Expected value explained: a simple way to make better decisions
Should you take the safe option or the risky one? Expected value (EV) gives you a way to compare. It is just multiplication and addition, and you can use it on everything from games to career choices.
The idea in one line
For each possible outcome, multiply how good it is (its value) by how likely it is (its probability). Add those up. The total is the expected value.
Example: you can take a sure $20,000, or a 30% chance at $100,000. The risky option has an EV of 0.30 x $100,000 = $30,000. On average, it is the better bet, as long as you can handle the 70% chance of getting nothing.
Judge the decision, not the result
Poker player Annie Duke calls the opposite mistake "resulting": judging a choice only by how it turned out. Results come from decision quality plus luck. Someone who drives drunk and gets home safely made a bad decision with a good outcome. A well-researched investment that fails may have been a good decision with bad luck.
Studies show we do this all the time. People rate the exact same decision as better when the outcome was good (Baron and Hershey, 1988).
A 2x2 you can use after any big choice
- Good decision, good outcome: earned reward. Keep doing it.
- Good decision, bad outcome: bad luck. Do not change much.
- Bad decision, good outcome: dumb luck. This is the most dangerous one, because it teaches you the wrong lesson.
- Bad decision, bad outcome: just deserts. Learn from it.
When not to rely on EV
EV works best when you get to make many similar bets. Be careful when one bad outcome would be a disaster you cannot recover from, such as losing money you need for rent. In those cases, avoid the risk even if the math looks good.
Plug your own numbers into the free EV and odds calculator.
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Sources
- Duke, A. (2018). Thinking in Bets. Portfolio.
- Baron, J., and Hershey, J. C. (1988). Outcome bias in decision evaluation. Journal of Personality and Social Psychology.