What is Improbable is Probable
Rare events are not as surprising as they seem because given enough opportunities, even highly improbable events will occur. This principle explains why streaks of lucky guesses are often mistaken for skill.
THE IDEA
Once you’ve truly absorbed this fundamental truth, the Baltimore stockbroker has no power over you. That the stockbroker handed you ten straight good stock picks is very unlikely; that he handed somebody such a good run of picks, given ten thousand chances, is not even remotely surprising. In the British statistician R. A. Fisher’s famous formulation, “the ‘one chance in a million’ will undoubtedly occur, with no less and no more than its appropriate frequency, however surprised we may be that it should occur to us.”
When to use it
Evaluating investment advisors' track records
Assessing the significance of clinical trial results
Understanding the probability of coincidences in everyday life
Distinguishing skill from luck in sports statistics
FROM THEORY TO EVERYDAY LIFE
In practice
Stockbroker's Lucky Streak
A stockbroker gives you ten straight good stock picks. While the probability of that happening by chance to you is very low, given that many brokers give many picks, it is almost certain that some broker will have such a streak.
Lottery Winner Surprise
The odds of winning the lottery are millions to one, yet someone wins every drawing. The surprise that 'it happened to me' is a misunderstanding of probability over many trials.
A MOMENT TO REFLECT
Put it to work.
How can you tell the difference between a genuinely skilled stock picker and one who is just lucky?
What are some real-world situations where you might mistake a rare event for something meaningful?
Given the law of large numbers, why should you be skeptical when someone claims to have a perfect track record?
Often confused with
References
- Statement on improbable events — Ronald A. Fisher
CONTINUE THE CONVERSATION
Source texts
- How Not to Be Wrong The Power of Mathematical Thinking (Ellenberg, Jordan)