Expected Value (EV) in Sports Betting: Formula & Examples

What Is Expected Value?

Expected Value (EV) is the average amount you can expect to win or lose on a bet if you placed it infinite times. It's the most important concept in profitable sports betting, rooted in probability theory and decision theory dating back to the 17th-century work of Pascal and Fermat.

Positive EV (+EV): A bet that will profit over time Negative EV (-EV): A bet that will lose over time Zero EV: A bet that will break even over time

Every bet has an expected value. Understanding how to calculate it separates professional bettors from recreational gamblers. As Investopedia explains, expected value is "a key variable in most decision-making scenarios" and forms the foundation of modern portfolio theory in finance.

The EV Formula

The basic expected value formula is:

EV = (Probability of Winning × Amount Won) - (Probability of Losing × Amount Lost)

Where:

• Probability of Winning: Your estimated true probability (as a decimal)
• Amount Won: Your profit if the bet wins (payout minus stake)
• Probability of Losing: 1 minus probability of winning
• Amount Lost: Your stake

Simplified for a standard bet:

EV = (Probability × Decimal Odds × Stake) - Stake

Or as a percentage of stake (EV%):

EV% = (True Probability × Decimal Odds) - 1

Step-by-Step EV Calculation

Example 1: Coin Flip

A fair coin flip has 50% probability for heads. You're offered +120 odds on heads ($100 bet wins $120 profit).

Step 1: Convert odds to decimal

• +120 American = 2.20 decimal

Step 2: Identify true probability

• Fair coin = 50% = 0.50

Step 3: Calculate EV

EV% = (0.50 × 2.20) - 1
EV% = 1.10 - 1
EV% = 0.10 or +10%

Result: This is a +10% EV bet. For every $100 wagered, you expect to profit $10 on average.

Example 2: Football Spread

You believe the Chiefs have a 55% chance to cover -3.5 at -110 odds.

Step 1: Convert odds

• -110 American = 1.909 decimal

Step 2: True probability

• Your estimate = 55% = 0.55

Step 3: Calculate EV

EV% = (0.55 × 1.909) - 1
EV% = 1.05 - 1
EV% = 0.05 or +5%

Result: This is a +5% EV bet.

Example 3: Underdog Moneyline

An underdog is offered at +300 odds. You believe they have a 30% chance to win.

Step 1: Convert odds

• +300 American = 4.00 decimal

Step 2: True probability

• Your estimate = 30% = 0.30

Step 3: Calculate EV

EV% = (0.30 × 4.00) - 1
EV% = 1.20 - 1
EV% = 0.20 or +20%

Result: This is a +20% EV bet.

Understanding Implied Probability

Sportsbook odds imply a probability. To find value, compare implied probability to true probability.

Converting odds to implied probability:

American to Probability:

• Positive odds (+150): 100 / (odds + 100) = 100/250 = 40%
• Negative odds (-150): |odds| / (|odds| + 100) = 150/250 = 60%

Decimal to Probability:

• 1 / decimal odds = implied probability
• 2.50 decimal: 1/2.50 = 40%

If your true probability > implied probability, the bet is +EV.

Example:

Book offers Lakers at +200 (implied 33.3%). You estimate Lakers have 40% chance.

40% > 33.3% → Positive EV

EV% = (0.40 × 3.00) - 1 = +20%

Why Sportsbooks Have Edge (Usually)

Sportsbooks build in a margin (vig) that makes most bets -EV for bettors.

Example: Standard -110/-110 market

Both sides at -110 (1.909 decimal):

• Each side implied: 1/1.909 = 52.4%
• Total implied: 52.4% + 52.4% = 104.8%

The extra 4.8% is the vig. On a fair 50/50 proposition, both bets are -EV:

EV% = (0.50 × 1.909) - 1 = -4.55%

To profit, you must find bets where your edge exceeds the vig.

How to Find +EV Bets

Method 1: Build Better Probability Estimates

If your probability estimates are more accurate than the market's, you find +EV bets.

