Base Rates, Base Rate Fallacy, and Bayes Theorem
A Base Rate is a type of probability that describes the likelihood of an event when no new or more specific information is available.
Another way to think about it is that Base Rates cover the general or usual chance that something will (or will not) happen, as opposed to recent or more specific information that may alter the probability for the event.
The key idea is that Base Rates cover what usually happens if nothing new or interesting occurs to impact the outcome.
Base Rate Neglect or Base Rate Fallacy refers to our tendency to ignore data about what usually happens and instead focus just on new, recent, or interesting information.
Bayes Theorem is a mathematical equation where you can input the Base Rate for an event along with the probabilities associated with new information to get the actual overall probability for the event.
- The average high temperature for New York City in the month of October
- How many people have a particular disease, on average
- How many breakdowns a particular brand of automobile tends to experience
- The percentage of people that are medical professionals
Why It Is Useful
Base Rates are the single most useful probability number you can use when trying to predict an outcome.
Case 1: If you know that the average high temperature for NYC in October is 64 degrees (Fahrenheit), that's typically a better predictor of what tomorrow will be like than what the local weather person predicts.
64 degrees is what usually happens, and the forecast can slide your assessment of what the temperature will be up or down a bit, but you should always start with the Base Rate of 64 degrees first and then move from there.
Case 2: Let's say 1% of the population of The Known World has Greyscale.
Let's also say that there's a test for Greyscale that is 80% accurate. It detects people with Greyscale with 100% accuracy but it also generates a false positive 20% of the time for people that don't have Greyscale.
Now let's imagine you are tested and show as positive for Greyscale. What are the odds you actually have it?
The answer is not 80%. Remember the Base Rate, which is that 1% of all people have Greyscale. That is where you start. You then apply the results of the test to that 1% and slide upwards, at which point the actual odds of you having Greyscale are less than 5% (see the Wikipedia explanation with these same numbers here).
If you read the example above and came up with an 80% probability of having Greyscale, then you suffer from Base Rate Neglect (as do I, along with the rest of humanity).
Case 3: Let's say you see a person wearing a doctor's coat and a stethoscope, but you also know that only 1% of the population are doctors. What are the odds this person is a doctor?
As usual, you start with 1% and work upwards based on the evidence you see.
Are you in a hospital, at a party, or just walking down the street? Each bit of evidence you see can move your assessment upwards a little or a lot, depending on the weight you assign to that evidence.
If you start with the Base Rate though, your assessment will be better than that of most other people.
How It Fits Into The Latticework
Base Rates can help you predict the outcomes of a wide range of events.
It should be paired with other types of probability though, such as Expected Value and the Law of Small Numbers.
It can also be used to defend against Cognitive Biases, including our tendency to focus on individual stories and anecdotes.
For example, think of the person who drinks, smokes, and eats fast food all day yet cites his uncle who lived to 101 on the same diet. This is someone who should have started with a Base Rate before using his uncle as evidence ...
Also, Base Rates are directly related to the Outside View as described by Daniel Kahneman and Amos Tversky.
Read about Base Rates and Base Rate Fallacy, and then read about Bayes Theorem (see below).
Then practice trying to determine what the Base Rates would be for various events.
Think about upcoming sporting events and political elections and see if you can pick out the variables that are actual Base Rates that indicate what usually happens.
- Wikipedia: Base Rates, Base Rate Fallacy, and Bayes Theorem
- Book: Think Bayes by Allen B. Downey
- Book: Thinking Fast And Slow by Daniel Kahneman
Please share your thoughts on this Mental Model or the post itself in the comments below!
Great post. Loving this new format and breakdown!!! Keep it up!
Great explanation, Andrew. Thanks!
Think Bayes is great. The book is available for free from the publisher here: