What Is Expected Value in Sports Betting?

Expected Value (EV) is the average amount you can expect to win or lose per bet if you placed the same wager thousands of times. A positive EV (+EV) means the bet is mathematically profitable over time; a negative EV (-EV) means the sportsbook has the edge. Every profitable bettor in history -- from professional syndicates to quantitative trading desks -- operates on one principle: only place bets with positive expected value.

The Expected Value Formula

The simplest way to express EV using decimal odds is:

If the result is positive, the bet has value. If negative, the sportsbook has the advantage. The formula works because it compares what you should receive (based on the true probability) against what the sportsbook is actually offering.

Breaking It Down

There are two components you need:

1. True Probability -- the actual likelihood of an outcome occurring, independent of what any bookmaker says. Estimating this accurately is the hard part, and where edges are found.

2. Decimal Odds -- the price the sportsbook is offering. This represents the bookmaker's implied probability plus their margin (vig/juice).

When your estimated true probability exceeds the implied probability baked into the odds, you have a +EV bet.

Worked Example: NBA Moneyline

Suppose the Boston Celtics are playing the Miami Heat. After analyzing form, injuries, rest days, home-court advantage, and historical matchup data, you estimate the Celtics have a 62% chance of winning. The sportsbook offers odds of 1.72 (implied probability: 58.1%).

For every $100 wagered on this bet, you expect to profit $6.64 on average over the long run. This is a strong +EV opportunity.

What If the Odds Were Lower?

Same game, same 62% estimate, but the odds drop to 1.55 (implied: 64.5%):

The bet is now negative EV. The sportsbook's price already accounts for more probability than you believe exists. Even if you think the Celtics win, this bet destroys value over hundreds of wagers.

Why Expected Value Matters More Than Win Rate

Most recreational bettors obsess over win rate. But win rate without context is meaningless. Consider two bettors:

Bettor A: 65% win rate, average odds 1.40. ROI = (0.65 x 1.40) - 1 = -9%. Losing money despite winning most bets.

Bettor B: 48% win rate, average odds 2.30. ROI = (0.48 x 2.30) - 1 = +10.4%. Profitable despite losing more often than winning.

EV captures the full picture: the relationship between probability and price. Win rate alone cannot.

The Law of Large Numbers

A single +EV bet can absolutely lose. If you have a 62% edge, you still lose 38% of the time. This is where recreational bettors give up -- they place five +EV bets, lose three, and conclude the system is broken.

The Law of Large Numbers guarantees that as sample size increases, your actual results converge toward the expected value. Academic research in efficient market theory (Shin, 1991; Forrest & Simmons, 2008) has shown this convergence in sports betting markets with r² values exceeding 0.85 across tens of thousands of events.

In practical terms: 50 bets tell you almost nothing. 500 bets start to reveal your edge. 2,000+ bets and your ROI will closely approximate your average EV.

How to Estimate True Probability

The quality of your EV calculation is entirely dependent on the accuracy of your probability estimate. There are three main approaches:

1. Pinnacle No-Vig as Benchmark

Pinnacle operates with margins as low as 1.5-2% on major markets. Removing the vig from their odds gives you the market's best estimate of true probability. Academic literature (Buchdahl, 2003) has demonstrated that Pinnacle's closing line correlates with actual outcomes at r² = 0.997 -- making it the most efficient probability estimate publicly available.

If Pinnacle's no-vig price is 1.80 (55.6% implied) and another bookmaker offers 1.95 on the same outcome, you likely have +EV.

2. Statistical Models

Building models using regression, Elo ratings, or machine learning on historical data. This requires significant data engineering but can uncover edges in less efficient markets like player props, minor leagues, and in-play markets.

3. Hybrid Approaches (What OdinPicks Uses)

At OdinPicks, the engine combines multiple data sources: odds from 9 bookmakers, Pinnacle no-vig benchmarks, AI-driven research (form, injuries, head-to-head, xG for football, pace/rest for NBA), and applies Claude AI to estimate probability. The system only publishes picks with EV > +3%, sized using fractional Kelly criterion. Every pick is timestamped with a SHA-256 hash for verifiability.

EV and Bankroll Management

Finding +EV bets is only half the equation. The other half is how much to stake. The mathematically optimal answer is the Kelly Criterion:

Where b = decimal odds - 1, p = true probability, q = 1 - p.

Full Kelly maximizes long-term growth but creates severe drawdowns. Most professionals (including OdinPicks) use fractional Kelly (1/4 Kelly), which sacrifices ~50% of optimal growth in exchange for ~75% reduction in maximum drawdown. This is the standard in professional betting and investment management.

Common Misconceptions About EV

“If a bet is +EV, it should win”

No. A +EV bet with 55% true probability loses 45% of the time. EV tells you about the average outcome across many repetitions, not the result of a single event.

“Parlays can be +EV”

Technically yes, but only if every leg is independently +EV and there is no correlation that the bookmaker has already priced in. In practice, the vig compounds multiplicatively across legs: a 5% edge on a single bet becomes a ~15% disadvantage on a 4-leg parlay with standard margins. Read more about accumulator math.

“Following tipsters guarantees +EV”

Only if you get the same odds or better. A pick published at 2.10 that you take at 1.90 might be -EV even if the tipster's original bet was +EV. This is why line movement and timing matter, and why CLV tracking is critical.

How to Verify Your EV Estimates

The best way to validate whether your +EV estimates are accurate is Closing Line Value (CLV). If you consistently bet at odds better than the closing line, your probability estimates are sound. Pinnacle's closing line is the gold standard benchmark because it reflects the most efficient market consensus.

OdinPicks tracks CLV on every published pick. If our picks consistently beat the closing line, it confirms our probability model is accurate -- independent of short-term win/loss results.

Practical Steps to Start Betting +EV

1. Open accounts with multiple sportsbooks to access the best odds for each bet.

2. Learn to calculate implied probability from decimal odds: Implied % = 1 / Decimal Odds.

3. Use Pinnacle no-vig lines as your baseline for true probability.

4. Only bet when your estimated probability exceeds the implied probability by a meaningful margin (at least +3% EV).

5. Use fractional Kelly sizing -- never flat-bet the same amount regardless of edge.

6. Track every bet, including the odds at entry and the closing line, to measure CLV over time.

7. Evaluate your performance after 300+ bets, not after 30.

Frequently Asked Questions