Raffles, Deworming, and Statistics

Sometimes statistics can help when it’s hard to decide what to do.
You’re at a local art fair, and they’re raffling off a car worth $10,000. Five hundred tickets are being sold, each for $10. Does it make financial sense to buy a ticket? (For the moment, let’s set aside other questions about raffles and just focus on the benefit for you, the potential ticket-buyer.)
You can use a statistical concept called “expected value” to help you decide. Expected value is calculated by multiplying the probability of each potential outcome by its value, then adding these results together to get the average result of an action.
Let’s figure this out—a car is on the line. First, we multiply the probability of each potential outcome by its value.
We might win the car. Assuming all tickets are sold, the probability of winning the car is 1 in 500, and the value of winning the car is $10,000.
1/500 x $10,000 = $20
We probably won’t win the car. The probability of not winning the car is 499 in 500.
499/500 x $0 = $0
Then, we add the results together to get the average result of an action.
$20 + $0 = $20
Thus, the expected value of purchasing a raffle ticket under the conditions specified above is $20. That $20 represents the average result of buying a raffle ticket. It’s twice the ticket’s cost, making the raffle ticket a pretty good bet. In any one instance, you probably won’t win, but if you repeatedly make these kinds of bets, over time you’re likely to come out ahead.
(One important note that we’ll come back to later: Because it’s an average, the expected value doesn’t indicate what we think will actually happen in any specific instance. In fact, in this case our action of buying a raffle ticket cannot generate the expected value. We cannot win $20. We can win the $10,000 car or nothing.)
You might be saying to yourself: I’m still not that convinced about buying a raffle ticket, but I’m even less sure how this relates to GiveWell’s funding decisions.
GiveWell sorts through hundreds of funding opportunities, looking for the ones that are most cost-effective. We decide among multiple programs that differ from one another, not just in terms of the conditions they treat, the interventions themselves, or the locations they

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