Expected Value (+EV) Betting

What Is Expected Value?

Expected Value (EV) is a mathematical concept borrowed from probability theory. In sports betting, it measures the gap between the true probability of an outcome and the implied probability embedded in the odds you're offered.

When your true edge exceeds what the book is pricing in, you have a positive expected value (+EV) bet. When the book has the edge over you, the bet is negative EV (–EV).

The formula is simple: EV = (Probability of Winning × Profit) − (Probability of Losing × Stake)

Example: A coin flip at even money. True odds = 50%. The book prices it at -110 (implied probability = 52.4%). You're paying more than you should—this is a –EV bet. But if they post +110 on the same flip, your EV is positive and you should bet every time.

How to Find +EV Bets

+EV spots don't announce themselves. You have to hunt for them systematically using three core methods:

• 1. Line Shopping: The most underrated edge in betting. Different books post different prices on the same game. If DraftKings has the Chiefs at -3 (-110) and FanDuel posts -2.5 (-110), those are meaningfully different bets. Always compare prices before placing. Opening accounts at 4–6 sportsbooks is the single highest-EV action most recreational bettors can take.
• 2. Beating the Closing Line: The closing line—the final price before a game starts—is the most accurate market consensus. Professional bettors consistently get better prices than the closing line. If you bet a team at -2.5 and the line closes at -4.5, you beat the market. That's CLV (Closing Line Value), and it's one of the best proxies for long-term EV.
• 3. Building or Using Models: Quantitative bettors build their own power ratings or use projection models. If your model says a team should be priced at -150 but a book is hanging -115, that gap is your edge. The model has to be right more often than not—and you'll know it is when you consistently beat the closing line.
• 4. Exploiting Promos and Boosts: Many sportsbooks offer odds boosts (e.g., Patriots ML goes from -130 to +100). When a boost crosses zero into positive territory on a likely outcome, you have a mathematical +EV spot regardless of your handicapping.

Implied Probability: The Critical Conversion

Every set of American odds implies a probability. Understanding this conversion is foundational.

• Favorite (negative odds): Implied Prob = |Odds| ÷ (|Odds| + 100)
• Underdog (positive odds): Implied Prob = 100 ÷ (Odds + 100)

Example: -110 → 110 ÷ 210 = 52.38%. You need to win more than 52.38% of -110 bets to profit long-term. At +110 → 100 ÷ 210 = 47.62%. You only need to win 47.63% to profit.

The gap between -110 and +110 on the same bet is the vig (juice)—the book's built-in margin. Reducing that margin is core to +EV betting.

The Law of Large Numbers: Why EV Works Over Time

EV is not a guarantee on any single bet. It's a prediction over hundreds or thousands of bets. A coin flip at +110 has positive EV—but you can still lose 7 in a row. This is variance. It's real and it hurts. What you can do:

• Track every bet (odds, stake, result, CLV).
• Size bets consistently—2% of bankroll or less per play.
• Never deviate from your process because of short-term results.
• Run at least 500 bets before drawing conclusions about your edge.

Professional sports bettors operate on margins of 2–5% ROI over large sample sizes. That sounds small—but it compounds. A 3% ROI on $1,000 per week in action is $30/week, $1,560/year. Scale up and the numbers become serious.

Key Rules for +EV Bettors

• EV is about the next 1,000 bets—not the next one.
• You can lose 8 +EV bets in a row and still be playing correctly.
• Closing line value (CLV) is your most reliable performance metric.
• Never bet more than 2–3% of bankroll on any single game.
• Tracking results is not optional—it's how you know if your edge is real.
• Shop lines before every bet. The few minutes save real money at scale.
• Beware of books that limit or ban winners. It's a backhanded compliment.

Common +EV Mistakes

Most bettors who understand EV still make these errors:

• Betting –EV for entertainment: There's nothing wrong with recreational betting. But don't confuse it with investment. Pick a small bankroll for fun bets and a separate one for +EV plays.
• Overconfidence in your model: Your projection model can be wrong. The market is often smarter. Validate your model vs. CLV before betting real money.
• Ignoring the vig: Every –110 bet costs you money over time. Even if you're right 51% of the time at –110, you're roughly breaking even—not winning.
• Parlaying +EV plays: Combining +EV legs into a parlay reduces your actual EV (the book's margin compounds). Bet +EV plays straight.