Using the Kelly Criterion for +EV Bets
Optimize your betting stakes for maximum long-term bankroll growth
5 minute read
For serious sports bettors seeking an edge, few tools are as powerful as the Kelly Criterion. This mathematical formula, developed by John L. Kelly Jr. at Bell Labs in 1956, has become a cornerstone betting strategy for professional bettors and investors alike. The Kelly Criterion answers one crucial question: how much of your bankroll should you wager on a specific bet to maximize long-term growth?
Unlike flat betting or arbitrary percentage systems, the Kelly formula calculates the optimal stake size based on your edge—the difference between your estimated probability and the bookmaker's implied probability. When applied correctly, it provides a scientific approach to bankroll management that can significantly increase your returns over time while minimizing risk of ruin.
Edge-Based Sizing
Bet size scales proportionally with your advantage
Bankroll Optimization
Mathematically proven to maximize growth rate
Risk Management
Prevents overbetting while capitalizing on strong edges
Understanding the Kelly Criterion
The Kelly Criterion is essentially a formula that calculates the optimal fraction of your bankroll to wager on a bet with positive expected value. Unlike fixed staking plans, Kelly adjusts your bet size based on the magnitude of your edge—the greater your advantage, the larger the recommended stake. This approach to optimal betting is increasingly popular among data-driven sports bettors.
The Formula
The standard Kelly formula for betting is:
b = decimal odds - 1 (the net odds)
p = your estimated probability of winning
q = your estimated probability of losing (1 - p)
This formula calculates the fraction of your bankroll to wager. For example, if Kelly returns 0.05 (or 5%), you should bet 5% of your current bankroll on this opportunity.
Simplified Version
A more intuitive way to express the Kelly formula is:
Edge = Your probability - Bookmaker's implied probability
Odds = Decimal odds - 1
This version makes it clearer that Kelly recommends larger bets when your edge is higher and smaller bets when the odds (potential payout) are higher.
Kelly Criterion Fundamentals
When to Use Kelly
The Kelly Criterion should only be applied when:
You have a positive expected value (+EV)
The formula only works when you have a genuine edge. If your EV is negative or zero, Kelly will recommend a bet size of zero.You can accurately estimate probabilities
Kelly is highly sensitive to probability inputs. Inaccurate estimates can lead to overbetting and potential ruin.You're focused on long-term growth
Kelly optimizes for maximum compounded growth over many bets—it doesn't guarantee short-term profits.
A Practical Example
Let's walk through a real-world example to illustrate how Kelly works in sports betting:
Scenario:
• Sportsbook offers the Cleveland Cavaliers at +250 (decimal odds 3.50) to win
• Your model gives Cleveland a 33% chance of winning (probability 0.33)
• Bookmaker's implied probability is 1/3.50 = 28.6%
• Your edge is 33% - 28.6% = 4.4%
Applying the Kelly formula:
p = 0.33
q = 1 - 0.33 = 0.67
Kelly % = (2.50 × 0.33 - 0.67) / 2.50
Kelly % = (0.825 - 0.67) / 2.50
Kelly % = 0.155 / 2.50
Kelly % = 0.062 or 6.2%
The Kelly Criterion recommends betting 6.2% of your bankroll on Cleveland. With a $1,000 bankroll, that's a $62 wager.
Fractional Kelly - A Safer Approach
While "full Kelly" provides mathematically optimal growth, many professional bettors use a modified approach called "fractional Kelly" to reduce volatility and risk. This refinement to the sports betting strategy is especially important when working with imperfect information.
Why Use Fractional Kelly?
The full Kelly formula assumes your probability estimates are perfectly accurate—a virtually impossible standard in real-world betting. Fractional Kelly helps account for this uncertainty by recommending a more conservative bet size.
Common Fractions:
• Half Kelly (0.5×): Bet half of what the Kelly formula recommends
• Quarter Kelly (0.25×): Bet one-quarter of the Kelly recommendation
• Eighth Kelly (0.125×): Extremely conservative approach for high uncertainty
Using our previous example with the Cavaliers at +250 with a full Kelly recommendation of 6.2%:
- Half Kelly: 3.1% of bankroll ($31 on a $1,000 bankroll)
- Quarter Kelly: 1.55% of bankroll ($15.50 on a $1,000 bankroll)
Pros: Significantly reduces drawdown risk and volatility, more forgiving of probability estimation errors
Cons: Slower bankroll growth compared to full Kelly when estimates are accurate
Kelly vs. Other Staking Methods
How does the Kelly Criterion compare to other popular staking methods? Let's examine the key differences between this optimal betting approach and more conventional strategies:
Kelly Criterion
- Adjusts bet size based on edge and odds
- Mathematically optimal for bankroll growth
- Higher volatility in results
- Requires accurate probability estimates
- Best for sophisticated bettors with proven edge
Flat/Percentage Betting
- Fixed percentage of bankroll per bet (e.g., 2%)
- Simpler to implement and track
- Lower volatility and drawdown risk
- Same stake regardless of edge size
- Better for beginners or casual bettors
Kelly offers faster growth when your edge estimates are accurate but comes with higher risk. Flat betting provides more stability but potentially slower growth. Many successful bettors start with flat betting and gradually transition to fractional Kelly as they gain confidence in their probability estimates. This evolution in betting strategy is common as bettors become more sophisticated in their approach.
Practical Implementation Tips for a Winning Sports Betting Strategy
- Start with quarter or half Kelly to reduce volatility while you test the waters.
- Set a maximum stake limit (e.g., never bet more than 5% of bankroll) regardless of what Kelly suggests.
- Track your probability estimates against actual outcomes to refine your models over time.
- Consider using Kelly for your strongest +EV bets and flat betting for less certain opportunities.
- Never use full Kelly across multiple simultaneous bets—this dramatically increases risk.
Common Kelly Mistakes
Watch out for these potential pitfalls when using the Kelly Criterion:
• Overestimating your probability edge (leading to overbetting)
• Using Kelly when you don't have statistically significant sample sizes
• Attempting to apply Kelly to correlated bets (like parlays)
• Ignoring the psychological impact of higher variance
• Failing to adjust your approach when your models aren't performing as expected
Kelly Criterion Calculator
Calculate Your Optimal Bet Size
Kelly Fraction:
Sample Result: 3.2% of Bankroll
With a $1,000 bankroll, bet $32
Note: The Kelly formula internally converts American odds to decimal format:
• For positive odds (+150): Decimal = (American/100) + 1 = 2.50
• For negative odds (-110): Decimal = (100/|American|) + 1 = 1.91
Maximizing Long-Term Growth with Kelly
The Kelly Criterion represents the pinnacle of mathematical sophistication in sports betting bankroll management. When applied correctly with accurate probability estimates, it provides the optimal framework for long-term bankroll growth while managing risk.
For most bettors, a fractional Kelly approach (quarter to half Kelly) offers the best balance between capitalizing on +EV opportunities and protecting against the inherent variance in sports betting. Combined with diligent record-keeping and continuous refinement of your probability models, the Kelly Criterion can be a powerful tool in your optimal betting arsenal.
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