Key Takeaways
- Expected value (EV) measures the average profit or loss per bet over time
- Positive EV (+EV) means a bet is profitable in the long run; negative EV (-EV) means it's not
- EV depends on two things: the true probability of winning and the payout odds
- Most bets at a sportsbook are -EV by design because the vig ensures the house has an edge
- Finding +EV bets consistently requires accurate probability estimates
What Is Expected Value?
Expected value is the mathematical average of all possible outcomes of a bet, weighted by their probabilities. It tells you how much you'd expect to win (or lose) per bet if you made the same bet thousands of times.
The formula:
EV = (Probability of Winning × Profit if Win) - (Probability of Losing × Loss if Lose)
A Simple Example
You flip a fair coin. Heads pays $120, tails costs $100.
- Probability of heads: 50%
- Probability of tails: 50%
- EV = (0.50 × $120) - (0.50 × $100) = $60 - $50 = +$10
This is a +EV bet. On average, you'd make $10 per flip. You'd take this bet every time.
Now change the payout: heads pays $90, tails costs $100.
- EV = (0.50 × $90) - (0.50 × $100) = $45 - $50 = -$5
This is -EV. Over time, you'd lose $5 per flip. You'd avoid this bet.
EV in Sports Betting
Let's apply this to a real player prop. Suppose a sportsbook offers:
Player X Over 22.5 Points at -110 odds
At -110, a $110 bet profits $100 if it wins. The implied probability is 52.4%.
But what if your model estimates the true probability of the Over at 58%?
- EV = (0.58 × $100) - (0.42 × $110) = $58 - $46.20 = +$11.80 per $110 bet
That's a +EV bet. The market is underpricing this outcome.
Now suppose your model gives it only a 48% chance:
- EV = (0.48 × $100) - (0.52 × $110) = $48 - $57.20 = -$9.20 per $110 bet
That's -EV. The market is correctly priced (or even generous to the Under side).
Why EV Matters More Than Win Rate
A common mistake is judging bets by win rate alone. Consider two bettors:
Bettor A: 60% win rate, but only bets heavy favorites at -200
- Average profit per win: $50
- Average loss per loss: $100
- EV per bet = (0.60 × $50) - (0.40 × $100) = $30 - $40 = -$10
Bettor B: 45% win rate, but selects underdogs at +180
- Average profit per win: $180
- Average loss per loss: $100
- EV per bet = (0.45 × $180) - (0.55 × $100) = $81 - $55 = +$26
Bettor A wins more often but loses money. Bettor B wins less often but profits over time. EV captures this. Win rate alone doesn't.
The Role of Probability Estimation
EV calculation requires knowing the true probability of an outcome. The challenge is that nobody knows the true probability with certainty. Every probability estimate is a model, a best guess based on available data.
The better your probability estimates, the better your EV calculations, and the better your long-term results.
What Makes a Good Probability Model?
Strong models share several characteristics:
- They're calibrated: when the model says 60%, the outcome should happen about 60% of the time
- They account for uncertainty: a player projected for 22 points could score anywhere from 8 to 40
- They incorporate relevant factors: matchup strength, minutes projection, pace, rest, and role changes
- They update with new information: injury reports, lineup changes, and market movements
Monte Carlo simulation is one approach that handles uncertainty well. By running thousands of simulated games, it produces a full probability distribution rather than a single point estimate.
Finding +EV Bets
Here's the practical workflow:
- Estimate true probability: use a model, research, or both
- Calculate implied probability from odds: convert the sportsbook's odds
- Compare: if your estimated probability exceeds implied probability, the bet is +EV
- Size appropriately: bigger edge suggests larger sizing (within bankroll limits)
Edge Calculation
The "edge" is the difference between your estimated probability and the implied probability:
Edge = Estimated Probability - Implied Probability
A bet at -110 (implied 52.4%) with an estimated 58% probability has a 5.6% edge. Not every +EV bet wins, but consistently finding 3-5% edges leads to long-term profitability.
The Long Run
EV is a long-run concept. In the short term, anything can happen. A strong +EV bet can lose. A terrible -EV bet can win. Variance is real and unavoidable.
What EV guarantees is this: if you consistently make +EV bets with proper bankroll management, your results will converge toward profitability over a large enough sample.
How large? For sports betting, a meaningful sample is typically 500-1,000+ bets. This is why tracking, patience, and discipline matter as much as analysis.
How Propboard Identifies +EV Opportunities
Propboard runs Monte Carlo simulations across every NBA and NCAAB player prop market, producing calibrated probabilities for each outcome. These probabilities are compared against real-time odds from 10 sportsbooks to calculate edge estimates.
Picks are graded from A+ to C based on edge magnitude and model confidence. Start your free trial to see which of today's props offer the strongest expected value.
Related Reading
- Bankroll Management 101 for how to size your bets once you've identified +EV opportunities
- What Makes a Good Player Prop Model? for what separates a reliable probability model from noise
Frequently Asked Questions
Can a +EV bet still lose?
Yes. Expected value is a long-run concept. A bet with positive expected value will lose plenty of times in the short term. What matters is that over hundreds or thousands of similar bets, the math works in your favor. A single outcome tells you nothing about whether the bet was good or bad.
How many bets do I need for EV to matter?
Most serious bettors consider 500 to 1,000 bets the minimum for meaningful results. Below that, variance dominates and your record could look very different from your true edge. This is why bankroll management and patience are just as important as finding +EV opportunities.
Is a high win rate the same as positive EV?
No. A bettor who wins 65% of their bets on heavy favorites at -300 can still lose money overall, while someone hitting 42% on +200 underdogs can be solidly profitable. EV accounts for both the probability of winning and the payout, which win rate alone ignores.
How do I calculate edge on a player prop?
Subtract the implied probability (from the sportsbook's odds) from your estimated true probability. For example, if a prop is priced at -110 (implying 52.4%) and your model gives the Over a 58% chance, your edge is 5.6%. Propboard calculates this automatically across every prop market.
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