# Base Rates and Base Rate Neglect: The Taxicab Problem Explained > The base rate fallacy is ignoring how common something is when judging a specific case. Learn the taxicab problem, the math, and how to use base rates well. Canonical: https://mentarium.io/mental-models/base-rates.md Mental model 6 min read By [Nemo](https://mentarium.io/about) Updated October 30, 2026 > A **base rate** is how often something happens in a relevant population, before you look at any specific case. **Base rate neglect** (the base rate fallacy) is ignoring that number in favor of vivid case details. Kahneman and Tversky showed it with the taxicab problem, where most people overweight a witness and ignore how few cabs are Blue. - **Category**: Mental model (probability and forecasting) - **Origin**: Daniel Kahneman and Amos Tversky, 1970s - **Best used for**: Forecasts, diagnoses, hiring and any "will this work?" question - **Related**: Probabilistic thinking, expected value, survivorship ## Ask yourself - How often does this kind of thing happen in general? - What is the right reference class for this case? - Am I judging by how well the story fits rather than how common the outcome is? - How much should this specific evidence move me away from the base rate? - What happened to most people who tried exactly this? ## What is a base rate? A base rate is how often something happens in the relevant population, before you know anything about the particular case. If about one in ten restaurants in your area closes within its first year, that is a base rate for “will this new restaurant survive year one?” Base rate neglect, also called the base rate fallacy, is ignoring that number. Given a specific story (a talented chef, a great location), people judge by how convincing the story is and forget to ask how often stories like it end well. The fix is simple to state: start with the base rate, then adjust for the specifics. As a mental model, base rates are your default starting point for any prediction about a case: a hire, a project, a diagnosis, an investment. ## Where it comes from The idea is old (it is built into Bayes’ theorem from the 18th century), but the psychology of ignoring it comes from Daniel Kahneman and Amos Tversky. In the 1970s they showed that people judge probability mainly by representativeness: how much a case resembles a typical example. When a description sounds like an engineer, people say it is probably an engineer, even when told the group contains far more lawyers. Their best-known demonstration is the **taxicab problem**: > A cab was involved in a hit-and-run at night. Two cab companies operate in the city: 85% of cabs are Green and 15% are Blue. A witness identified the cab as Blue. Tested under similar conditions, the witness correctly identifies each color 80% of the time. What is the probability the cab was Blue? Most people answer 80%, the witness’s accuracy. The correct answer is about 41%. Here is why, imagining 100 accidents: - 15 involve Blue cabs. The witness correctly says “Blue” for 12 of them. - 85 involve Green cabs. The witness wrongly says “Blue” for 17 of them (20% of 85). - So “Blue” is said 29 times, and only 12 of those are right. 12 ÷ 29 ≈ 41%. The witness is good, but Green cabs are so common that the witness’s errors on them outnumber the correct Blue calls. Kahneman and Tversky also found that when the base rate was given a causal framing (Green cabs cause more accidents), people used it much more. We ignore statistics but listen to stories. Kahneman later connected this to the “outside view”: forecasting a project by looking at how similar projects went, rather than at the details of yours. That is base rates applied to planning. ## How to use base rates 1. **Name the reference class.** What group does this case belong to? “First-time founders’ startups,” “kitchen remodels in my city,” “candidates hired from referrals.” Pick a class broad enough to have data and narrow enough to be relevant. 2. **Find or estimate the base rate.** Look up data if it exists. If not, estimate from experience and write the number down before reading more details. 3. **Read the specific evidence.** Now look at the case: the résumé, the plan, the test result. 4. **Ask how diagnostic the evidence is.** How much more likely is this evidence if the outcome is true versus false? Weak or common evidence should move you a little; strong, rare evidence can move you a lot. 5. **Adjust from the base rate, not from zero.** Your final estimate should start at the base rate and move toward the evidence. If you land far from the base rate, write down why. This is the backbone of [probabilistic thinking](https://mentarium.io/mental-models/probabilistic-thinking), and it feeds directly into [expected value](https://mentarium.io/mental-models/expected-value) calculations. Mentarium Decision Coach · free Use this with your AI Connect the free Decision Coach to Claude or ChatGPT and it walks you through the Decision Loop, picks the right Model Stack and runs the Bias Radar on your reasoning. [Connect it free](https://mentarium.io/coach) ## 3 real-world examples ### Business Say a team estimates a software migration will take three months. The plan is detailed and everyone is confident. A base rate check asks: how long did the last five migrations of similar size take, here or at comparable companies? If most ran well past their estimates, the honest forecast starts there. This is the cure for the [planning fallacy](https://mentarium.io/biases/planning-fallacy): the details of your plan feel unique, but the base rate knows how plans like yours usually go. (A hypothetical example.) ### Personal life Medical tests are the most important everyday case. Take a hypothetical screening test that catches 90% of true cases and gives a false positive 5% of the time, for a condition that affects 1 in 1,000 people. In 100,000 people, about 90 true cases test positive, but so do about 5,000 healthy people. A positive result means roughly a 2% chance of having the condition, not 90%. This is why doctors follow a positive screen with a second test rather than a diagnosis. ### Investing A stock pitch arrives with a compelling story: visionary founder, huge market, early traction. The base rate question is how often companies with that profile delivered the returns implied by their price. Remember that the stories you hear are filtered: you hear about the winners, which is the [survivorship](https://mentarium.io/mental-models/survivorship) problem. The base rate includes the companies nobody writes about anymore. ## Common mistakes - **Choosing the wrong reference class.