Expected Value (EV)

Expected Value (EV)

Mathematics

Definition

A statistical measure of what a bettor expects to win or lose per bet on average, given the odds and the true probability of winning. A positive EV (+EV) bet is theoretically profitable in the long run, while a negative EV bet will lose money over time.

Formula

$EV = (P_\text{win} \times \text{profit}) - (P_\text{loss} \times \text{stake})$. Alternatively, $EV = (\text{true probability} \times \text{decimal odds}) - 1$ (in decimal format).

Example

If you bet \$100 on an underdog with a 25% true win chance at +400 (which implies 20%), the **expected value** = 0.25×\$400 - 0.75×\$100 = \$100 - \$75 = +\$25. This is a +EV bet (you’d expect to earn \$25 on average per \$100 bet). Conversely, a -EV bet might have you expecting to lose money on average.