Expected Value in Sports Betting
What expected value means, how to calculate it for any bet, and why a positive-EV bet still loses more than half the time. With worked examples and the sample sizes required to tell skill from noise.
6 min read
Expected value is what a bet is worth on average, across every possible outcome, weighted by how likely each one is. It is the difference between a bet that was good and a bet that won — two things that correlate far less than the betting public assumes.
The formula
EV = (P(win) × profit if it wins) − (P(lose) × stake)
Three inputs: your probability estimate, the profit the price pays, and your stake. The price gives you two of them. The first is yours, and it is the hard part.
A worked example
A $100 bet at +150 on an outcome you believe happens 45% of the time.
- Profit if it wins: $150
- P(win) = 0.45, P(lose) = 0.55
EV = (0.45 × 150) − (0.55 × 100) = 67.50 − 55.00 = $12.50
Twelve dollars fifty per hundred staked, which is a 12.5% edge — very large by betting standards, and a sign you should double-check the 45%.
A more realistic example
A $100 bet at -110 on an outcome you believe happens 54% of the time.
- Profit if it wins: $90.91
EV = (0.54 × 90.91) − (0.46 × 100) = 49.09 − 46.00 = $3.09
A 3.1% edge. Modest, unglamorous, and roughly what a genuinely skilled bettor achieves.
Comparing against the right number
A common error: comparing your estimate against the raw posted price.
The posted price includes the sportsbook's margin. At -110 / -110, the raw implied probabilities are 52.38% each, but the sportsbook's genuine estimate is 50% each — the extra is the fee. If your model says 53% and the raw price says 52.38%, it looks like a small edge. Against the sportsbook's real 50%, it is a three-point disagreement, which is a much bigger claim about your model than you may have intended to make.
Remove the vig first, then compare. How to remove the vig from betting odds covers the arithmetic.
Where the probability comes from
The formula is trivial. The input is not, and no calculator will supply it.
A model. Historical data, simulations, or a rating system that outputs a probability. Serious, time-consuming, and easy to do badly — a model fitted hard enough to past seasons will describe them beautifully and predict nothing.
Market comparison. If a high-limit sportsbook with sharp pricing has a market at a no-vig 56% and a slower book is offering +100 (50%), the first book's number is a defensible probability estimate and the second book's price is a bet. This is where most practical +EV betting comes from, and it requires no modelling at all — only accounts at several books and the discipline to check.
Judgement. The weakest source, and the one almost everyone actually uses. Human probability estimates on games we care about are reliably overconfident. If your estimates regularly differ from the market by more than a few points, the market is more likely right than you are.
Why +EV bets lose so often
This is the part that breaks people.
A +EV bet at +200 that is genuinely a 40% proposition loses 60% of the time. Ten such bets will most often produce four wins and six losses. Three wins and seven losses is entirely ordinary. Two and eight happens.
The expected value is positive across all of them. Each individual result tells you essentially nothing.
| Edge | Bets needed to be reasonably confident it is real |
|---|---|
| 1% | Many thousands |
| 3% | Low thousands |
| 5% | Around a thousand |
| 10% | A few hundred |
These are rough magnitudes, not precise thresholds, and they assume your bets are independent and similarly priced. The point they make is the important one: the sample size required to distinguish a real edge from luck is far larger than a season of betting. Anyone judging a strategy on fifty bets is reading noise.
ROI, and what it does and does not tell you
Return on investment is the realised counterpart to expected value:
ROI = total profit ÷ total staked
Stake $10,000 across a season and finish $420 up, and your ROI is 4.2%.
ROI is the right summary metric because it accounts for stake size, unlike win rate. A 60% win rate on heavy favourites can easily lose money; a 42% win rate on underdogs can be excellent. Only ROI sees both.
Its weakness is the same as every realised figure: over a short run it mostly measures luck. A 4.2% ROI over 150 bets is not evidence of a 4.2% edge. It is consistent with a 4.2% edge, with no edge, and with a 2% disadvantage having a good season.
Closing line value
The practical workaround for needing thousands of bets.
Closing line value is whether the price you took was better than the price the market settled at. Bet a team at +150 and watch it close at +130, and you beat the closing line.
It is useful because the closing line is the sharpest publicly available estimate of a game's true probability, and because it gives you a signal on every single bet rather than only on the ones that resolve informatively. A bettor who consistently beats the close is almost certainly finding real edges, whatever their current profit says. A bettor who consistently loses to the close is not, however well the season is going.
CLV converges on the truth in dozens of bets rather than thousands. That is the whole reason to care about it.
Related reading
- How to remove the vig from betting odds — the step that makes an EV calculation honest.
- Tracking your bets: the metrics that matter — recording results so the sample is real.
- Line shopping: why the best price matters more than the best pick — the most reliable source of positive expected value available to a recreational bettor.
Frequently asked questions
- What is expected value in sports betting?
- Expected value is the average profit or loss a bet would produce if you could place it an unlimited number of times. It is calculated from your estimated probability of winning and the payout offered, and it is positive when the price is better than the true odds.
- How do you calculate expected value?
- EV = (probability of winning × profit if it wins) − (probability of losing × stake). A $100 bet at +150 that you believe wins 45% of the time has an EV of (0.45 × $150) − (0.55 × $100) = $12.50.
- Can a positive EV bet lose?
- Frequently. A +EV bet at +200 that is genuinely a 40% shot loses 60% of the time. Expected value describes the long-run average, not the next result, and a run of losses says nothing about whether the bet was correct.
- How many bets do you need before results are meaningful?
- More than most people assume. At typical betting variance, distinguishing a 2% edge from break-even with reasonable confidence takes well over a thousand bets. Short-run results are dominated by luck.
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BestSlip Analytics Desk
Odds & Analytics
The analytics desk covers the measurement side of betting — implied probability, vig removal, expected value, return on investment and sample size. The work is descriptive: it explains how a number is calculated and what it can support, never what anyone should wager.
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