Expected value (EV) is the theoretical average result of a decision repeated many times: EV = (estimated probability × odds − 1) × stake. It never predicts a single bet, and it's only as good as the estimated probability behind it. Operators' margins make EV negative on average, though an independent, accurate estimate can flip that on one specific decision.
The short version
Expected value (EV) is the average result of a decision if you could repeat it a huge number of times under identical conditions. EV = (estimated probability × decimal odds − 1) × stake. An EV of +£1 doesn't mean you'll win £1 on this bet. It's an average that only exists through repetition, and it's only as good as the estimate behind it.
A positive EV is a mathematical estimate. The bet behind it can still lose.
What an expected value is made of
You need three ingredients: a possible gain, a possible loss, and an estimated probability that weighs the two. Drop one and you're left with a hunch.
The gain and the loss come straight from the odds and the stake. The probability doesn't come from the odds at all. People overlook that a lot, and the value bet page goes into it.
The formula
EV = (estimated probability × decimal odds − 1) × stake. The bracket is the theoretical edge: what the bet would be worth, per pound staked, if the estimate were accurate. The stake just scales it.
With odds of 2.20 and a probability estimated at 50%, the edge comes to +10%, or an EV of +£1 on a £10 stake.
Look at where each number comes from. The 2.20 is printed on the screen. The 50% is somebody's guess, and it's the one doing all the work. Take five points off it and the edge is gone. To my mind that 50% is the whole example; the formula only echoes whatever number it is fed.
Calculator
The value bet calculator does exactly this job. It gives you the theoretical edge and the expected value that follows from it.
Calculate a theoretical expected value
Enter the odds on offer, your estimated probability and the stake you have in mind.
Comma or dot accepted: 2,20 as well as 2.20.
Your own estimate, which must come from a source other than the odds themselves.
Only used to illustrate the return. Nothing is stored.
Result
- Implied probability
- 45.45%
- Estimated fair odds
- 2.00
- Theoretical edge
- +10.00%
- Expected value
- +€1.00
Warning:
The theoretical edge depends on your estimated probability, never on the offered odds alone. A positive value does not announce a winning bet.
Positive EV, negative EV: what each one describes
A positive EV means that, if your estimate is accurate, the decision pays off on average over time. A negative EV is the mirror image. Neither says anything about one bet taken alone. A positive-EV bet can lose, and a negative-EV bet can win.
"Positive EV = a winning bet."
A positive EV is a mathematical estimate, and the bet it describes can still lose. It's only as good as the probability behind it. A biased estimate can give you a positive EV that's simply wrong.
Why expected value is negative on average
Operators build a margin into every price. If the only estimate you use is the odds themselves, that margin makes your expected value negative. It's the starting point on the budget page: over the long run, a loss is the expected result.
Does that clash with a positive-EV calculation? No, they work at two different scales. Across all possible bets, with no independent estimate, EV is negative, and the margin guarantees it. On one specific decision, an estimate made independently of the odds, and genuinely better than the market's, can flip the sign. The hard part is the quality of that estimate, not the formula. The value bet page makes the same point: comparing a price with itself only reveals the bookmaker's margin. Even margin-free odds are still derived from market prices, so they aren't an independent estimate.
Why "average" doesn't mean "what will happen"
A single bet never delivers its expected value. It wins or it loses. EV only becomes an observable average when you repeat the decision many times and the estimate stays valid for the whole period.
A value bet compares odds with an estimate and detects a gap. Expected value turns that gap into a figure, the theoretical average you'd expect. ROI is what you actually observed once bets were settled, never a projection.
Three related ideas, each doing a different job.
EV depends on the quality of the estimate
No formula fixes a bad probability. The value bet page covers where the estimate comes from, what makes it fragile and why it sometimes differs from the market. It asks for the same things: independence from the odds, calibration, and care with sources.
This page doesn't redo that work. Learning how to read odds, how to calculate an implied probability and how to turn an estimate into fair odds is the same mechanic, whatever you call the result afterwards.
EV and the price you get
The EV you work out before a bet depends on the odds at the moment you decide. If the odds move between your estimate and the bet being placed, the expected value changes even though your probability hasn't. That's why closing line value and odds movements stay relevant once you have an estimate. The price you get matters as much as the estimate.
Why results drift away from the expected value
Over a small number of decisions, results can land a long way from the theoretical expected value without anyone having made a mistake. That's variance. It's also why a good or bad record neither confirms nor refutes an estimate.
A positive expected value doesn't rule out a bad run. The next page covers what variance does to a small number of decisions.
Why results swing, even with a good estimate →
Responsible gambling: a positive EV protects you from nothing. Sports betting carries a risk of financial loss. Set yourself a budget, don't chase your losses, and use the deposit limits and self-exclusion tools available. Learn more about responsible gambling.
Put it into practice
Apply this guide to real odds.
See a market reading
A real match with its odds, movements and 0-100 signal.
Open the demoMargin calculator
Measure a bookmaker's margin on any market.
Calculate the marginDig into the market
Odds movements are only part of the story. Here are the next topics to read.
Profitability and risk: the complete guide
The full picture: profit, ROI, expected value, variance, sample size, drawdown, risk.
Read the guideValue bet: what the edge actually measures
Spotting the gap, the step before you calculate the EV.
Understand value betsVariance: why results swing
Why what you observe so often drifts away from the theoretical expected value.
Understand varianceWhat budget should you set for sports betting?
Why the expected value of a stake is negative on average.
See the budgetImplied probability from the odds
The first conversion, bookmaker margin included.
Do the calculationClosing line value
Comparing the odds you took with the closing odds, whatever the result.
Understand CLVFrequently asked questions
What is expected value (EV) in sports betting?
It's the theoretical average result of a bet, worked out from an estimated probability and the odds on offer. It's an average over many repeats. It tells you nothing about how one particular bet will end.
Does a positive EV guarantee a win?
No. A positive EV is a mathematical estimate. The bet can still lose, and the EV is only as good as the probability you fed into it.
Why is expected value negative on average in sports betting?
Operators build a margin into every price. If the only estimate you use is the odds themselves, that margin makes your expected value negative. An independent, accurate estimate can produce a positive EV on one specific decision without changing that overall average.
What's the difference between a value bet and expected value?
A value bet compares a price with an estimate and spots a gap. Expected value turns that gap into a figure: the theoretical average you'd expect if the estimate is accurate. One detects, the other quantifies.
Where does the probability used to calculate an EV come from?
It has to come from a source that's independent of the odds: a statistical model, a consensus of sources, or your own analysis, labelled as such. Using the odds' own implied probability just compares a price with itself.
Does OddScore calculate expected value for its users?
No. OddScore converts odds into probabilities, strips out each operator's margin and tracks how the odds move. It doesn't produce a sporting probability independent of the market, so there's no ready-made EV to pick up.
Sources & methodology
This page draws on the standard definition of mathematical expectation applied to gambling, on academic work estimating expected loss rates in betting markets, and on OddScore's own odds-analysis method. The Gambling Commission and BeGambleAware are there for UK player guidance and free support.
- Convert the offered odds into their implied probability, margin included.
- Compare that probability with an estimate obtained independently of the odds.
- Calculate the expected value as (estimated probability × odds − 1) × stake.
- Remember at every step that a positive EV is a theoretical average over many repeats, never the outcome of one bet.