Expected value in betting explained
Expected value is the single most important concept in profitable betting. Here's what it means, how to calculate it, and why it matters more than how often you win.
What is expected value?
Expected value (EV) is the average amount you would win or lose per bet if you placed the same bet thousands of times. It accounts for both the probability of winning and the payout when you do.
Think of it like this: if you flip a fair coin and win $3 on heads but lose $1 on tails, your expected value per flip is:
You will not win $1 on every flip. You will win $3 half the time and lose $1 half the time. But on average, over many flips, you gain $1 per flip. That is your expected value.
The formula for betting
In sports betting, the EV formula simplifies to:
If EV is positive, the bet is mathematically favourable. If EV is negative, the bookmaker has the edge.
Step-by-step calculation
- Estimate the true probability of the outcome (e.g., 55% = 0.55)
- Note the decimal odds being offered (e.g., 2.10)
- Multiply: 0.55 × 2.10 = 1.155
- Subtract 1: 1.155 − 1 = 0.155
- Result: +15.5% EV
This means for every $100 wagered on this bet, you would expect to profit $15.50 on average over many repetitions.
Positive EV vs negative EV
Positive EV (+EV): You have an edge. The odds pay more than the true probability warrants. Over time, you profit.
Negative EV (−EV): The bookmaker has the edge. The odds pay less than they should. Over time, you lose.
Most bets offered by bookmakers are negative EV — that is how they make money. The margin (overround) built into every market ensures that the average bettor loses 3-8% on every dollar wagered over the long run.
Finding positive EV bets means finding situations where your probability estimate disagrees with the bookmaker enough to overcome the margin. These opportunities exist, but they are not on every match.
EV in action — a football example
Our AI model says Napoli has a 40% chance of beating Inter Milan away. The bookmaker offers 3.50 on Napoli, implying only a 28.6% chance (1 ÷ 3.50).
This is an unusually large edge. In practice, edges of 5-15% are more common and still meaningful over hundreds of bets.
What happens over 100 such bets
If you placed 100 bets at $10 each, all with +10% EV:
- Total staked: $1,000
- Expected profit: $1,000 × 10% = $100
- Actual profit will vary — could be $50 or $200 depending on variance
- But the more bets you place, the closer you get to the expected $100
Common misconceptions
- “I lost, so it was not a value bet.” Wrong. A value bet can lose. Expected value is about what happens over many bets, not one. If you flip a coin and lose, the coin was still fair.
- “Small edges are not worth it.” A +3% EV per bet, compounded over hundreds of bets, adds up. Professional bettors and trading firms make money on margins this thin. The key is volume and consistency.
- “EV is all that matters.” EV tells you the direction, but bankroll management determines whether you survive long enough to realize the edge. Even with +10% EV, betting your entire bankroll on one bet risks ruin.
Key takeaway: Expected value is the only metric that determines long-term profitability in betting. A high win rate means nothing if the odds are too short. A low win rate can still be profitable if the odds are generous enough. Always ask: “Is this bet positive EV?” — not “Will this bet win?”