Expected value is a way to describe the average result implied by a probability estimate and a quoted price over many repeated examples. It is a mathematical comparison, not a prediction, recommendation, or guarantee. Readers should also review Bettista’s methodology and safer-gambling guidance.
The basic formula
For a two-outcome example, expected value can be written as EV = (probability of the outcome x net return) – (probability of the other outcome x amount at risk). Using decimal prices, the same comparison can be expressed per unit as EV = (probability x decimal price) – 1. The formula is only as reliable as the probability estimate supplied to it.
A neutral example
Suppose an analyst assigns a 55 percent probability to an outcome and the quoted decimal price is 1.90. The calculation is 0.55 x 1.90 – 1, which produces 0.045, or 4.5 percent per unit before any other costs or uncertainty are considered. This number describes the assumptions in the example. It does not say what will happen in one match.
Why the estimate matters most
A small change in the probability estimate can reverse the result. Team news, opponent quality, sample size, venue, weather, and model design can all move the estimate. A precise output from weak inputs is still weak analysis, so a range is often more honest than a single number.
Limitations of the calculation
Expected value does not remove variance, model error, changing prices, incomplete information, or the possibility that the underlying assumptions are wrong. It also does not prove that a quoted price is inefficient. Use it as a way to audit reasoning and record assumptions, not as a promise about an outcome.
What a responsible analysis records
Record the probability range, the inputs used, the time of the quote, and the facts that would change the estimate. Revisit the assumptions after the event without changing the original number. That creates an auditable research record and keeps the calculation separate from a call to action.
For a broader statistical framework, see the NIST reference on the Poisson distribution and Bettista’s football model explainer.
Last updated: 10 September 2026.