Base Rate Neglect

A test for a rare disease is 99% accurate. You test positive. What’s the probability you have the disease? Intuition says 99%. But if the disease affects 1 in 10,000 people, the math says otherwise. Among 10,000 tested, roughly 1 has the disease (true positive) and 100 test falsely positive (1% error × 9,999 healthy). You’re one of 101 positive tests, and only 1 has the disease: less than 1% probability.

This is base rate neglect: ignoring how common something is in the population when evaluating evidence about individuals. The test accuracy matters, but so does how rare the condition is. Evidence must be weighed against prior probability — and we systematically fail to do this.

Daniel Kahneman and Amos Tversky documented this extensively. People judge profession by stereotype match, ignoring how many engineers versus lawyers exist. They judge risk by vividness, ignoring how often the vivid outcome actually occurs. The available, salient, specific overwhelms the abstract base rate.

The mechanism is substitution. Answering “how likely is this specific evidence given this hypothesis?” is easier than answering “how likely is this hypothesis given this specific evidence?” We substitute the easy question for the hard one. But the hard question is the one we actually need to answer, and it requires the base rate.

Base rate neglect explains persistent errors. Fear of plane crashes despite their rarity (vivid examples overwhelm statistics). Overconfidence in pattern-matching despite low base rates for the pattern. Medical overtesting because positive tests seem compelling regardless of disease prevalence.

The practical correction is Bayesian: always start with how likely something was before the evidence, then update based on how strongly the evidence points. Strong evidence from an accurate test can still leave you with low probability when the base rate is low enough. Prior probability isn’t just context — it’s the foundation of rational inference.