What Is the Kelly Criterion for Sports Betting?
The Kelly Criterion is a mathematical formula that calculates the optimal percentage of your bankroll to wager on a bet, given the odds and your estimated probability of winning. Developed by John L. Kelly Jr. at Bell Labs in 1956 for information theory, it has become the gold standard for bankroll management among professional sports bettors, hedge funds, and anyone managing capital under uncertainty. The core insight is simple: bet proportionally to your edge. Large edge, larger bet. Small edge, smaller bet. No edge, no bet.
The Kelly Criterion Formula
Where:
f* = the fraction of your bankroll to wager
b = the decimal odds minus 1 (the net payout per unit wagered)
p = your estimated true probability of winning
q = the probability of losing (1 - p)
An equivalent form that some bettors find easier to work with:
Both formulas produce exactly the same result. The Kelly fraction tells you the optimal stake as a percentage of your current bankroll.
Worked Example 1: NBA Moneyline
You estimate the Denver Nuggets have a 58% chance of beating the Phoenix Suns. The sportsbook offers odds of 1.85.
Full Kelly says to wager 8.59% of your bankroll. On a $10,000 bankroll, that is $859.
But Hold On -- That Is Too Much
A single bet at 8.59% of your bankroll is aggressive. If you lose three such bets in a row (entirely possible -- a 42% loss probability means three consecutive losses happen 7.4% of the time), you have lost nearly 25% of your bankroll. This is where fractional Kelly comes in.
Why Nobody Uses Full Kelly
Full Kelly assumes your probability estimate is perfect. In sports betting, it never is. If the Nuggets actually have a 53% chance instead of your estimated 58%, Full Kelly dramatically over-bets relative to the true edge. Overestimating probability by even a few percentage points leads to massive over-staking and eventual ruin.
Edward Thorp (the mathematician who beat blackjack and went on to manage one of the most successful hedge funds in history) extensively studied Kelly and concluded that fractional Kelly is superior in practice for three reasons:
1. Estimation error. Your probability inputs are always uncertain. Fractional Kelly provides a buffer for inaccuracy.
2. Drawdown reduction. Full Kelly produces maximum drawdowns of 50-80% in simulations. Most humans -- even professionals -- cannot psychologically tolerate watching half their bankroll evaporate.
3. Diminishing returns of aggressiveness. Going from 1/4 Kelly to Full Kelly quadruples your risk but only doubles your long-term growth rate. The risk-reward tradeoff is poor.
Fractional Kelly: The Professional Standard
The industry standard among professional bettors is 1/4 Kelly (also called quarter Kelly). You divide the Full Kelly stake by 4:
Using our Nuggets example:
On a $10,000 bankroll, you wager $215 instead of $859. Here is how different Kelly fractions compare in a simulation of 1,000 bets with a +5% average expected value:
| Kelly Fraction | Growth Rate | Max Drawdown | Ruin Risk |
|---|---|---|---|
| Full Kelly (1x) | 100% (optimal) | 50-80% | Moderate |
| 1/2 Kelly | ~75% | ~30% | Low |
| 1/4 Kelly | ~50% | ~15% | Very low |
| 1/8 Kelly | ~25% | ~7% | Negligible |
The 1/4 Kelly row represents the sweet spot: you sacrifice roughly half of the theoretical maximum growth rate but reduce maximum drawdown by approximately 75%. This is why it is the default at OdinPicks and across the professional betting industry.
Worked Example 2: Football Over/Under
You estimate the probability of Over 2.5 Goals in a Premier League match at 63%. The odds offered are 1.72.
This is a relatively strong bet. On a $5,000 bankroll, the stake is $145.
Worked Example 3: Tennis Match at Long Odds
You estimate an underdog has a 28% chance of winning a tennis match. The odds are 4.20.
At longer odds, the Kelly fraction is naturally smaller even with a meaningful edge. This is the formula's built-in risk management -- it automatically reduces exposure on higher-variance bets.
Worked Example 4: No Edge -- Kelly Says Do Not Bet
A coin-flip game at odds of 2.00 with 50% true probability:
Kelly says: do not bet. When there is no edge, the optimal stake is zero. This is one of the most powerful features of the Kelly framework -- it forces discipline by mathematically confirming that a no-edge bet deserves no capital.
Worked Example 5: Negative Edge
A bet at odds of 1.90 with true probability of 50% (typical of a -110 spread with vig):
A negative Kelly fraction means the bet has negative expected value. The formula is telling you that you would need to bet against this outcome (take the other side) to have value. In practice: walk away.
Implementing a Bankroll Cap
Even with 1/4 Kelly, some bets can produce large stake recommendations. OdinPicks imposes a 3% maximum cap per individual bet. If 1/4 Kelly suggests 4.5%, the actual stake is capped at 3%.
Why cap? Two reasons:
1. Correlation risk. If you have multiple bets on the same day, the events may be correlated (e.g., two NBA games where rest days affect both). Capping individual bets limits your total exposure.
