Expected Value

When we’re uncertain about how our decisions will play out, it’s helpful to consider the expected value of our actions – or, the average outcome of all possibilities, according to their likelihood. In some sense, it can provide an idea of what we should “expect on average” from an uncertain risk we’re about to take. And since almost all meaningful decisions are made with some uncertainty about their outcomes, considering expected value can help us improve our decision making in the real world.

Deciding under uncertainty

When making decisions, we rarely know everything that is relevant to the outcomes of our choices. This is true even in small decisions we make every day, like whether to ride a bike or catch a bus in the morning. We might not know how much traffic there will be today, or whether it will rain on the way back – both of which might affect our decision. But these uncertainties become even more important in large decisions, like which career path to pursue.

Imagine you’re considering two career paths. The first option you’re considering is computer programming. Based on some small coding projects you’ve worked on, you’re fairly confident that you’d be a decent programmer. You’d also be able to get a job and have a very respectable salary. Even more importantly, you’d be able to contribute to almost any cause through your direct work. Still, you don’t think you’re an exceptionally good programmer that would revolutionize the field you work in.

The second option you’re considering is becoming a singer/songwriter. On this path, there’s a pretty good chance you’ll end up with no money and no work experience after a while. However, there’s some small chance you’ll become a world-famous star, achieving incredible fame and enormous amounts of money (allowing you to donate a significant portion of it to charity). Given the uncertainty inherent to this kind of decision, you don’t know which option will end up having a better outcome. How can you still intelligently make such a decision? Should you choose the path with the opportunity for the best possible outcome? Or perhaps a “safe bet” that performs well even if things go badly?

Calculating expected values

Expected values are a tool in statistics that captures what the outcome will be “on average” when we can’t predict something with certainty. To calculate an action’s expected value, we take the possible consequences of an action, work out how valuable they would be, multiply them by their probability of happening, and then add them all together.

For example, imagine that you could buy a lottery ticket for $1 that has a 1% chance of winning $50. Buying the ticket has an expected value of minus 49 cents. This is because the 1% of $50 is only worth 50 cents, but the 99% of losing a dollar is worth minus 99 cents. Therefore, it may not be a great investment… you probably shouldn’t buy the ticket.


Most decisions we make are more complicated than whether or not to buy lottery tickets. It can be hard to identify or define the exact value of different outcomes (how much more would you enjoy being a pop star than a programmer?). It can also be challenging to know the exact probabilities involved (how likely are you to succeed in show business given your skills and personality?).

Despite the complexity, we still need to make decisions under uncertainty. It’s often the case that what you can measure is only an instrumental tool for assessing what you actually care about.

For example, most people want more money, but that money only matters to us because it can make us and others happier. In these cases it might make sense to be risk averse, prioritizing certainty in an outcome even at the expense of a lower expected value. However, if we’re evaluating what we truly care about or truly scalable projects with little diminishing returns, there is a strong case to be made for using expected value estimates when faced with uncertainty.

Additional resources