Quick Definition
The Kelly Criterion is a mathematical formula that calculates the optimal bet size to maximize long-term bankroll growth while minimizing risk of ruin. Developed by John L. Kelly Jr. at Bell Labs in 1956, this formula helps bettors determine exactly what percentage of their bankroll to wager based on their perceived edge over the sportsbook.
Formula:
Bet Size % = (Edge / Decimal Odds - 1) × 100
Or simplified:
Kelly % = (Win Probability × Decimal Odds - 1) / (Decimal Odds - 1)
The Kelly Criterion is used by professional gamblers, investors, and traders worldwide because it provides a mathematically proven method to balance growth and risk. Unlike arbitrary bet sizing methods, Kelly accounts for both your edge and the specific odds offered, ensuring you never overbet your advantage or underutilize profitable opportunities.
How Kelly Criterion Works
Example 1: NFL Spread Betting
Scenario: Kansas City Chiefs -3.5 vs. Las Vegas Raiders
Bet details:
- Odds: -110 (1.909 decimal)
- Sportsbook implied probability: 52.38%
- Your model's win probability: 58%
- Your edge: 5.62%
- Current bankroll: $5,000
Kelly calculation:
Kelly % = (0.58 × 1.909 - 1) / (1.909 - 1) = 0.107 / 0.909 = 11.8%
Full Kelly result: Bet 11.8% of bankroll = $590
Half Kelly result: Bet 5.9% of bankroll = $295
Outcome if Chiefs cover: Win $268 (Half Kelly), new bankroll = $5,268
Outcome if Chiefs don't cover: Lose $295 (Half Kelly), new bankroll = $4,705
Example 2: NBA Moneyline Favorite
Scenario: Boston Celtics vs. Detroit Pistons
Bet details:
- Celtics moneyline: -350 (1.286 decimal)
- Sportsbook implied probability: 77.78%
- Your analysis shows: 82% win probability
- Your edge: 4.22%
- Current bankroll: $10,000
Kelly calculation:
Kelly % = (0.82 × 1.286 - 1) / (1.286 - 1) = 0.055 / 0.286 = 19.2%
Full Kelly result: Bet 19.2% of bankroll = $1,920
Quarter Kelly result: Bet 4.8% of bankroll = $480
Outcome if Celtics win: Win $137 (Quarter Kelly), new bankroll = $10,137
Outcome if Celtics lose: Lose $480 (Quarter Kelly), new bankroll = $9,520
Why Quarter Kelly here: Even with 82% confidence, favorites at -350 carry significant risk. The 18% chance of losing warrants conservative sizing despite the edge.
Example 3: MLB Underdog Value Bet
Scenario: Oakland Athletics vs. New York Yankees
Bet details:
- Athletics moneyline: +185 (2.85 decimal)
- Sportsbook implied probability: 35.09%
- Your statistical model shows: 42% win probability
- Your edge: 6.91%
- Current bankroll: $8,000
Kelly calculation:
Kelly % = (0.42 × 2.85 - 1) / (2.85 - 1) = 0.197 / 1.85 = 10.6%
Full Kelly result: Bet 10.6% of bankroll = $848
Half Kelly result: Bet 5.3% of bankroll = $424
Outcome if Athletics win: Win $784 (Half Kelly), new bankroll = $8,784
Outcome if Athletics lose: Lose $424 (Half Kelly), new bankroll = $7,576
Key insight: Underdog value bets often show larger Kelly percentages because the edge is magnified by higher odds. However, lower win probability means more variance, making fractional Kelly even more important.
