Expected value (EV) describes the theoretical average result of a decision repeated a large number of times: EV = (estimated probability × odds − 1) × stake. It never predicts the outcome of a single bet, and it's only as good as the estimated probability that feeds it. The operators' margin makes the expected value structurally negative on average; an independent, accurate estimate can occasionally reverse that on a specific decision.
The essentials in a few seconds
Expected value (EV) describes the theoretical average result of a decision, if it were repeated a large number of times under identical conditions. EV = (estimated probability × decimal odds − 1) × stake. An EV of +€1 never means "I'm going to win €1" on this specific bet — it describes an average that only exists through repetition, and that's only as good as the estimate used to calculate it.
A positive EV is a mathematical estimate, not a promise. The bet it describes can still lose.
What an expected value is made of
Three ingredients, none of them optional: a possible gain, a possible loss, and an estimated probability weighing the two. Remove any one of the three and all that's left is a hunch.
The possible gain and the possible loss come directly from the odds and the stake. The estimated probability never comes from the odds themselves — that's the point most often overlooked, and it's covered in detail on the page devoted to the value bet.
The formula
EV = (estimated probability × decimal odds − 1) × stake. The term in brackets is the theoretical edge: what the bet would be worth, per euro staked, if the estimate were accurate. The stake only 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.
Calculator
The value bet calculator covers exactly this: it produces the theoretical edge and the expected value that follows from it.
Calculate a theoretical expected value
Enter the offered odds, your estimated probability and the intended stake.
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 case describes
A positive EV describes a decision whose estimate, if accurate, would produce a gain on average over time. A negative EV describes the opposite. Neither says anything about a bet taken in isolation — a positive-EV bet can lose, a negative-EV bet can win.
"Positive EV = a winning bet."
A positive EV is a mathematical estimate. The individual bet can still lose, and the EV is only as good as the estimated probability that feeds it — a biased estimate produces a positive EV that's just as wrong as a negative one.
Why expected value is structurally negative on average
The margin built into every odd by operators makes the expected value negative for a bettor who would use only that odds as the estimate. That's the starting point set out on the page about budget: over time, a loss isn't one unfavourable scenario among others, it's the expected result.
This fact and the positive-EV calculation developed here don't contradict each other — they describe two different scales. On average, across every possible bet and with no independent estimate, the expected value is negative: the margin guarantees it. On a specific decision, an estimate produced independently of the odds and genuinely more accurate than the market can occasionally reverse that calculation. The difficulty isn't in the formula, it's entirely in the quality of that estimate — a point already made by the value bet: comparing a price with itself reveals nothing but the bookmaker's margin, and even a margin-free odd is still extracted from market prices, not an independent estimate.
Why "average" doesn't mean "what's going to happen"
A single bet never realises its expected value: it wins, or it loses. EV only exists as an observable average provided it's repeated a large number of times, with an estimate that stays valid over the whole period.
Value bet — a comparison between an odds and an estimate, which detects a gap.Expected value — turning that gap into a figure: the theoretical average expected.ROI — the performance observed once bets are settled, never a projection.
Three related notions, but distinct.
EV depends entirely on the quality of the estimate
No formula corrects a bad probability. Where this estimate comes from, what makes it fragile and why it sometimes diverges from the market are covered in detail on the page devoted to the value bet, which sets the same requirements: independence from the odds, calibration, and vigilance about sources.
This page doesn't redo that work — understanding how to read an odd, how an implied probability is calculated and how to turn an estimate into fair odds is the same mechanic, whatever name you give it afterwards.
EV and the price obtained
The EV calculated before a bet depends on the odds at the moment the decision is made. Odds that move between the estimate and the execution change the expected value, even if the estimated probability stays the same. That's why closing line value and odds movements stay relevant even once an estimate is set: the price you act at matters as much as the estimate itself.
Why the observed result diverges from the expected value
Over a small number of decisions, the observed result can stray far from the theoretical expected value, without any mistake having been made. That's what variance describes — the logical next step for understanding why a positive or negative record neither validates nor invalidates an estimate.
A positive expected value doesn't prevent a run of unfavourable results. What variance does to a small number of decisions is covered on the next page.
Why results fluctuate, even with a good estimate →
Responsible gambling. A positive theoretical expected value protects against no actual loss. A stake can be lost in full. Set a budget before you play and use the limit-setting or self-exclusion tools licensed operators provide. Learn more about responsible gambling.
Dig 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
Detecting the gap, the step before calculating the EV.
Understand value betsVariance: why results swing
Why an observed result often diverges from the theoretical expected value.
Understand varianceWhat budget should you set for sports betting?
Why the expected value of a stake is structurally negative on average.
See the budgetThe implied probability of an odd
The first conversion, bookmaker margin included.
Do the calculationClosing line value
Comparing the odds you took with the closing odds, independently of the result.
Understand CLVFrequently asked questions
What is expected value (EV) in sports betting?
It's the theoretical average result of a bet, calculated from an estimated probability and the odds on offer. It describes an average over a large number of repeats, never the outcome of one specific bet.
Does a positive EV guarantee a win?
No. A positive EV describes a mathematical estimate. The individual bet can still lose, and the EV depends entirely on the quality of the probability used to calculate it.
Why is expected value negative on average in sports betting?
Because the margin built into every odd by operators makes the expected value structurally negative for a bettor who would use the odds themselves as the estimate. An independent, accurate estimate can occasionally produce a positive expected value on a specific decision, without changing that overall average.
What's the difference between a value bet and expected value?
A value bet compares a price to an estimate and detects a gap. Expected value turns that gap into a figure: the theoretical average expected if the estimate is accurate. The first notion detects, the second quantifies.
Where does the probability used to calculate an EV come from?
It has to come from a source independent of the odds themselves — a statistical model, a consensus of sources, a personal analysis acknowledged as such. Using the odds' own implied probability amounts to comparing a price with itself.
Does OddScore calculate expected value for its users?
No. OddScore converts odds into probabilities, removes each operator's margin and tracks how they evolve. The platform produces no sporting probability independent of the market and therefore provides no ready-made EV.
Sources & methodology
This page draws on the standard definition of mathematical expectation applied to gambling, on the academic literature estimating expected loss rates in betting markets, and on the odds-analysis methodology developed by OddScore.
- 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.
- Recall at every step that a positive EV describes a theoretical average over many repeats, never the outcome of one bet.