All-in-One Guide to Using the Kelly Formula in Sports Betting: Maximizing Gains While Minimizing Risk
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By Julez • March 13, 2025
The Kelly Formula, also known as the Kelly Criterion, is a popular mathematical formula used in sports betting and investing to determine the optimal bet size. It helps maximize long-term growth by balancing the potential for high returns with the need to minimize the risk of losing your bankroll. This all-in-one guide explains how to use the Kelly Formula in sports betting, introduces a modified approach to manage risk, and provides practical steps to make the most of this strategy without risking excessive losses.
1. Understanding the Kelly Formula and Its Benefits in Sports Betting
The Kelly Formula is based on maximizing the logarithmic growth of your bankroll over the long term. It calculates the optimal betting size as a percentage of your total bankroll based on your edge in a bet. The idea is to bet more when you have a high edge and less (or not at all) when you have a small or negative edge.Kelly Formula Basics:
FORMEL Where: f = fraction of the bankroll to wager, b = decimal odds - 1 (odds in terms of return on investment), p = probability of winning, q = probability of losing (1 - p). Example Calculation: Suppose you have identified a bet with decimal odds of 2.20, and you estimate the probability of winning to be 55% (or p = 0.55).Using the Kelly formula:
FORMELSimplifying this gives you the percentage of your bankroll you should wager on this bet. In this case, the Kelly formula will output a fraction indicating how much of your bankroll to bet based on the estimated edge.
2. Using a Fractional Kelly for Lower Risk
The full Kelly Formula suggests an aggressive betting size, which maximizes growth but can also lead to significant drawdowns during losing streaks. To mitigate this, many bettors use a Fractional Kelly, betting only a portion (e.g., half or a quarter) of the full Kelly amount. Half Kelly: Betting half of the Kelly amount reduces volatility while retaining much of the growth potential. It is considered safer, especially for sports betting, where variance is high. 𝑓 half-Kelly = 1 2 × Kelly Bet Size f half-Kelly = 2 1 ×Kelly Bet Size Quarter Kelly: For highly conservative betting, using a quarter Kelly offers an even lower-risk approach, betting only 25% of the Kelly recommendation.3. Step-by-Step Guide to Applying the Kelly Formula in Sports Betting
Here's a step-by-step approach to using the Kelly Formula for your bets: Estimate Your Winning Probability (p): Begin by estimating the probability of a bet winning. This can be done through statistical analysis, historical data, or model-based predictions. Be conservative with this estimation to avoid over-betting. Calculate the Kelly Bet Size (f): Convert the decimal odds to b by subtracting 1 from the odds. Use the Kelly Formula: 𝑓 = 𝑏 𝑝 − 𝑞 𝑏 f= b bp−q Adjust Using a Fractional Kelly: Decide if you want to reduce your risk by using a fractional Kelly. Multiply the full Kelly bet size by 0.5 for a Half Kelly or 0.25 for a Quarter Kelly to reduce volatility. Determine the Bet Amount: Multiply your calculated f (fraction of the bankroll to bet) by your total bankroll to find the actual bet amount. Reassess Regularly: The Kelly Formula is dynamic, meaning that each bet affects your bankroll size and, in turn, the recommended bet size. Recalculate the Kelly amount after each bet to account for changes in your bankroll.4. Practical Tips for Using the Kelly Formula Effectively
Be Conservative with Probability Estimates: Avoid overestimating your edge, as this is one of the biggest risks in using the Kelly Formula. Overestimating p (probability of winning) can lead to betting too large and risking significant losses. Set a Betting Cap for High Volatility Events: For bets with highly variable outcomes, it’s prudent to cap your bet size, even if the Kelly calculation suggests a larger amount. For example, avoid betting more than 5-10% of your bankroll on any single bet, regardless of the formula’s output. Use a Larger Fractional Kelly When Starting: Beginners and recreational bettors might consider starting with a quarter Kelly or even a one-eighth Kelly. This helps manage the learning curve and builds confidence without risking too much of the bankroll. Combine with Other Bankroll Management Strategies: The Kelly Formula is most effective when combined with other bankroll management practices, such as setting limits on losses, diversifying bets, and avoiding emotional betting.5. Evaluating the Risks of the Kelly Formula
