Expected Value (EV): The One Calculation Behind Every Good Bet
How to calculate expected value for any bet, where your probability estimate should come from, how big the swings around EV really are, and the mistakes that make +EV bets lose money.
The formula
Expected value is what a bet is worth on average if you could place it thousands of times. Per $1 staked: EV = (probability of winning × profit if it wins) − (probability of losing × $1).
Positive EV means the price pays more than the risk deserves. Negative EV means you're paying for entertainment. Almost every bet at standard prices is slightly negative EV unless your estimate of the chance to win is better than the market's.
- Coin flip at −110
- 0.50 × 0.909 − 0.50 = −4.5%
- 55% shot at −110
- 0.55 × 0.909 − 0.45 = +5.0%
- 30% shot at +250
- 0.30 × 2.5 − 0.70 = +5.0%
- 30% shot at +200
- 0.30 × 2.0 − 0.70 = −10.0%
Same 30% chance, different price, completely different bet. Price decides value.
Where the probability comes from
Everything rests on the probability. Three common sources: the no-vig market price (a strong default, since it's hard to beat), a model built from data, or your own read of news the market hasn't priced yet.
Be honest about how sure you are. A model that says 58% when the market says 52% is usually wrong, not brilliant. Big disagreements with a liquid market deserve suspicion first and a bet second.
The swings are bigger than you think
At −110, each bet's result swings by roughly a full unit either way. Over 100 bets that adds up to a standard deviation of about 9.5 units. So even a genuinely +3% bettor (expected +3 units over 100 bets) will often be down after 100 bets.
This is why serious bettors size small and judge over large samples. Variance isn't a sign the math is wrong; it's the math.
- Expected result
- +3.1 units
- Typical swing (1 SD)
- ±9.5 units
- Roughly 2 in 3 seasons
- Between −6 and +13 units
- Chance of being down after 100
- About 37%
Mistakes that turn +EV into losses
Overconfidence: treating a rough estimate as precise. Stale prices: calculating EV on a number that's already gone. Correlation: counting the same edge twice across related bets. And over-sizing: even +EV bets can bust a bankroll if each one is too large a share of it.
Try this Write down your probability before you look at the price. It keeps the market from talking you into a number.
Frequently asked questions
What counts as a good EV?
In liquid markets, honest edges are small, often 1–5%. Claims of 15–20% EV on main lines usually mean the probability estimate is off.
Can a +EV bet lose?
Yes, constantly. EV describes the long run, not the next game.
Is the no-vig line the true probability?
It's the market's best estimate without the book's cut. It's a strong baseline, not a certainty.
Keep reading
American, decimal and fractional odds decoded, how to turn any price into a break-even percentage, how to strip out the sportsbook's cut, and why a few cents of price matter more than most picks.
What closing line value is, how to calculate it for spreads, totals and moneylines, how to track it in five columns, and how to read it honestly without fooling yourself.
How to set a bankroll, size each bet, survive losing streaks that are completely normal, use Kelly sizing safely, and put limits in place before you need them.