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How to calculate a value bet
A bet is value when your chance of it winning beats the chance its price implies. Check any price against your own figure or a sharp market’s margin-free price.
The short answer
A bet is value when you rate its chance of winning higher than the chance its price implies. To check, multiply your probability by the decimal odds: p × d > 1 means value, and whatever is left above 1 is your expected profit per £1.
Example: you make a side 48 per cent and the price is 6/5 (2.20). 0.48 × 2.20 = 1.056, so the bet is worth +5.6p per £1. The price implies 45.45 per cent, below your 48.
Use your own probability, or paste a sharp bookmaker’s whole market and let the calculator take the margin out and use the result as your estimate. It gives the edge, the expected value on your stake and the shortest price worth taking. Nothing is stored or sent.
Worked example 1: your own estimate
- Convert the price. 6/5 is 2.20 in decimal odds, and 1 ÷ 2.20 = 45.45 per cent. That is the break-even probability: the chance the price claims.
- Compare. Your 48 per cent is 2.55 points above it, so the price is too long for your view.
- Expected value: 0.48 × 2.20 − 1 = 0.056, which is +5.6p per £1, or £0.56 on a £10 stake, on average.
- Shortest price worth taking: 1 ÷ 0.48 = 2.0833. On a UK coupon the shortest price above that is 11/10; at evens or 21/20 the same opinion would not be value.
Worked example 2: using a sharp market as your probability
Most people do not have a model good enough to beat the market. The next best thing is to treat the sharpest available price, with its margin removed, as the true chance, and look for softer bookmakers who are slower to move. Here a sharp book prices a match at 2.10, 3.50 and 3.90.
| Outcome | Sharp price | Implied | Margin removed |
|---|---|---|---|
| Home | 2.10 | 47.62% | 46.76% |
| Draw | 3.50 | 28.57% | 28.06% |
| Away | 3.90 | 25.64% | 25.18% |
The implied chances add to 101.83 per cent, so dividing each by 1.0183 removes the margin and leaves the home side at 46.76 per cent, a fair price of 2.14. A softer bookmaker offering 2.25 on the home side is then worth 0.4676 × 2.25 − 1 = +5.2p per £1. The calculator removes the margin proportionally; the margin remover shows three other methods, which mostly differ on long prices.
What value is not
Value is not a short price that looks safe, and it is not a big price that looks tempting. A side at 4/5 that you make 55 per cent is a small loser, 0.55 × 1.80 − 1 = −1p per £1, even though it is “the likely winner”. An 8 per cent chance at 9/1 is 0.08 × 10 − 1 = −20p, however large the payout looks. The only question is whether the price beats the probability.
The result of one bet tells you almost nothing either way. A value bet at 6/5 still loses more than half the time. Over a season, the better test is closing line value: whether the prices you take tend to beat the margin-free closing price.
How big an edge to expect
On major football markets, honest edges are small, a few pence per pound at most. If the calculator shows 15p or 20p on a Premier League match result, the likelier explanation is that your probability is too high. Once you have an edge you trust, the Kelly calculator sizes the stake.
Chapter 4 of The Stat Man, What Is Value, Actually?, builds this test from first principles, and the chapter 4 worked solutions work through five priced scenarios to a bet or no-bet ruling.
Questions
Frequently asked questions
How do you calculate a value bet?
Multiply your probability of the bet winning by the decimal odds. If the answer is above 1, the bet is value, and the amount above 1 is your expected profit per £1 staked. 48 per cent at 6/5 (2.20) gives 0.48 × 2.20 = 1.056, so the bet is worth 5.6p per £1 on average.
What is expected value in betting?
Expected value is what you would win or lose, on average, for every £1 staked if the same bet could be made many times over. For decimal odds d and probability p it is p × d − 1. It says nothing about whether one particular bet wins; it is what a long run of similar bets returns.
Where should my probability come from?
Either from a model you have tested against results, or from the sharpest market you can find with its margin removed. The second mode of the calculator does that: type every outcome’s price from a sharp book and it uses the margin-free probability as your estimate.
Does a value bet always win?
No. A value bet loses often; it is a bet whose price is better than its chance, so a long run of them should come out ahead. Judge your bets by the price you took and by closing line value, not by whether each one won.
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