Sports Betting Math Guide

Master the mathematics that separate winning bettors from losing ones. Learn implied probability, expected value, vig calculation, and optimal bet sizing with our free calculators.

Math & Probability Calculators

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 OddsDecimalImplied Probability
-2001.5066.7%
-1501.6760.0%
-1101.9152.4%
+1002.0050.0%
+1502.5040.0%
+2003.0033.3%
Try the Implied Probability Calculator

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.

Calculate Expected Value

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 Market

Kelly 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.

Calculate Your Kelly Bet Size

Breakeven Win Rates

To be profitable at any odds, you need to win more often than the breakeven percentage:

OddsBreakeven %To Profit, Win
-11052.4%>52.4%
-10551.2%>51.2%
+10050.0%>50.0%
+15040.0%>40.0%
+20033.3%>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.

Responsible Gambling

Sports betting should be fun, not a financial burden. Only bet what you can afford to lose. If gambling stops being enjoyable, please seek help.

National Problem Gambling Helpline: 1-800-522-4700

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