Process:

1. Gather relevant data (team stats, injuries, matchups)
2. Build a model or use systematic analysis
3. Output probability estimates
4. Compare to bookmaker implied probabilities
5. Bet when your probability is significantly higher

Method 2: Compare Sharp to Soft Books

Sharp books (Pinnacle, Circa) have efficient odds. Retail books often have softer lines.

Process:

1. Use sharp book odds as "true" probability estimate
2. Find retail books offering better odds on the same outcome
3. Calculate EV based on sharp book implied probability

This is how value betting software works.

Method 3: Exploit Market Inefficiencies

Certain situations create systematic mispricings:

• Public bias toward favorites and overs
• Slow adjustment to injury news
• Less attention on props and minor leagues

Our value bet scanner automates this by comparing odds across 400+ books.

EV Is About the Long Run

Critical understanding: +EV bets still lose sometimes.

A +10% EV bet with 50% win probability:

• Wins 50% of the time → you profit
• Loses 50% of the time → you lose your stake

The edge manifests over volume.

After 1 bet: Could be +$120 or -$100 After 100 bets: Expected profit ~$1,000, but actual range $500-$1,500 After 1,000 bets: Expected profit ~$10,000, variance tightens significantly

This is why:

• You need proper bankroll management
• You track Closing Line Value (not just results)
• You bet consistently over time
• Short-term results don't validate or invalidate your approach (see our guide on variance)

EV and Stake Sizing

How much to bet on +EV opportunities? The Kelly Criterion answers this:

Kelly % = (Probability × (Decimal Odds - 1) - (1 - Probability)) / (Decimal Odds - 1)

Or simplified:

Kelly % = Edge / (Decimal Odds - 1)

Example:

+10% edge at +100 odds (2.00 decimal):

Kelly % = 0.10 / 1.00 = 10% of bankroll

In practice, use fractional Kelly (25-50%) to reduce variance.

Our Kelly calculator computes optimal stake for any bet.

Common EV Mistakes

1. Using implied probability as true probability

The book's odds aren't "true." They include vig and may be mispriced. You need your own probability estimate.

2. Ignoring vig in calculations

A +105/-105 market might look close to fair, but it has ~2.4% vig. Factor this in.

3. Overconfident probability estimates

If you think you have 70% on something the market prices at 50%, check yourself. Large edges are rare.

4. Judging by short-term results

Winning doesn't mean you found +EV. Losing doesn't mean you didn't. Track CLV to verify edge.

5. Betting -EV because "it feels right"

Gut feelings aren't probability estimates. Math beats intuition in betting.

Using EV in Practice

Daily process:

1. Identify potential bets (from model or software)
2. Calculate/verify EV for each
3. Skip anything below your threshold (e.g., 2% minimum)
4. Size bets using Kelly criterion
5. Track bets with EV% and closing odds
6. Review CLV to verify you're capturing edge

Example workflow:

• Software flags: Lakers +150, sharp consensus at +120
• Your calculation: If +120 is fair (implied 45.5%), then +150 at 40% implied is +EV
• EV% = (0.455 × 2.50) - 1 = +13.75%
• Stake: Fractional Kelly suggests ~3% of bankroll
• Place bet, record, track closing line

Tools for EV Calculation

Our free EV calculator: Calculate Expected Value

Input:

• Your probability estimate
• The odds offered
• Your stake

Output:

• EV in dollars
• EV as percentage
• Whether the bet is +EV or -EV

For automated EV finding:

Our value bet scanner calculates EV for thousands of bets across 400+ sportsbooks, highlighting +EV opportunities in real-time.

Key Takeaways

• EV = (Probability × Payout) - Stake is the fundamental formula
• +EV bets profit long-term, even when individual bets lose
• Compare true probability to implied probability to find edge
• Sportsbook vig makes most bets -EV by default
• To find +EV: Build better models or compare sharp to soft books
• Volume matters: EV manifests over hundreds/thousands of bets
• Kelly criterion determines how much to stake on +EV bets
• Track CLV to verify you're actually finding edge
• Use tools to automate EV calculation and discovery

Ready to find +EV bets?

Use our EV Calculator to analyze any bet, or let our value bet scanner automatically find positive expected value opportunities across hundreds of sportsbooks.