Example 4: Soccer Total Goals Market
Scenario: Manchester City vs. Burnley - Over 3.5 Goals
Bet details:
- Over 3.5 goals: +130 (2.30 decimal)
- Sportsbook implied probability: 43.48%
- Your expected goals model: 48% probability
- Your edge: 4.52%
- Current bankroll: $6,500
Kelly calculation:
Kelly % = (0.48 × 2.30 - 1) / (2.30 - 1) = 0.104 / 1.30 = 8.0%
Full Kelly result: Bet 8.0% of bankroll = $520
Half Kelly result: Bet 4.0% of bankroll = $260
Outcome if over 3.5 goals: Win $338 (Half Kelly), new bankroll = $6,838
Outcome if under 3.5 goals: Lose $260 (Half Kelly), new bankroll = $6,240
Kelly Criterion Performance Comparison
| Betting Strategy | Bet Size Method | Edge Required | Variance Level | Growth Rate | Risk of Ruin | Best For |
|---|---|---|---|---|---|---|
| Full Kelly | 100% of formula | Accurate edge estimate | Very High | Maximum theoretical | Low (if edge correct) | Mathematical purists |
| Half Kelly | 50% of formula | Good edge estimate | Moderate | ~75% of full Kelly | Very Low | Professional bettors |
| Quarter Kelly | 25% of formula | Rough edge estimate | Low | ~50% of full Kelly | Minimal | Conservative players |
| Fixed 2% Units | Always 2% bankroll | Any positive edge | Very Low | Steady but slower | Very Low | Beginners |
| Fixed 5% Units | Always 5% bankroll | Consistent edge | Moderate-High | Fast but risky | Moderate | Aggressive bettors |
| Martingale | Double after loss | None needed | Extreme | Negative long-term | Guaranteed eventually | Nobody (avoid) |
| Flat Betting | Same $ amount always | Any positive edge | Low | Linear only | Low | Casual bettors |
When to Use Kelly Criterion vs Fixed Unit Betting
Use Kelly Criterion When:
You have quantifiable edge from data models: If you're using statistical models, machine learning algorithms, or systematic approaches that output specific win probabilities, Kelly is ideal. For example, if your NFL model predicts 56.8% win probability on a -110 line, you have concrete numbers to input into the formula.
You've proven your edge over 500+ bets: Kelly requires accurate edge estimation. If your tracked betting history shows consistent positive ROI over hundreds of bets, you can trust your probability assessments enough to use Kelly sizing.
You're comfortable with mathematical variance: Kelly betting means bet sizes fluctuate significantly. One bet might be 2% of bankroll, another 8%. You need the emotional discipline to accept this variance and trust the math.
You have adequate bankroll depth: A minimum of 50-100 betting units allows Kelly to work properly. With $5,000 and Half Kelly suggesting 4% bets, you have 25 units at $200 each—enough to weather variance.
You can recalculate after every bet: Kelly requires updating bet sizes based on current bankroll. If you win and your bankroll grows to $5,500, your next 4% bet is $220, not $200.
Use Fixed Unit Betting When:
You're a beginner learning the ropes: Start with simple 1-2% fixed units while you develop your handicapping skills. Focus on finding +EV bets before optimizing bet sizing.
Your edge estimation is subjective: If you're betting based on "feel," injury analysis, or qualitative factors rather than statistical models, you can't accurately input win probabilities into Kelly. Fixed units are safer.
You prefer simplicity and consistency: Fixed 2% units mean every bet is the same size. Easy to track, easy to manage, and psychologically comfortable for most bettors.
You're betting recreationally: If sports betting is entertainment rather than profit-focused, fixed small units (1% or less) let you enjoy the action without complex calculations.
Your sample size is too small: With only 50-100 bets tracked, you don't have statistical confidence in your edge. Use fixed units until you've proven consistent profitability.
Real Bettor Scenarios:
Scenario A - Data Analyst: Sarah uses Python to scrape odds, builds regression models for NBA totals, and has 800 bets showing 5.2% ROI. She uses Quarter Kelly because her models are proven but she wants lower variance. Verdict: Kelly appropriate.
Scenario B - Casual Fan: Mike bets NFL games based on watching teams and reading injury reports. He has no tracked history and estimates win probability based on confidence level. Verdict: Use fixed 2% units.
Scenario C - Line Shopping Pro: James finds +EV opportunities by comparing odds across 8 sportsbooks. He bets only when he finds 3%+ edge based on market consensus. Uses Half Kelly on 2-3 bets per week. Verdict: Kelly appropriate.
Common Kelly Criterion Mistakes
❌ Mistake 1: Overestimating Your Edge
Wrong approach: "I really like the Chiefs here. I'd say they have a 65% chance to cover -3.5 even though the line suggests 52%. I'll bet Full Kelly at 13% of my bankroll!"