2. Estimation uncertainty. The larger the Kelly recommendation, the more sensitive it is to errors in your probability estimate. A 3% cap provides additional protection against overconfidence.
Kelly Criterion vs. Flat Betting
Flat betting (wagering the same amount on every bet regardless of edge) is simple but mathematically inferior. Here is why:
Flat bet scenario: You always bet 2% of your bankroll. A +3% EV bet gets the same stake as a +12% EV bet. You are under-betting strong opportunities and proportionally over-betting weak ones.
Kelly scenario: The +3% EV bet gets ~0.8% of bankroll; the +12% EV bet gets ~3% (capped). Your capital allocation matches your edge on each bet.
Over 1,000 bets, Kelly-based staking outperforms flat staking by 30-60% in expected growth, according to Monte Carlo simulations. The advantage compounds over time because larger edges receive proportionally more capital.
Try the Calculator
We built an interactive Kelly Criterion calculator so you can run these calculations instantly. Input your estimated probability and the decimal odds, and the tool computes Full Kelly, 1/2 Kelly, 1/4 Kelly, and recommended stake size based on your bankroll.
Common Mistakes When Using Kelly
1. Using Full Kelly
As discussed above, Full Kelly assumes perfect probability inputs. In practice, use 1/4 Kelly unless you have exceptional confidence in your probability model (and even then, 1/2 Kelly is the maximum that most professionals recommend).
2. Not Recalculating After Wins and Losses
Kelly is a proportional system. Your stake should be a percentage of your current bankroll, not your starting bankroll. If you start with $10,000 and lose $2,000, your next bet should be based on $8,000. If you win and grow to $12,000, your next bet scales up accordingly. This automatic adjustment is a key feature -- it reduces bet size during losing streaks and increases it during winning streaks.
3. Ignoring the Formula When “Feeling Confident”
The entire point of Kelly is to remove subjective judgment from staking decisions. If the formula says 1.5% of bankroll, bet 1.5%. Do not bump it to 5% because you “really like this pick.” Your confidence is already reflected in the probability input. Double-counting it by overriding the stake is a path to ruin.
4. Applying Kelly Without a Genuine Edge
Kelly only works when you have positive expected value. If your probability estimates are not better than the market, Kelly-staking a series of -EV bets will lose money faster than flat staking because it allocates more to bets you incorrectly believe have the most edge.
How OdinPicks Uses Kelly
Every pick published on OdinPicks includes a stake recommendation in units, calculated as follows:
1. Estimate true probability using Pinnacle no-vig benchmark + AI contextual analysis.
2. Calculate Full Kelly using the formula above.
3. Divide by 4 (1/4 Kelly).
4. Apply 3% cap.
5. Round to nearest 0.25 units (where 1 unit = 1% of bankroll).
This process ensures that stake sizes are mathematically justified, proportional to edge, and conservative enough to weather inevitable losing streaks. Combined with CLV tracking to validate our probability estimates, it forms a complete system for long-term profitable betting.
Frequently Asked Questions
What is the Kelly Criterion in simple terms?
The Kelly Criterion is a formula that tells you what percentage of your bankroll to bet based on your edge. The bigger your estimated advantage over the sportsbook, the more you bet. If you have no edge, Kelly says to bet nothing. It maximizes long-term bankroll growth while managing risk.
What is the Kelly Criterion formula for betting?
The formula is: f* = (b x p - q) / b, where f* is the fraction of your bankroll to bet, b is the decimal odds minus 1, p is your estimated probability of winning, and q is the probability of losing (1 - p). Most professionals divide the result by 4 (quarter Kelly) for practical use.
Why do professional bettors use 1/4 Kelly instead of Full Kelly?
Full Kelly assumes your probability estimate is perfectly accurate, which it never is. Quarter Kelly provides a buffer against estimation errors, reduces maximum drawdowns from ~60% to ~15%, and only sacrifices about half of the theoretical growth rate. It is the optimal tradeoff between growth and risk for real-world conditions.
Can Kelly Criterion lose money?
Yes, in the short term. Kelly optimizes for long-term growth, not short-term results. You can experience significant drawdowns even with correct probability estimates. However, if your edge is genuine, Kelly staking ensures that your bankroll grows over a sufficiently large sample of bets.
What bankroll do I need to use the Kelly Criterion?
Most professionals recommend a starting bankroll of at least 100 units (where 1 unit = 1% of your bankroll). This provides enough cushion to absorb natural variance. For a $50 per unit bettor, that means a $5,000 bankroll. The key rule: never bet with money you cannot afford to lose.
How is Kelly Criterion different from flat betting?
Flat betting uses the same stake regardless of edge size. Kelly betting adjusts the stake proportionally to the edge -- larger edge, larger bet; smaller edge, smaller bet. Over time, Kelly staking produces 30-60% higher growth because it allocates more capital to the strongest opportunities.
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