depends on the cost of a missed defect and the cost of checking a false alarm. The calculation supplies information; it does not select the business objective.
Now imagine reducing the false-positive rate from 10 percent to 1 percent while retaining the same detection rate. The system would flag 90 defects and 99 good components. Approximately 47.6 percent of warnings would then be correct. That is a major improvement, but still different from 90 percent.
Use relevant base rates
A base rate is only useful if its population fits the decision. A defect rate for one factory, material, or production process should not automatically be applied to another. A recent process change may also make an older average a poor starting point.
Ask where the number came from, what cases were included, and whether the current case belongs to that group. Starting with a base rate does not mean ignoring specific evidence. It means making the initial assumption explicit before deciding how much the new evidence should change it.
When the relevant frequency is uncertain, examine several plausible starting values. If a conclusion changes dramatically across a reasonable range, the uncertainty belongs in the decision rather than being hidden behind a single estimate.
Connect the signal to an action
Google’s explanation of classification thresholds makes a related point: changing the threshold changes which cases are flagged and the balance between missed positives and false alarms. The appropriate setting depends on the task and consequences. [3]
For the quality-control example, a warning might trigger inspection rather than automatic rejection. That response allows the system to be useful without treating every signal as a final judgment.
Whenever a probability sounds persuasive, ask what group it describes and what the denominator contains. Clear reasoning begins by identifying the population behind the percentage and the action that the evidence can reasonably support.
Sources
Research, reflection, and a wider perspective.
