If something might go well or badly, think about how good each result is and how likely it is. Then pick the choice that comes out best on average.
Expected value means multiplying each possible result by its chance of happening, then adding them up. It lets you compare choices fairly when you can't be sure how they'll turn out.
Expected value is the probability-weighted sum of outcomes. Use it to compare options under uncertainty, then check two things it hides: the spread of outcomes (risk of ruin) and the quality of the probability estimates.
The idea
You can't know how a choice will turn out. You can estimate how likely each outcome is and what each would be worth. Multiply each value by its probability, add them up, and you have the expected value. Do that for every option and compare.
A worked example
A service desk is deciding whether to let a model auto-close password reset tickets. The numbers below are illustrative.
| Outcome | Probability | Value per ticket |
|---|---|---|
| Closed correctly | 0.95 | +£4 (agent time saved) |
| Closed wrongly, user reopens | 0.05 | −£12 (extra handling and annoyance) |
Expected value per ticket = (0.95 × £4) + (0.05 × −£12) = £3.80 − £0.60 = £3.20.
At 2,000 tickets a month, that's about £6,400 a month in favour of auto-closing, if the estimates hold.
Where it misleads
It hides the spread. Two options can have the same expected value while one occasionally produces a disaster. If one wrong decision could cause a data breach or a safety incident, expected value alone isn't enough. Set a hard limit on the worst case and only compare options that stay inside it.
It's only as good as the probabilities. "0.95" above is a guess until you've measured it. Run a small trial, count the results, and update. The page on calibration covers how to check your estimates.
Using it at work
You rarely need precise numbers. Rough estimates, written down, beat a debate where nobody states what they believe. The value of the exercise is that everyone can see the assumptions and argue about the right ones.