How it works
Expected value is what a bet makes on average, over many bets like it, if your chance is right. A bet at a decimal price returns that price for each $1 staked as often as it wins, and nothing the rest of the time. So on average it returns your chance × the price; take away the $1 staked and that is the EV per $1.
The edge answers a different question: how far your chance is above the chance the price implies, in percentage points. The break-even chance is the line between the two. Below it the bet loses money on average, however good it looks.
The formula
EV per $1 = chance × decimal − 1
Expected profit = stake × EV per $1
Edge = chance − 1 ÷ decimal
Break-even chance = 1 ÷ decimal
EV per $1 = edge × decimalThe same thing written another way.
A worked NFL example
You give an NFL underdog at +130 a 46% chance to win, and stake $100.
- Decimal price: 1 + 130 ÷ 100
- 2.30
- Break-even chance: 1 ÷ 2.30
- 43.48%
- Your edge: 46% − 43.48%
- +2.52 pts
- EV per $1: 0.46 × 2.30 − 1
- +5.8%
- Expected profit on $100
- +$5.80
Over many bets like this one, that is about $5.80 per $100. Any single bet wins $130 or loses $100, and at 46% it loses more often than it wins.
Common mistakes
- Treating a positive EV as a likely win. The bet above still loses 54 times in 100. EV is an average over many bets, not a forecast for one.
- Using the market’s chance as your own. Put a no-vig chance in and the EV comes out negative: at −110 both ways, a fair 50% gives −4.5%, the cost of the margin. Value needs a chance of your own that the market doesn’t share.
- Overstating your chance. EV moves fast with it. At +130, 44% instead of 46% cuts the EV from +5.8% to +1.2%, and 42% makes it −3.4%.
- Mixing up edge and EV. The edge here is +2.5 pts; the EV is +5.8%. Since EV is the edge × the price, the same edge is worth more at a longer price.
In Unitley
Unitley shows the no-vig price and expected value for the NFL games it covers, and its analyst works through the same math and shows its working. About the analyst.