Right approach: "My model shows 58% win probability, but I'll discount to 56% to account for model uncertainty. I'll use Half Kelly to further reduce risk from edge overestimation."
Why it matters: If your actual edge is 3% but you think it's 10%, Kelly will suggest betting 3.3x more than optimal. Over 100 bets, this overconfidence can devastate your bankroll.
Dollar impact example:
- $10,000 bankroll, you think edge is 10% (Kelly says 10% = $1,000 bets)
- Real edge is only 3% (should bet ~$300)
- After 50 bets at 55% win rate: Expected bankroll = $8,200 (lost $1,800)
- If you'd bet correctly: Expected bankroll = $10,450 (gained $450)
- Overconfidence cost: $2,250
❌ Mistake 2: Using Full Kelly Without Understanding Variance
Wrong approach: "Kelly says 12% of bankroll, so I'll bet exactly $1,200 on this game. Math is math!"
Right approach: "Kelly suggests 12%, but Full Kelly has massive variance. I'll use Half Kelly at 6% ($600) to capture 75% of growth with 50% of variance."
Why it matters: Full Kelly can produce 20-30% bankroll swings even with positive edge. Most bettors can't psychologically handle watching their bankroll drop 25% despite making +EV bets.
Variance comparison over 100 bets (5% edge, 53% win rate):
- Full Kelly: 90th percentile = +45% bankroll, 10th percentile = -18% bankroll
- Half Kelly: 90th percentile = +28% bankroll, 10th percentile = -7% bankroll
- Quarter Kelly: 90th percentile = +16% bankroll, 10th percentile = -3% bankroll
❌ Mistake 3: Not Recalculating Based on Current Bankroll
Wrong approach: "I started with $5,000, and Kelly said to bet $250 (5%). I'll just keep betting $250 on every game."
Right approach: "After each bet, I recalculate 5% of my current bankroll. Won last bet? New bankroll is $5,227, so next bet is $261. Lost? Bankroll is $4,773, next bet is $239."
Why it matters: Kelly's power comes from geometric growth—betting more as you win, less as you lose. Fixed dollar amounts eliminate this advantage.
10-bet sequence example ($5,000 start, 5% Kelly):
- Dynamic Kelly: W-W-L-W-L-W-W-W-L-W = $5,847 final (+16.9%)
- Fixed $250 bets: Same results = $5,750 final (+15.0%)
- Difference: $97 lost by not recalculating
❌ Mistake 4: Applying Kelly to Parlays or Correlated Bets
Wrong approach: "I have 5% edge on Chiefs -3.5 and 5% edge on Over 47.5 in the same game. Kelly says 5% on each, so I'll bet $500 on Chiefs and $500 on Over."
Right approach: "These bets are correlated—if Chiefs cover, the Over is more likely. I need to reduce total exposure. I'll bet 3% on Chiefs ($300) and 2% on Over ($200) to account for correlation."
Why it matters: Kelly assumes independent bets. When outcomes are correlated, you're concentrating risk in a single game. If both lose, you suffer double damage.
Correlation risk example:
- Uncorrelated bets: Two 5% Kelly bets = 10% total exposure, outcomes independent
- Correlated bets: Two 5% Kelly bets in same game = 10% exposure, but 70% correlation means effective exposure is ~13-14%
- Result: You're over-betting by 30-40% without realizing it
❌ Mistake 5: Ignoring Bet Limits and Market Liquidity
Wrong approach: "Kelly says bet $2,000 on this obscure college basketball total. I'll place the full amount even though the book limits this market to $500."
Right approach: "Kelly suggests $2,000, but this is a limited market. I'll bet the $500 max, which is 1.25% of my bankroll instead of 5%. I'll find other +EV opportunities for the remaining allocation."
Why it matters: Smaller markets have lower limits and higher risk of line movement or bet rejection. Forcing full Kelly stakes into illiquid markets leads to worse prices and account limitations.
