How expected value is calculated
Expected value is what a bet is worth on average if you could place it many times. It weighs the profit if the bet wins by the chance it wins, and subtracts the stake weighed by the chance it loses.
The answer depends entirely on your win probability. A positive EV built on a guess is still a guess, so compare your estimate with the no-vig price too.
- EV = p × (stake × (decimal odds − 1)) − (1 − p) × stake.
- ROI = EV ÷ stake. Edge = p − break-even rate (1 ÷ decimal odds).
- EV is zero when your probability equals the price’s break-even rate.
Questions
What is expected value in betting?
The average amount a bet wins or loses per bet if repeated many times, given the odds and the true chance of winning. Positive EV means it pays more than it risks on average.
Does positive EV mean I will win?
No. A single bet still wins or loses. EV describes the long-run average and relies on your probability being accurate.
How do I find my win probability?
From your own research or model, from a no-vig price, or from historical rates. The price itself only tells you the break-even rate.
What is the difference between EV and ROI?
EV is in dollars for the stake you entered; ROI is EV divided by the stake, so it compares bets of different sizes.
Put it into practice: Player prop research · Sportsbook odds comparison. Livdy shows every book’s price side by side and the game logs behind every prop hit rate.