** “Restaurants” and “restaurants opened by chefs with prior successful restaurants” have different base rates. Too broad loses relevance; too narrow loses data. - **Ignoring the evidence entirely.** Base rates are a starting point, not a verdict. Strong, specific evidence should move you. - **Treating “this case is special” as evidence.** Every case feels special from the inside. Specialness is what the base rate already accounts for. - **Confusing the two directions.** The chance a test is positive if you are sick is not the chance you are sick if the test is positive. The base rate is what connects them. - **Using a stale base rate.** If conditions changed (new technology, new regulation), last decade’s numbers may no longer apply. ## Base rates vs specific evidence | | Base rate | Specific evidence | |---|---|---| | What it is | How often the outcome happens in the group | Details about this particular case | | How it feels | Abstract, boring, easy to ignore | Vivid, persuasive, memorable | | Kahneman’s term | Outside view | Inside view | | Main risk if overused | Missing what is truly different here | Overconfidence in a good story | | Taxicab problem | 15% of cabs are Blue | Witness says Blue, 80% reliable | | Right role | The starting point | The adjustment | ## The Mentarium take If we could make one change to how people predict outcomes, it would be this: write the base rate down before you read the case. Once you have heard the story, the base rate feels irrelevant, and you will anchor on the details. Writing it first gives the boring number a fighting chance. In the [Mentarium Decision Loop](https://mentarium.io/decision-making/decision-making-process), base rates belong in the Decide step, where you write your prediction and confidence. Your confidence percentage should start at the base rate. If your plan to launch a product says “80% chance of hitting our target” and similar launches hit theirs a third of the time, either you have strong evidence for the gap or your number is a hope. Before any forecast, write three lines: the reference class, the base rate, and what makes your case different. If the third line is empty, your forecast is the base rate. **Counters** [Planning Fallacy](https://mentarium.io/biases/planning-fallacy) ## FAQ ### What is the base rate fallacy? It is the error of ignoring how common an outcome is in general when judging a specific case. People focus on vivid details of the case and treat the background frequency as irrelevant, which leads to confident but wrong probability estimates. ### What is the taxicab problem? A problem used by Kahneman and Tversky: 85% of a city's cabs are Green and 15% are Blue, and a witness who is right 80% of the time says the cab in an accident was Blue. Most people say 80%. The correct answer, combining both numbers, is about 41%. ### What is an example of base rate neglect? Assuming a quiet, bookish stranger is more likely a librarian than a salesperson. There are far more salespeople than librarians, so even if the description fits librarians better, the stranger may still be more likely to work in sales. ### How do you avoid base rate neglect? Start every estimate with the base rate for the right reference class, then adjust for the specific evidence, usually less than feels natural. Writing the base rate down before reading case details helps. ### Is base rate neglect the same as the representativeness heuristic? They are closely linked. Kahneman and Tversky argued that people judge probability by how representative a case seems, by how well it matches a stereotype, and that this is what crowds out the base rate. ## Related models & biases [Mental model Probabilistic Thinking Probabilistic thinking is the habit of treating outcomes as likelihoods rather than certainties: estimating how likely each possibility is, updating those estimates as new evidence arrives, and judging decisions by the quality of the reasoning and the odds at the time, not only by how they turned out.](https://mentarium.io/mental-models/probabilistic-thinking) [Mental model Expected Value Expected value is the average result you would get from a choice if you could make it many times: each possible outcome multiplied by its probability, then added up. It lets you compare risky options on one number, as long as you also check the worst case, since a good average can hide a ruinous outcome.](https://mentarium.io/mental-models/expected-value) [Mental model Survivorship Survivorship, as a mental model, is the habit of asking what is missing from the evidence before you learn from it: the failures, dropouts and dead projects that never made it into view. Its rule is 'always ask for the graveyard', and its classic example is Abraham Wald's WWII analysis of where to armor returning aircraft.](https://mentarium.io/mental-models/survivorship) [Cognitive bias Planning Fallacy The planning fallacy is the tendency to underestimate how long a task will take and how much it will cost, even when you know similar tasks have run over before. People plan from the best-case story of their own project and ignore the track record of projects like it.](https://mentarium.io/biases/planning-fallacy) [Cognitive bias Overconfidence Bias Overconfidence bias is the tendency to be more sure of your judgments, abilities or predictions than the evidence justifies. Researchers split it into three forms: overestimating your own performance, overplacing yourself relative to others, and overprecision, being too certain your beliefs are accurate. It is one of the most studied and most costly biases.](https://mentarium.io/biases/overconfidence-bias) The Mentarium Field Guide 60 mental models, organized by the decision in front of you Each model on one or two pages: when to use it, the questions to ask, an example and the trap. Plus the 25 biases that break decisions and 12 ready Model Stacks. [See Field Guide · $14](https://mentarium.io/shop/field-guide) The Mentarium Field Guide 60 mental models, organized by the decision in front of you [See Field Guide · $14](https://mentarium.io/shop/field-guide)