Concept
Read expected value as a weighted average of possibilities
An expected outcome need not be an outcome that ever occurs once.
When it fits
- A model gives one expected result for a decision with several possible outcomes.
When to avoid it
- Expected value alone does not determine a sensible personal or safety-critical decision.
The idea
Multiply each possible outcome by its probability and add the products. Then inspect the actual possibilities as well as their average. A low expected cost can coexist with a rare loss that is unacceptable to the person bearing it.
An example
An invented process with a 90% chance of zero rework and a 10% chance of 100 minutes has expected rework of 10 minutes, though neither run takes exactly 10.
Check your result
The expectation is accompanied by its assumptions and important tail outcomes.
Keep this limit in mind
- Expected value alone does not determine a sensible personal or safety-critical decision.
Connected ideas
Useful withPut variation beside the average
Evidence and sources
A discrete expected value is the sum of possible outcomes weighted by their probabilities, and it need not be a possible single outcome.
An expectation does not describe tail risk, affordability of a loss or the reliability of the probabilities.
Introductory Statistics 2e, 4.2: Mean or Expected Value and Standard Deviation · Expected-value definition