Understanding Implied Probability
Implied probability is the win percentage suggested by betting odds. It's the foundation of all sports betting math.
Conversion Formulas
Negative odds: Implied % = |Odds| / (|Odds| + 100)
Positive odds: Implied % = 100 / (Odds + 100)
Common Odds → Probability
| American Odds | Decimal | Implied Probability |
|---|---|---|
| -200 | 1.50 | 66.7% |
| -150 | 1.67 | 60.0% |
| -110 | 1.91 | 52.4% |
| +100 | 2.00 | 50.0% |
| +150 | 2.50 | 40.0% |
| +200 | 3.00 | 33.3% |
Expected Value (EV): The Key to Profitable Betting
Expected Value is the average amount you expect to win or lose per bet over time. Positive EV (+EV) bets are profitable long-term; negative EV (-EV) bets lose money over time.
EV Formula
EV = (Win Probability × Profit) - (Loss Probability × Stake)
Example: Finding +EV
A sportsbook offers Chiefs -3 at +100 (50% implied). Your analysis shows the Chiefs have a 55% true probability to cover.
EV = (0.55 × $100) - (0.45 × $100) = $55 - $45 = +$10 per $100 bet
This is a +10% EV bet. Over 100 bets, you'd expect to profit ~$1,000.
The Golden Rule: If your estimated true probability exceeds the implied probability, the bet is +EV. Consistent +EV betting is the only path to long-term profit.
Understanding Vig (Juice)
The vig (vigorish) or juice is the sportsbook's commission built into the odds. It's why both sides of a 50/50 bet are -110 instead of +100.
How Vig Works
At -110/-110, each side has 52.4% implied probability. Total: 104.8%. The extra 4.8% is the vig.
-110/-110
4.5% vig
-105/-105
2.4% vig
-102/-102
1.0% vig
Lower vig = easier to profit. Shopping for the best lines and using reduced juice books (-105) can turn a losing bettor into a winning one.
Calculate Vig on Any MarketKelly Criterion: Optimal Bet Sizing
The Kelly Criterion is a formula that tells you the optimal percentage of your bankroll to bet based on your edge and the odds.
Kelly Formula
Kelly % = (bp - q) / b
Where: b = decimal odds - 1, p = win probability, q = loss probability (1-p)
Example
You find a +150 bet (b = 1.5) where you estimate 45% win probability (p = 0.45, q = 0.55).
Kelly % = (1.5 × 0.45 - 0.55) / 1.5
Kelly % = (0.675 - 0.55) / 1.5
Kelly % = 8.3% of bankroll
Pro Tip: Most sharp bettors use "Half Kelly" or "Quarter Kelly" to reduce variance. Full Kelly is mathematically optimal but can lead to large swings.
Breakeven Win Rates
To be profitable at any odds, you need to win more often than the breakeven percentage:
| Odds | Breakeven % | To Profit, Win |
|---|---|---|
| -110 | 52.4% | >52.4% |
| -105 | 51.2% | >51.2% |
| +100 | 50.0% | >50.0% |
| +150 | 40.0% | >40.0% |
| +200 | 33.3% | >33.3% |
Frequently Asked Questions
What is implied probability in betting?
Implied probability is the win percentage suggested by betting odds. For -110 odds, the implied probability is 52.4%. If you believe the true probability is higher, the bet has positive EV.
What is a +EV bet?
A +EV bet is one where your estimated true probability exceeds the implied probability. Over time, consistently making +EV bets leads to profit regardless of individual outcomes.
How much vig do sportsbooks charge?
Standard vig is 4.5-5% on -110/-110 markets. Reduced juice books offer -105 (2.4% vig) or even -102 (1% vig). Lower vig makes it easier to profit long-term.