Market liquidity impact:
- NFL primetime game: Can bet $5,000+ without moving line
- Mid-major college basketball: $500 bet might move line from +3.5 to +3
- Obscure prop bet: $200 might trigger manual review and limit your account
❌ Mistake 6: Forgetting About Multiple Simultaneous Bets
Wrong approach: "I found 4 good bets today, each showing 6% Kelly. I'll bet 6% of my bankroll on all four—that's $2,400 total on my $10,000 bankroll."
Right approach: "I have 4 bets at 6% Kelly each. That's 24% total exposure. I'll reduce each to 4% Kelly to keep total exposure at 16%, or bet full Kelly on my top 2 picks only."
Why it matters: Kelly assumes you're betting once, then recalculating. Multiple simultaneous bets compound your risk. A bad day could wipe out 20-30% of your bankroll.
Simultaneous bet risk:
- One 6% Kelly bet: Risk 6% of bankroll
- Four 6% Kelly bets: Risk 24% of bankroll if all lose (unlikely but possible)
- Expected scenario (2 win, 2 lose): Still down 3-4% on the day despite +EV bets
- Solution: Scale each bet to 3-4% when betting multiple games
Strategic Implementation Guide
Step 1: Build Your Edge Detection System
Before using Kelly, you must have a reliable method to identify +EV bets and estimate win probability. Options include:
- Statistical models: Build regression models, Elo ratings, or expected goals frameworks
- Market comparison: Compare odds across 8+ sportsbooks to find outliers (Pinnacle closing line is gold standard)
- Bet tracking analysis: After 500+ bets, identify which bet types show consistent profit
Action item: Spend 3-6 months tracking bets with fixed 2% units. Calculate your actual ROI by sport, bet type, and odds range. This data reveals where your edge exists.
Step 2: Create a Kelly Calculator Spreadsheet
Build a Google Sheet or Excel file with these columns:
- Date and game details
- Odds (American and decimal)
- Your estimated win probability
- Implied probability from odds
- Calculated edge
- Full Kelly percentage
- Half Kelly percentage
- Current bankroll
- Recommended bet size
- Actual bet placed
- Result and new bankroll
Action item: Use formulas to auto-calculate Kelly percentages. Formula: =(WinProb*DecimalOdds-1)/(DecimalOdds-1)
Step 3: Start with Quarter Kelly for 100 Bets
Don't jump straight to Full or Half Kelly. Begin conservatively:
- First 100 bets: Quarter Kelly (25% of formula)
- Track results meticulously
- Calculate actual ROI vs expected ROI
- Assess if your edge estimates are accurate
Success metric: If your actual results are within 2-3% of expected results, your probability estimates are solid. If you're consistently overperforming or underperforming by 5%+, recalibrate your edge estimation.
Step 4: Establish Bankroll Management Rules
Set strict parameters before implementing Kelly:
- Minimum bankroll: 50x your average bet size (if Half Kelly suggests 4%, you need $5,000+ bankroll)
- Maximum single bet: Never exceed 10% of bankroll regardless of Kelly calculation
- Maximum daily exposure: Cap total at-risk amount at 20-25% of bankroll
- Bankroll refresh schedule: Recalculate bankroll weekly or after every 10 bets
- Withdrawal policy: Only withdraw profits above your starting bankroll to preserve unit sizing
Action item: Write these rules down and commit to following them even during winning or losing streaks.
Step 5: Implement Edge Estimation Conservatism
Always discount your estimated edge to account for uncertainty:
- Model-based estimates: Reduce by 20-30% (if model says 56%, use 54.5%)
- Market-comparison estimates: Reduce by 10-15% (if market suggests 3% edge, use 2.5%)
- Subjective handicapping: Reduce by 40-50% or don't use Kelly at all
Why this matters: It's better to underbet a real edge than overbet a perceived edge. The cost of overestimating is far greater than underestimating.
Step 6: Choose Your Kelly Fraction
Based on your risk tolerance and edge confidence:
- Full Kelly: Only if you have 1,000+ bet sample proving accurate edge estimation and high risk tolerance
- Half Kelly: Sweet spot for most professionals—captures 75% of growth with 50% of variance
- Quarter Kelly: Conservative approach for newer bettors or those with less edge confidence
- One-Eighth Kelly: Ultra-conservative for recreational bettors who want Kelly principles with minimal variance
Action item: Most bettors should start at Quarter Kelly and move to Half Kelly only after 250+ bets show consistent edge.
