Imagine you take a medical test that's 99% accurate, and it comes back positive for a rare disease. How worried should you be? Most people—including many doctors—assume the answer is very worried. After all, 99% accuracy sounds nearly perfect.

But here's the uncomfortable truth: if the disease is rare enough, that positive result is probably wrong. This isn't a flaw in the test. It's a flaw in how we instinctively think about probability. Understanding this error could change how you interpret medical results, news statistics, and risk assessments for the rest of your life.

Before any test is performed, there's already a probability that you have a condition. This is called the base rate or prior probability. If a disease affects 1 in 10,000 people, your baseline chance of having it—before any testing—is 0.01%. This number matters enormously, yet our brains consistently ignore it.

When we hear about test accuracy, we focus entirely on that impressive-sounding percentage. A 99% accurate test feels like a guarantee. But accuracy describes how the test performs given that you have or don't have the condition. It doesn't tell you the probability you're sick given a positive result. These are completely different questions, and confusing them is the heart of base rate neglect.

Think of it this way: if you're searching for a needle in a haystack, even an excellent metal detector will beep at some pieces of straw. When needles are rare and straw is abundant, most beeps won't be needles—no matter how good your detector is. The rarity of what you're looking for shapes the meaning of every positive signal you receive.

Takeaway

Always ask 'how common is this?' before interpreting any test result or statistic. The background frequency of an event determines how much a single data point should shift your beliefs.

Let's work through a concrete example. Suppose a disease affects 1 in 1,000 people, and a test is 99% accurate—meaning it correctly identifies 99% of sick people and correctly clears 99% of healthy people. You test positive. What's the chance you're actually sick?

In a group of 1,000 people, about 1 person has the disease. The test will almost certainly catch them (99% sensitivity). But of the 999 healthy people, 1% will get false positives—that's roughly 10 people. So you have about 11 positive results total: 1 true positive and 10 false positives. Your chance of actually being sick is only about 9%, not 99%.

This is the false positive paradox. When a condition is rare, even highly accurate tests produce more false alarms than true detections. The math is counterintuitive but inescapable. Medical professionals who ignore this routinely overestimate disease likelihood, leading to unnecessary anxiety, additional invasive tests, and sometimes harmful treatments for conditions patients never had.

Takeaway

A positive test result for a rare condition is often wrong, even when the test is highly accurate. Before panicking, calculate how many false positives you'd expect among all the healthy people tested.

Bayesian reasoning offers a framework for updating beliefs correctly. You start with a prior probability (the base rate), encounter new evidence (the test result), and calculate a posterior probability that accounts for both. You don't need complex formulas—a simple mental habit works: always consider how common something is before interpreting evidence about it.

When evaluating any claim or result, ask two questions. First: what's the base rate? How often does this happen in general? Second: how much should this specific evidence shift my estimate? A single witness claiming to see a crime might seem convincing, but if the accused behavior is extremely rare, you need stronger evidence to overcome that prior improbability.

This applies far beyond medicine. Rare interview candidates who seem perfect might just be good at interviewing. Unusual stock picks that back-tested well might be flukes among thousands of tested strategies. Dramatic news stories feel common because they're selected for drama, not because the underlying events are frequent. Training yourself to mentally supply missing base rates is one of the most practical reasoning skills you can develop.

Takeaway

When encountering surprising evidence, pause and estimate the base rate before updating your beliefs. Ask: 'How common is this, and does this evidence truly justify a dramatic shift in probability?'

Base rate neglect isn't just an academic curiosity—it's a thinking error with real consequences in medicine, law, and everyday judgment. Our intuitions about probability systematically fail when rare events are involved.

The antidote is simple but requires practice: before interpreting any test, claim, or piece of evidence, ask about the background frequency. How common is this? That single question can save you from the statistical trap that catches even experts.