Definition
Mean, or expectation, is the long-run average result of a bet or outcome if the same situation could be repeated many times. In betting, it is often measured as expected value (EV):
EV = (probability of winning x profit if win) - (probability of losing x amount risked)
A positive expectation means the average result is above zero. A negative expectation means the average result is below zero.
Worked Example
A bettor risks $110 to win $100 at -110 odds. Their projection says the bet wins 54% of the time.
EV = (0.54 x $100) - (0.46 x $110)
EV = $54 - $50.60
EV = $3.40
The expectation is +$3.40 per $110 bet. That does not mean this exact bet will win. It means the projected long-run average is a $3.40 gain each time this same edge is priced the same way.
If the bettor’s true win probability were 52%, the EV would be:
EV = (0.52 x $100) - (0.48 x $110)
EV = $52 - $52.80
EV = -$0.80
Why It Matters
Expectation helps a bettor separate good prices from bad prices. It is most useful when comparing a personal projection to the sportsbook’s price before deciding whether a bet is worth making.