Step 7: Monitor and Adjust Monthly
Kelly isn't set-and-forget. Review performance every month:
- Calculate actual ROI vs expected ROI
- Review largest wins and losses—were bet sizes appropriate?
- Assess emotional response to variance—can you handle larger Kelly fractions?
- Check if edge estimates are accurate (compare predicted win rate to actual)
- Adjust Kelly fraction up or down based on results and comfort
Red flags to watch: If actual results are more than 5% worse than expected over 100+ bets, you're either overestimating edge or experiencing extreme bad variance. Reduce Kelly fraction until you identify the issue.
Real-World Historical Example: 6-Month Kelly Implementation
Bettor Profile: Alex, an NFL bettor with 2 years of fixed-unit experience showing 4.2% ROI over 400 bets. Decides to implement Half Kelly for the 2023 NFL season.
Starting parameters:
- Bankroll: $10,000
- Strategy: NFL spreads and totals only
- Edge estimation: Statistical model based on EPA and success rate metrics
- Kelly fraction: Half Kelly (50% of formula)
- Bet frequency: 8-12 bets per week during season
| Month | Bets Placed | Win Rate | Avg Bet Size | Total Wagered | Profit/Loss | Ending Bankroll | ROI |
|---|---|---|---|---|---|---|---|
| September | 42 | 54.8% | $387 | $16,254 | +$623 | $10,623 | +3.8% |
| October | 48 | 52.1% | $412 | $19,776 | +$287 | $10,910 | +1.5% |
| November | 51 | 47.1% | $425 | $21,675 | -$891 | $10,019 | -4.1% |
| December | 53 | 56.6% | $389 | $20,617 | +$1,124 | $11,143 | +5.5% |
| January | 46 | 54.3% | $433 | $19,918 | +$734 | $11,877 | +3.7% |
| Playoffs | 18 | 61.1% | $462 | $8,316 | +$612 | $12,489 | +7.4% |
Season totals:
- Total bets: 258
- Overall win rate: 53.9%
- Total wagered: $106,556
- Total profit: $2,489
- ROI: 2.3%
- Bankroll growth: +24.9%
Key Observations from Alex's Implementation:
Variance management worked: November's losing month (-$891) represented only 8.9% bankroll decline because Half Kelly automatically reduced bet sizes. Under fixed 5% units, the same losing streak would have cost $1,455 (29 losses × $50 fixed unit), a 14.6% bankroll hit.
Bet sizing adapted naturally: Notice how average bet size increased from $387 in September to $462 during playoffs as bankroll grew. This compounding effect is Kelly's primary advantage—you automatically bet more when you have more capital.
ROI vs bankroll growth divergence: Alex's 2.3% ROI was actually lower than his historical 4.2%, but his bankroll grew 24.9%. This demonstrates Kelly's power—even with slightly worse performance, proper sizing maximized growth.
Emotional discipline required: Alex noted that November was psychologically challenging. Watching bet sizes decrease as the bankroll shrank felt like "giving up," but this automatic adjustment prevented deeper losses.
Edge estimation accuracy: Alex's model predicted 54.5% win rate; he achieved 53.9%. This 0.6% difference is acceptable variance over 258 bets and validated his edge estimation process.
Platform Integration: Using Kelly with Modern Sportsbooks
Implementing Kelly in today's betting environment requires understanding how different platforms affect your strategy:
Odds Shopping and Kelly
Kelly calculations are extremely sensitive to odds differences. A bet that's 3% Kelly at -110 might be 5% Kelly at -105.
Best practice: Calculate Kelly percentage for each available line across your sportsbooks. Always take the best odds, but recalculate the Kelly percentage for that specific line.
Example:
- Your model: Chiefs -3 has 58% win probability
- Book A offers -110: Kelly = 3.6%
- Book B offers -105: Kelly = 4.8%
- Book C offers -115: Kelly = 2.1%
Always bet at Book B, but bet 4.8% of bankroll, not 3.6%.
