Expected Value
Thinking
The scratch card promises a jackpot. You buy one on a whim, then another, then make it a daily habit on the way to work. A year later you've spent hundreds of pounds and won back twelve.
What is Expected Value Thinking?
Expected Value Thinking is a decision-making tool that has you weigh each possible outcome by both its payoff and its odds, then compare the totals. For each option you multiply the value of an outcome by the chance it happens, and add those products across every outcome. The total, called the expected value, tells you what a choice is worth on average if you faced it many times over. The size of a possible prize alone never tells you whether a choice is worth it, because a tiny chance of a big win can still be worth almost nothing once you account for the odds.
Many decisions involve uncertainty, and the mind tends to fix on the best case or the worst case rather than the weighted average of all of them. A bright jackpot or a frightening risk grabs your attention out of proportion to how likely it is. Putting the probability into the calculation pulls the decision back to reality, so you stop being dazzled by big numbers and stop being scared by unlikely ones.
How to use it
Run a choice through five steps. Rough, honest numbers work better than precise, wishful ones.
- List the possible outcomes of the choice.
What could actually happen if you go ahead? - Estimate the payoff of each outcome.
Put a value on each in money, time, or whatever matters. Gains count as positive, losses as negative. - Estimate the odds of each outcome.
Give each a rough probability. They needn't be exact, only honest. - Multiply each payoff by its odds and add them up.
The total is the expected value of that option. - Compare options by expected value and prefer the higher one.
Use the same steps again for choices you face often.
Worked example
You're buying a £400 washing machine, and at the till the shop offers an £80 extended warranty for three years beyond the standard guarantee. Rather than deciding on the fear of a costly breakdown, you work out the expected value. A machine like this fails in that window maybe once in ten times, and a repair would cost around £150. So the warranty's expected payout is about a tenth of £150, roughly £15.
You're being asked to pay £80 to cover an average loss of £15, so you decline the warranty and keep the difference. The occasional machine will break and cost you the repair, yet across all the appliances you'll ever buy, turning down these warranties leaves you clearly better off. The expected value made the right call obvious where the fear of a breakdown would have pushed you the other way.