Expected value in betting, in plain numbers
Expected value is what a bet is worth on average if you could repeat it forever. How to work it out from a chance and a price, with a real BAI8 card.
On this page
Expected value (EV) is what a bet is worth on average if you could place it over and over. For a decimal price, it is your chance times the price, minus one. If that is above zero, the bet pays more than it costs on your numbers. It says nothing about whether this particular bet wins.
The formula, once
EV per unit staked = probability × decimal price − 1.
That is all. Win and you get the price back, lose and you get nothing. The probability is the hard part, and it is only as good as whoever made it.
A real card
Here is the Southampton card from our Desk this morning:
| Our chance | Best price seen | Chance × price | EV per unit |
|---|---|---|---|
| 38.0% | 3.10, LeoVegas (SE) | 1.18 | +0.18 |
On our numbers, a unit on Southampton at 3.10 is worth about 1.18 units back on average. Note this is not the same as the "edge" on our cards: the edge is the gap in points between our chance (38.0%) and the price's implied chance (32.3%), here 5.8 points. Both say the same thing in different units. The card itself is in Norwich v Southampton prediction and odds.
Why EV and results disagree
Southampton still fail to win 62% of the time on our own numbers. EV only shows up over many bets. Our record shows how noisy that is: five positive edge calls so far, one won. That is not evidence for or against EV; it is what small samples look like.
Where EV goes wrong
- The probability is wrong. EV inherits every error in the chance you feed it. A model that is 5 points too keen turns a positive EV negative.
- The price is gone. EV at 3.10 means nothing if you can only get 2.80.
- Staking ignores it. Even a positive EV bet can ruin you if the stake is too large; see staking without going broke.
What this does not tell you
EV does not tell you how much to stake, how long a bad run can last, or whether our probabilities are any good. It tells you, if the chance is right, whether the price is generous.
18+. Bet only what you can afford to lose.
Common questions
What is expected value in betting?
The average result of a bet if you could place it many times: your chance of winning times the profit, minus your chance of losing times the stake.
How do you calculate expected value from decimal odds?
Multiply your probability by the decimal price and subtract 1. A positive result means the bet is worth more than it costs, on your numbers.
Does positive expected value mean the bet will win?
No. It describes the average over many bets. Any single bet can and often does lose.