Betting Limits and Kelly
Professional bettors often face limits below their Kelly recommendation. When limited:
- Don't force full Kelly across multiple books: If your Kelly bet is $500 but you're limited to $200, bet $200 and move on. Don't place $300 more at worse odds just to hit your Kelly amount.
- Adjust bankroll allocation: If consistently limited, consider that sport/market as having a smaller effective bankroll allocation.
- Track "Kelly efficiency": Monitor what percentage of your desired Kelly bets you can actually place. Below 60% efficiency suggests you need new outs or different markets.
Live Betting Considerations
Kelly becomes more complex with live betting because:
- Your bankroll changes throughout the day
- You may have correlated positions on the same game
- Edge estimation is harder with rapidly moving lines
Recommended approach: Set aside a separate "live betting bankroll" (20-30% of total) and apply Kelly within that subset. Recalculate bankroll only once daily, not after each bet.
Parlay and Same-Game Parlay Adjustments
Standard Kelly doesn't apply to parlays because:
- Correlation between legs is difficult to model accurately
- Compound probability makes edge estimation unreliable
- Sportsbook pricing on SGPs includes hidden vig that's hard to quantify
If you must bet parlays: Use one-eighth Kelly or smaller, and treat it as entertainment rather than optimal bankroll strategy.
Advanced Kelly: Beyond the Basics
Simultaneous Kelly (Multiple Bets at Once)
When placing multiple bets simultaneously, you can't simply calculate Kelly for each independently. The correct approach:
- Calculate individual Kelly percentages for each bet
- If total exceeds 15-20% of bankroll, you're over-leveraged
- Scale all bets down proportionally to reach acceptable total exposure
Example: You identify 5 bets, each showing 6% Kelly (30% total). Scale each to 3.6% (18% total) to maintain proper risk management.
Kelly with Bonuses and Promotions
Sportsbook promotions change Kelly calculations:
- Profit boosts: Increase decimal odds in formula by boost percentage
- Risk-free bets: Treat as having higher win probability (you get a second chance)
- Odds boosts: Recalculate Kelly with boosted odds—often turns marginal bets into strong Kelly plays
Warning: Don't let promotions seduce you into betting without edge. A 50% profit boost on a bet with no edge is still a losing proposition.
Final Recommendations: Your Kelly Action Plan
Based on your experience level, here's your implementation roadmap:
Beginner Bettors (Less than 100 bets tracked)
- Don't use Kelly yet. You don't have enough data to estimate edge accurately.
- Bet 1-2% fixed units while building your track record
- Focus on developing edge before optimizing bet sizing
- Study Kelly principles so you're ready when you have proven edge
Intermediate Bettors (100-500 bets, positive ROI)
- Start with Quarter Kelly
- Track every bet with closing line value (CLV) to validate edge
- Recalculate bankroll weekly, not daily
- Set a 6-month review to assess if you can move to Half Kelly
- Maintain separate spreadsheet tracking Kelly recommendations vs actual bets
Advanced Bettors (500+ bets, consistent 3%+ ROI)
- Implement Half Kelly as your standard
- Develop statistical models for edge estimation rather than gut feel
- Consider Full Kelly only for your highest-confidence plays (top 10%)
- Use simultaneous Kelly calculations when betting multiple games
- Track Kelly efficiency and adjust based on actual variance experienced
Professional Bettors
- Customize Kelly fractions by market based on edge confidence
- Implement dynamic Kelly that adjusts based on recent performance
- Use Kelly across multiple bankrolls (different sports, different books)
- Consider fractional Kelly variations like "Kelly with a cap" for extreme edges
The bottom line: Kelly Criterion is the mathematically optimal bet sizing strategy, but only when you have accurate edge estimation and emotional discipline to handle variance. Start conservative, prove your edge, then gradually increase your Kelly fraction as your confidence and bankroll grow. The bettors who succeed with Kelly are those who respect both its power and its requirements.
Learn how to apply the Kelly Criterion with our comprehensive Kelly Criterion Calculator guide including real examples and common mistakes to avoid.