Value betting masterclass · Module 1: The foundations · Lesson 4 of 25 · About 6 min
Expected value betting means judging a bet by its average outcome rather than by whether it lands. You ask what the bet would return for every £1 if you could place it thousands of times. If that average is above zero, the price is on your side, at least on paper.
This guide covers the formula, several worked examples and the honest limits, including why one bet on its own tells you almost nothing.
Read the transcript
Expected value tells you what a bet is worth on average. The best way to understand it is to work one through from start to finish.
Say you rate a team a forty-seven per cent chance. The best price you can find is two point three, and you stake ten pounds.
If it wins, you get twenty-three pounds back, which is thirteen pounds profit. That happens about forty-seven times in a hundred. If it doesn't, you're ten pounds down, and that happens the other fifty-three times.
Now weight each result by its chance. Forty-seven per cent of thirteen pounds is six pounds eleven. Fifty-three per cent of ten pounds is five pounds thirty. The difference is plus eighty-one pence.
That's an expected value of plus eight point one per cent of your stake. It's the average across lots of bets like this one, not a promise about this particular match.
And it all depends on that forty-seven per cent being right. If the true chance is below forty-three and a half per cent, the edge disappears. Try your own numbers with the free E V calculator on ValueBets.uk, and please bet responsibly.
Key points
- EV per £1 staked = your probability × decimal odds − 1.
- £10 at 2.60 on a 42% chance has an EV of +£0.92.
- A positive EV is only as reliable as your probability estimate.
- EV only shows itself over hundreds of bets.
What expected value means
Every bet has two outcomes: it lands or it doesn’t. Expected value (EV) combines them into one figure by weighting each outcome by how likely it is.
So the crucial input is your own estimate of the chance. First turn the odds into an implied probability (Lesson 2 out of 25 in the Masterclass), then set it against the chance you believe is real. If your chance is higher than the price suggests, the EV is positive.
That idea sits at the centre of our value betting guide (Lesson 1 out of 25 in the Masterclass): you judge the price, not the team.
The EV formula
You can write it two ways, and both give the same answer.
- Short form: EV per £1 = p × decimal odds − 1
- Long form: EV = (p × profit if it lands) − ((1 − p) × stake)
Here p is your probability as a decimal, so 42% becomes 0.42. Multiply the short form by your stake to get the EV in pounds.
Worked example
You put £10 on Brighton to beat Everton at 2.60 (8/5), prices for illustration only, and you rate their real chance at 42%.
- Short form: 0.42 × 2.60 − 1 = 0.092, and 0.092 × £10 = +£0.92.
- Long form: a winner pays £16 profit, so 0.42 × £16 = £6.72. When it doesn’t land the £10 stake is spent, so 0.58 × £10 = £5.80. Then £6.72 − £5.80 = +£0.92.
On average, the bet is worth 92p to you. You will never actually collect 92p, though: each time it either pays £16 profit or returns nothing.
Use the calculator below with your own stake, odds and probability. It shows the EV in pounds and as a percentage edge.
Expected value calculator
What a poor price looks like
Most bets carry negative EV, because the bookmaker’s margin is built into the odds. It helps to recognise a poor price when you see one.
Worked example
- A 50% chance priced at 1.85: 0.50 × 1.85 − 1 = −0.075, so £10 has an EV of −75p.
- A 20% chance priced at 4.50 (7/2): 0.20 × 4.50 − 1 = −0.10, so £10 has an EV of −£1.00.
- A 40% chance priced at 2.40 (7/5): 0.40 × 2.40 − 1 = −0.04, or −40p per £10.
Look closely at the last one. The odds seem generous, yet the EV is still negative, because 2.40 only pays enough for a 41.7% chance and your estimate is lower. Accas make this worse, since the margin on each leg multiplies; our accumulator margin guide works through an example.
EV as a percentage edge
The short form already gives you a percentage: 0.092 is an edge of 9.2%. It means you expect £1.092 back for every £1 staked, on average, over a long run.
There is also a handy shortcut: divide the odds by your fair odds and take away 1. A 42% chance has fair odds of 1 ÷ 0.42 = 2.38, and 2.60 ÷ 2.38 − 1 is about 9%, the same edge.
Real edges are usually small, and 2% to 5% is far more common than 9%. If your sums show a huge edge, check your probability first, because the estimate being too optimistic is more likely than the price being too big. Our fair odds without the margin (Lesson 3 out of 25 in the Masterclass) page gives you a cleaner place to start.
Why EV only shows over many bets
EV is an average, and averages need plenty of results before they settle. In the short run, luck drowns out any edge.
Worked example
Take the Brighton bet again: £10 at 2.60 with a true 42% chance, placed many times over.
- After 100 bets you expect to be £92 up, but the spread is wide, roughly ±£128 for one standard deviation, so you finish ahead only about 3 times in 4.
- After 1,000 bets you expect to be £920 up, and the chance of being ahead rises to about 99%.
These figures assume your 42% is exactly right, which in practice it never quite is.
That is why a positive-EV bet may not land and a poor bet can come in. It is also why you should judge your process from your records over time. Our betting variance (Lesson 13 out of 25 in the Masterclass) guide shows how long a run without a winner can last.
The limits of expected value
EV is a way to judge prices, not a promise of profit. An edge is only real if your probability is better than the market’s, and that is genuinely hard.
A good test is whether you beat the closing price, and our closing line value (Lesson 9 out of 25 in the Masterclass) guide shows how to check. If you do bet, set your stake before you start and never raise it to win money back.
For the maths behind EV, the Wikipedia article on expected value gives the formal definition.
Related guides
- Value betting explained (Lesson 1 out of 25 in the Masterclass)
- Implied probability: odds to percentages (Lesson 2 out of 25 in the Masterclass)
- Kelly criterion staking (Lesson 12 out of 25 in the Masterclass)
- Betting variance
- Keeping betting records (Lesson 14 out of 25 in the Masterclass)
Lesson 4 of 25 · The foundations
18+ only. Betting should stay fun. Set a budget before you start, only bet what you can comfortably afford, and take a break whenever you need one. For free, confidential support, visit BeGambleAware.org or call the National Gambling Helpline on 0808 8020 133.