Kelly Criterion for Sports Betting: How to Size Your Bets

Finding positive expected value bets is only half the equation for profitable sports betting. The other half is knowing how much to wager. Bet too much and you risk ruin; bet too little and you leave money on the table. The Kelly Criterion solves this problem mathematically.

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that calculates the optimal bet size to maximize long-term bankroll growth. Developed by John Kelly at Bell Labs in 1956, it was originally designed for information theory but quickly found applications in gambling and investing.

The brilliance of Kelly is that it balances two competing objectives:

• Maximizing growth: Betting larger amounts to capitalize on edge
• Minimizing ruin: Avoiding bet sizes that could devastate your bankroll

Kelly achieves the mathematically optimal balance. No other betting strategy grows your bankroll faster while also ensuring you never go bust.

The Kelly Formula Explained

The basic Kelly formula is:

f* = (bp - q) / b

Where:

• f* = the fraction of bankroll to bet
• b = the decimal odds - 1 (or the ratio of profit to stake)
• p = probability of winning
• q = probability of losing (1 - p)

For example, if you believe you have a 55% chance to win a bet at +100 odds (even money):

• b = 1.0 (you profit $1 for every $1 bet)
• p = 0.55
• q = 0.45
• f* = (1.0 x 0.55 - 0.45) / 1.0 = 0.10 = 10%

Kelly says to bet 10% of your bankroll on this wager.

Kelly Criterion for Sports Betting

Sports betting complicates Kelly slightly because odds aren't always even money. Here's the adapted formula for American odds:

For positive odds (+150, +200, etc.):

Kelly % = ((Decimal Odds x Win Probability) - Loss Probability) / (Decimal Odds - 1)

For negative odds (-150, -200, etc.):

Kelly % = ((Win Probability x (100/|Odds|)) - (Loss Probability)) / (100/|Odds|)

The key insight: Kelly bet size increases with larger edge and decreases with longer odds. A small edge on a favorite warrants a smaller bet than the same edge on an underdog.

Fractional Kelly: Reducing Variance

Full Kelly can be aggressive. A 10% bet is substantial, and multiple bets at full Kelly can lead to large bankroll swings. This is where fractional Kelly comes in.

Most professional bettors use fractional Kelly, typically between 25% and 50% of the full Kelly recommendation:

• Quarter Kelly (25%): Very conservative, minimizes variance
• Half Kelly (50%): Good balance of growth and stability
• Full Kelly (100%): Maximum theoretical growth, high variance

Why use fractional Kelly?

1. Edge estimates are uncertain: If you overestimate your edge, full Kelly will overbet
2. Psychological comfort: Smaller swings are easier to tolerate
3. Error buffer: Provides margin for mistakes

Half Kelly, for instance, achieves 75% of the growth rate of full Kelly while significantly reducing variance and risk of ruin.

Practical Examples

Example 1: Betting a -110 Favorite

You find a bet at -110 odds where you estimate 56% true probability (market implies only 52.4%):

• Decimal odds: 1.909
• Win probability: 0.56
• Loss probability: 0.44
• Kelly = ((1.909 x 0.56) - 0.44) / 0.909 = 0.693 / 0.909 = 7.6%
• Half Kelly = 3.8% of bankroll

Example 2: Betting a +200 Underdog

You find a +200 underdog you estimate at 38% true probability (market implies only 33.3%):

• Decimal odds: 3.0
• Win probability: 0.38
• Loss probability: 0.62
• Kelly = ((3.0 x 0.38) - 0.62) / 2.0 = 0.52 / 2.0 = 2.6%
• Half Kelly = 1.3% of bankroll

Notice that despite similar edge percentages, the underdog bet is sized smaller. This accounts for the higher variance of plus-money wagers.

Example 3: When Kelly Says Don't Bet

If your edge calculation produces zero or negative Kelly, don't bet. For example:

• -110 odds with only 51% win probability
• Kelly = ((1.909 x 0.51) - 0.49) / 0.909 = 0.484 / 0.909 = 0.53%

This tiny Kelly suggests minimal edge. When accounting for uncertainty in your estimate, this bet probably doesn't have positive expected value.

Common Mistakes

1. Overestimating Edge

The most dangerous Kelly mistake. If you think you have 10% edge but actually have 5%, you'll overbet significantly. Always be conservative in edge estimates.

2. Ignoring Correlation

Betting multiple correlated events (same game, related outcomes) amplifies risk. Treat correlated bets as a single larger bet for Kelly purposes.

3. Using Full Kelly

Unless you're extremely confident in your edge calculations, full Kelly is too aggressive. Half Kelly or less is appropriate for most bettors.

4. Not Adjusting for Bankroll Changes

Kelly is a percentage of current bankroll, not initial bankroll. After wins, bet sizes increase; after losses, they decrease. This is a feature, not a bug.

5. Betting More Than Kelly Suggests

Betting more than Kelly actually reduces long-term growth rate while increasing ruin risk. There's never a mathematical reason to exceed Kelly.

Kelly Sizing with Prop Monkey

Calculating Kelly by hand for every bet is tedious. At Prop Monkey, we do the math automatically.

For every pick we surface, you'll see:

• Edge percentage: Your mathematical advantage on the bet
• Recommended bet size: Half-Kelly suggestion based on your bankroll
• Confidence rating: Our certainty in the edge calculation

Our bankroll management tools let you input your bankroll size, and we'll tell you exactly how many units to bet on each opportunity. No spreadsheets required.

This is particularly valuable when you're making multiple bets per day. We track your exposure and ensure you're never overextending on correlated positions.

Key Takeaways

• The Kelly Criterion calculates optimal bet size for maximum long-term growth
• Kelly balances growth potential against risk of ruin
• Most bettors should use fractional Kelly (25-50%) to reduce variance
• Never bet more than Kelly suggests, even when confident
• Proper bet sizing is just as important as finding edge

Want to learn more about finding edge in the first place? Read our complete guide to betting edge.