Expected Value

Expected value is what a bet is worth on average across every possible outcome. It is the only defensible reason to place one, and it is entirely independent of whether the bet wins.

Accepting that a bet can be correct and lose, and incorrect and win, is the mental shift that separates a bettor from a gambler.

The Calculation

Expected value is the probability of winning multiplied by the amount won, minus the probability of losing multiplied by the amount lost.

Worked example. You believe an outcome happens 55% of the time. It is priced at -110, so you risk 110 to win 100.

EV = (0.55 × 100) − (0.45 × 110) = 55 − 49.5 = +5.5

Every 110 risked returns 5.5 in expectation, a 5% return on turnover. Repeat that bet a thousand times and you expect to be up about 5,500 on 110,000 staked.

The same bet at a worse price. At -130 you risk 130 to win 100.

EV = (0.55 × 100) − (0.45 × 130) = 55 − 58.5 = −3.5

Identical opinion, negative expectation. The team did not change. This is why the number is not a detail.

Where Your Probability Comes From

The formula is trivial. The input is not, and it is where almost all error lives.

A probability estimate has to come from somewhere reproducible: a model, a well-defined situational database, or a documented process for adjusting a market number. "I think they win about 55% of the time" produced by feel is not an estimate, it is a preference wearing a percentage.

It also has to include your own uncertainty. If your process produces estimates accurate to within three percentage points, then a bet where you disagree with the market by two points has no edge you can demonstrate — the disagreement is inside your own error bars.

Why A Winning Bet Can Be A Bad Bet

Take a -400 favourite in a game you project as a 75% win. The price implies 80%. EV per 100 of profit sought:

EV = (0.75 × 25) − (0.25 × 100) = 18.75 − 25 = −6.25

Negative. And it will win three times out of four. A bettor placing that bet repeatedly wins the large majority of them and loses money steadily, while feeling successful most of the time.

The reverse is equally true. A +250 underdog you project at 33% has positive expectation and loses two times in three. It will feel wrong constantly and be correct throughout.

This asymmetry between how a bet feels and what it is worth is why disciplined bettors measure process rather than results over short horizons. See closing line value.

How Long Confirmation Takes

A 5% edge is real and slow. With standard-priced bets, distinguishing a 55% bettor from a 52% bettor to any reasonable confidence takes on the order of a thousand bets.

Which means a season of results, for most bettors, is not enough data to confirm or refute their edge. A 200-bet sample from a genuine 55% bettor can easily show 48% or 61%, and both readings are compatible with the underlying truth.

The practical response is to judge inputs rather than outputs: whether you consistently beat the closing number, whether your projections are calibrated, whether your sizing was consistent. Those signals arrive far faster than win rate does. See sample size.

Frequently Asked Questions