# Base Rate Error

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# TL;DR

`Specific information can lead us to dramatically wrong conclusions if we don't account for base rates as the context.`

When we encounter specific information, we quickly ignore the general information we need to interpret the specific one correctly.

Assume you observe a person to be introvert and you're asked if that person rather is a librarian or a sales person. Since librarians tend to be more shy than salespeople, most would say that, given the specific information of introversion, the person more likely is a librarian.

However, if we now add in the fact that, overall, there exist 20x as many salespeople as librarians (base rate), what should this information change?

It says that in order for the specific person to more likely be a librarian, introversion must be at least 20x as prevalent among librarians as among salespeople.

Put into numbers, this becomes clearer: Assume there exist 1,000,000 salespeople and 50.000 librarians. We rightly expect librarians to be much more introvert on average than salespeople. So let's say that 50% of librarians are introvert — but only 5% of salespeople. This means that there exist 25,000 introvert librarians and 50,000 introvert salespeople.

Now, again, how likely is it that the introvert person you observe is a librarian? Only half as likely as that it's a salesperson (25,000 / 50,000).

As soon as we factor in the base rate of the total number of introvert librarians and introvert salespeople, our specific observations of introversion needs to be looked at differently.

The same principle is at play if we put hospitalization statistics (specific information) in the context of the general population (base rate) as we will arrive at very different conclusions of health risks.

Assume that you observe that 50% of hospitalized Covid patients are vaccinated (specific information). Without knowing the % of vaccinated people in the general population, we can't assess the information properly. If 80% are vaccinated and 20% are unvaccinated (base rate), this means that being unvaccinated makes it 4x as likely to get hospitalized — although you can observe equally as many hospitalizations among vaccinated people.

The *Base Rate Fallacy* plays a huge role in policy making, law, finance, entrepreneurship and any other probability- or frequency-based decision making. The overestimation of specific prevalent information can lead to dramatically wrong conclusions. On the same note, understanding base rates and their impact on the interpretation of observations can make one more immune against misleading news and media stories.

# Go Deep

You can find a great and easy to understand primer on the Base Rate Fallacy, including real life examples, at The Decision Lab.

For a more general, yet slightly more mathematical and statistical description of Base Rate Errors, check out Wikipedia.

Two short videos that will help you understand how the Base Rate Error comes to life in different situations can be found here and here.

For a deeper dive (incl. resources) into rational thinking and reasoning, check out this MindVault post on Bayesian Thinking.

# Go Beyond

A few further resources you might like if you find above idea interesting:

(Book) Daniel Kahnemann: Thinking, Fast and Slow

(Book) Jonathan Evans: Thinking & Reasoning: A Very Short Introduction

(YouTube channel) Crash Course: Statistics

(Podcast) David McRaney: You Are Not So Smart

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