Expected value (EV) is what a bet wins or loses on average, if your win chance is right. A bet with positive EV is worth making at the right size; one with negative EV loses money over time, however often it happens to win.
The formula
EV = win chance × profit if it wins − lose chance × stake.
Example: you rate a team 63% to win, at −150, staking $100. A win pays $66.67 profit.
- 0.63 × $66.67 = $42.00
- 0.37 × $100 = $37.00
- EV = $42.00 − $37.00 = +$5.00
As a share of the stake, EV% = win chance × decimal odds − 1. Here 0.63 × 1.667 − 1 = +5%.
A coin flip at −110 shows the cost of the vig: 0.50 × 1.909 − 1 = −4.55%.
Edge
Edge is your chance minus the market's, in percentage points. At −220 the price implies 68.75%; if you rate the side 72%, your edge is 3.25 points.
Compare against two numbers:
- The price's implied probability (vig included) is break-even. Positive EV means your chance beats it.
- The no-vig chance is the market's fair view. Your edge against it is how far you disagree with the market. A large disagreement is more often a sign that your estimate is missing something than that the market is wrong.
What EV does not cover
- Pushes. A spread or total that can land exactly on the number returns the stake. Take the push chance out of the win and lose chances first.
- Your estimate. EV is only as good as the win chance you feed it. A model's chance is an estimate, not a fact.
- Variance. A +5% bet still loses 37% of the time. EV shows up over hundreds of bets, not one.
In Unitley
calc_ev takes American odds and your win chance and returns the edge over the price's implied probability, the EV in dollars for the stake and the EV per dollar. get_game_odds and get_player_props show the EV of FanDuel's price against the no-vig consensus.
Names set like this are Unitley’s tools: what your AI agent, or the analyst in the web app, calls to get these numbers. See the docs