Probability vs Expected Value
Expected value combines the probabilities and sizes of outcomes. A high chance of being right can still produce an expected loss when the occasional downside is large.
THE IDEA
Probability vs Expected Value
A common mistake in decision-making is to focus on how likely an event is to occur, ignoring the magnitude of the outcome. The table below illustrates this:
| Event | Probability | Outcome | Expectation |
|---|---|---|---|
| Market goes up | 70% | Up 1% | 0.7 |
| Market goes down | 30% | Down 10% | -3.00 |
| Total | -2.3 |
Despite a 70% chance of a positive outcome, the expected value is negative due to the large downside. Taleb criticizes judging a strategy only by how often it is right, without measuring its gains and losses. "Bullish" or "bearish" are terms used by those who do not engage in practicing uncertainty, like television commentators. Investors and businesses are paid in dollars, not probabilities. Thus, one should consider the magnitude of the outcome, not just its likelihood.
When to use it
Evaluating investment opportunities by calculating expected value rather than just probability of profit.
Strategic business decisions where high-impact, low-probability events (e.g., black swans) need to be weighted properly.
Insurance pricing: premiums are set based on expected losses, not just the chance of a claim.
Project risk management: assessing both the likelihood and impact of risks to prioritize mitigation efforts.
FROM THEORY TO EVERYDAY LIFE
In practice
Startup Investment
Suppose a startup has a 10% chance of a 100x payoff, while a bond has a 90% chance of a 5% gain. The products (10% × 100 = 10) and (90% × 0.05 = 0.045) describe only the stated successful outcomes. They are not complete expected net returns: the other outcomes are missing, and a payoff multiple must be put on the same basis as a net return before comparison.
Market Commentators
TV analysts often boast about their high prediction accuracy (e.g., 70% correct), but their recommendations may lead to large losses when they are wrong. Their success is tied to frequency, while investors care about net profit.
A MOMENT TO REFLECT
Put it to work.
Think of a recent decision where you focused on the likelihood of success rather than the potential payoff. How might changing your perspective alter the outcome?
Consider an investment with a 90% chance of a small gain and a 10% chance of a catastrophic loss. Is the expected value positive? What factors should you consider?
Why do television commentators and market strategists emphasize accuracy over expected payoff? How does this misalign with investor interests?
CONTINUE THE CONVERSATION
Source texts
- Fooled by Randomness The Hidden Role of Chance in the Markets and in Life (Nassim Nicholas Taleb)