Expected value (EV) in betting
Expected value is the average result of a bet if you could place it many times. It is the core idea behind judging a price.
The formula
EV = (probability of winning × profit if it wins) − (probability of losing × stake).
A worked example
A bet pays +150, so a $100 stake wins $150. Suppose your estimate of the true chance is 45%.
- Win: 0.45 × $150 = $67.50
- Lose: 0.55 × $100 = $55.00
- EV = $67.50 − $55.00 = +$12.50 per $100 staked
The price +150 implies a 40% chance (see implied probability). If the true chance is 45%, the price is too generous by 5 points and the bet has positive EV. If the true chance were 38%, the EV would be negative.
Why a positive-EV bet still loses often
EV is an average over many bets. A 45% bet loses 55% of the time, and a run of ten losses in a row happens. EV tells you whether a price is good, not whether this one bet will win.
The hard part: the probability
The formula is easy. The estimate of the true chance is not. Sportsbooks have models, data and traders, and their prices already reflect most information. The honest default is that most bets are slightly negative EV because of the vig: at -110 on both sides you must win about 52.4% just to break even.