What is expected value (EV) in betting?

EV is the idea underneath most serious betting decisions, and it is also one of the easiest things to get wrong with a calculator, because it is easy to mix up profit with total payout. Here is the formula stated precisely, a full worked example with the arithmetic checked, and the honest limits of what EV can and cannot promise you.

What expected value means in betting

Expected value is what a bet is worth on average, not what it pays out once. Imagine placing the exact same bet, at the exact same odds, against the exact same true probability, thousands of times over. EV is the average profit or loss per bet across all of those repeats. It is a long-run number. Any single bet only ever has two outcomes, win or lose, so a single bet never shows its EV. Only the average over many bets does.

A bet can be a good decision and still lose, and a bet can be a bad decision and still win. EV judges the decision, using the probability you believe is true, not the result that happened to come up. A bettor who only judges bets by whether they won is judging noise. A bettor who works out EV before the bet is judging the process.

The EV formula

Stated precisely, per unit stake:

EV = (probability of winning x profit if you win) - (probability of losing x stake)

Two things have to be right for this to mean anything:

• Profit if you win is the money you gain, not the total amount returned to you. At decimal odds of 2.20 on a 10 stake, you get 22 back if you win, but your profit is only 12 (22 minus the 10 stake you already committed). Mixing up total payout and profit is the single most common way people get this formula wrong.
• Probability of winning has to be your own honest estimate of the true chance, not the number implied by the bookmaker's odds. The bookmaker's implied probability already has their margin built in. Your own estimate is the only input that can make EV positive.

A full worked example: positive EV and negative EV

Say a team is priced at decimal odds of 2.20 to win a match. The implied probability at those odds is 1 divided by 2.20, which is about 45.5%. You have looked at the team's underlying numbers and you believe their true chance of winning is 52%.

Step by step, staking 10 units:

• Profit if you win: 10 x (2.20 - 1) = 10 x 1.20 = 12.
• Probability of winning (your estimate): 52%, so 0.52.
• Probability of losing: 48%, so 0.48.
• EV = (0.52 x 12) - (0.48 x 10)
• EV = 6.24 - 4.80
• EV = 1.44

Staking 10 units on this bet has an EV of positive 1.44 units, or 14.4% of stake. Over many repeats of this exact bet, at this exact price, against this exact true probability, you would expect to average a profit of 1.44 units per 10-unit bet.

The only difference between the two scenarios above is the probability estimate. The odds, the stake and the profit if you win are identical. That is the whole point of EV: it is not a property of the bet in isolation, it is a property of the bet combined with your view of the true probability.

Why EV depends entirely on your probability estimate

Every EV calculation runs on a number you supply yourself: your estimate of the true probability. Get that estimate wrong and the EV calculation is worthless, even though the arithmetic is correct. A positive EV number built on a bad probability estimate is not a positive EV bet. It is a wrong estimate wearing a formula.

This is the honest problem with EV betting: you can be right about the process and still lose money on any single bet. A 52% true probability still loses 48% of the time. Backing positive EV bets consistently does not mean winning consistently. It means the wins and losses balance out in your favour over a large enough number of bets, which is a different claim. Variance does not disappear because a bet was correctly priced. It just means the losses you take are, on average, outweighed by the size and frequency of the wins, over the long run.

FootyMetrics does not publish guaranteed outcomes because there is no such thing in betting. EV is a way to make better decisions with the information available, not a way to remove risk.

EV, fair odds and a value bet

A value bet and a positive EV bet describe the same thing from two angles. A value bet is one where you believe the true probability of an outcome is higher than the probability the market's odds imply. That is exactly the condition that produces a positive EV, because a higher true probability than the implied one means the probability times profit side of the formula outweighs the probability of losing times stake side.

Fair odds are the odds that exactly match a true probability, with no bookmaker margin included. If your estimate of a team's true win probability is 52%, the fair odds for that outcome are roughly 1 divided by 0.52, or about 1.92. Any price better than 1.92 you can actually get on the market, like the 2.20 in the example above, is a value bet against your own estimate, and it is positive EV for the same reason. See what are fair odds for how fair odds are built from a probability estimate.

Why sample size matters for EV to show up as profit

EV is a long-run average, and a long run is exactly what a single bet, or even a short run of bets, is not. A handful of positive EV bets can still lose more often than they win purely on variance, the same way a fair coin can land on the same side several times in a row without the coin being biased. The edge in a positive EV bet is real, but it needs enough repeats for the average to look like the average. This is closely tied to closing line value, which is one of the more reliable ways to check, bet by bet, whether your process is finding value before the sample is large enough for profit and loss alone to tell you anything. See what is closing line value for more on that.