What is Expected Value in Sports Betting?
Expected Value (EV) is the mathematical foundation of all profitable gambling. It represents the average amount a bettor can expect to win or lose per bet if the same wager were placed repeatedly over an infinite sample size.
The EV Formula
To calculate Expected Value, you must know the true probability of an event occurring (P_win), the probability of losing (P_loss), and the decimal odds offered.
Alternatively, the simplified percentage EV formula is:
Practical Example: Finding a +EV Bet
Suppose Arsenal is playing Chelsea. A sharp bookmaker (like Pinnacle) prices Arsenal to win at 2.10, Draw at 3.40, and Chelsea at 3.60. Using Shin's method, we calculate Arsenal's true probability of winning to be 46.5%.
Now, we check a recreational bookmaker and find Arsenal offered at odds of 2.25. What is the Expected Value?
- P_win: 0.465
- P_loss: 0.535 (1 - 0.465)
- Odds: 2.25
EV = (0.465 × (2.25 - 1)) - (0.535 × 1) = (0.465 × 1.25) - 0.535 = 0.58125 - 0.535 = +0.04625
This bet yields a +4.62% Expected Value. For every $100 wagered, you expect to make $4.62 in profit on average.
Closing Line Value (CLV)
How do you know if your estimated true probability is accurate? The most objective measure of a bettor's skill is Closing Line Value (CLV). The closing line represents the final odds offered right before an event begins, having absorbed all market liquidity and information.
If you consistently beat the sharp closing line (i.e., your betting odds are higher than the sharp closing fair odds), mathematics dictates you will be profitable over a large sample, regardless of short-term variance.
Common Mistakes
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