Although the Kelly Formula can be highly effective, it has inherent risks due to its aggressive nature: Over-Betting During Losing Streaks: During losing streaks, the Kelly Criterion can cause significant drawdowns since it recommends betting a percentage of your current bankroll. A series of losses can compound, eroding the bankroll faster than a flat-betting approach would. Risk of Overestimating the Edge: Misjudging the probability of winning (p) is a common risk. An overestimation leads to betting too large, increasing the risk of bankruptcy if your estimated edge does not materialize. Fluctuations in Bankroll: The Kelly Formula assumes a willingness to accept considerable fluctuations in bankroll. Bettors with a low tolerance for risk may find the swings in balance uncomfortable.6. Modified Kelly Approach for Conservative Betting
If the Kelly Formula feels too aggressive, a modified approach can provide a conservative solution while retaining most of the benefits: Capped Kelly Strategy: In this approach, you use the Kelly formula but cap the bet size at a maximum percentage (e.g., 5% of the bankroll). This prevents large bets on single outcomes, protecting against significant losses. Blended Kelly and Flat Betting: Use the Kelly bet size as an upper limit but employ a smaller, flat bet size for bets with a lower probability estimate. This can help stabilize betting amounts across different wagers. Use Kelly for High-Probability Bets Only: For bets with probabilities estimated above 60%, use a Half or Quarter Kelly. For bets with lower probabilities, use a conservative flat betting size.7. Example Calculation: Using the Kelly Formula in a Real-World Scenario
Suppose you have a bankroll of $1,000 and are considering a bet on an NBA game with odds of 2.50. You estimate the probability of the bet winning to be 55%. Step 1:Convert Odds to Return (b): 𝑏 = 2.50 − 1 = 1.50 b=2.50−1=1.50
Step 2: Use Kelly Formula: 𝑓 = ( 1.50 × 0.55 ) − ( 1 − 0.55 ) 1.50 = 0.825 − 0.45 1.50 = 0.25 f= 1.50 (1.50×0.55)−(1−0.55) = 1.50 0.825−0.45 =0.25 This result (0.25) suggests betting 25% of your bankroll.
Step 3: Apply Fractional Kelly: Half Kelly: 0.25 × 0.5 = 0.125 0.25×0.5=0.125, or 12.5% of bankroll ($125). Quarter Kelly: 0.25 × 0.25 = 0.0625 0.25×0.25=0.0625, or 6.25% of bankroll ($62.50).
Step 4: Bet Size Decision: Given the high variance in sports betting, a Quarter Kelly bet of $62.50 is prudent, providing a balance between growth and risk management.
8. Long-Term Strategy and Adjustments
To use the Kelly Criterion effectively over the long term, it’s essential to monitor your results and adjust your probability estimates based on performance.
Tracking Performance: Keep records of each bet, including the probability estimate, stake size, outcome, and bankroll balance. This will help you refine your probability estimates and identify any areas where your edge may need reassessment.
Refining Probability Models: The accuracy of your Kelly calculations depends on the accuracy of your probability estimates. Reassess your data, models, or approach periodically to improve the precision of your betting edge.
Conclusion: Using the Kelly Formula Wisely in Sports Betting The Kelly Formula is a powerful tool that allows bettors to maximize growth while minimizing risk, but it requires disciplined execution and realistic probability estimates. By using a Fractional Kelly or a modified approach, bettors can mitigate the formula’s aggressive nature, manage volatility, and protect against substantial drawdowns. When paired with careful bankroll management and conservative probability estimation, the Kelly Formula can be an effective strategy for achieving steady growth in sports betting.