What is the Kelly Criterion?
The Kelly Criterion is a formula that calculates the mathematically optimal fraction of your bankroll to wager on a bet, given your edge and the odds. Developed by John L. Kelly Jr. at Bell Labs in 1956, it was originally designed to maximize signal throughput — and later adopted by investors and bettors because it maximizes long-run bankroll growth.
The core idea: bet proportionally to your edge. Large edge → larger bet. Small edge → smaller bet. No edge → do not bet at all. This prevents the two most common bankroll mistakes: betting too little (leaving profit on the table) and betting too much (risking ruin during normal downswings).
The Kelly Formula
Full Kelly fraction (f*):
f* = (b × p − q) / b
Where: - f* = fraction of bankroll to wager - b = decimal odds − 1 (the net profit per unit wagered) - p = estimated win probability (as a decimal) - q = 1 − p (estimated lose probability)
Example with real numbers: - Prop: Over 25.5 Points at −110 American odds - Decimal odds: 1.909 - b = 1.909 − 1 = 0.909 - Estimated win probability: 58% → p = 0.58, q = 0.42 - f* = (0.909 × 0.58 − 0.42) / 0.909 = (0.527 − 0.42) / 0.909 = 0.107 / 0.909 ≈ 0.118
Result: Full Kelly recommends wagering approximately 11.8% of your bankroll on this bet.
Kelly Fraction at Different Edge Levels
| Win Probability Estimate | American Odds | Edge Over Implied Prob | Full Kelly % | Half Kelly % | Quarter Kelly % |
|---|---|---|---|---|---|
| 54% | -110 | +1.6% | 3.0% | 1.5% | 0.75% |
| 58% | -110 | +5.6% | 11.8% | 5.9% | 2.95% |
| 62% | -110 | +9.6% | 20.7% | 10.4% | 5.2% |
| 55% | +110 | +9.5% | 15.5% | 7.75% | 3.9% |
| 50% | -110 | -2.4% | 0% (no bet) | 0% (no bet) | 0% (no bet) |
Why Fractional Kelly Is Recommended
Full Kelly maximizes theoretical long-run bankroll growth, but it comes with serious practical problems:
1. **Probability estimation error**: If you estimate 58% win probability but the true probability is 54%, full Kelly will over-bet significantly, increasing risk of large drawdowns.
2. **Extreme volatility**: Full Kelly can recommend bet sizes of 10-20%+ of bankroll on a single prop. Even with a genuine edge, you will experience brutal downswings that are psychologically very difficult to sustain.
3. **The math is unforgiving**: A single catastrophic loss at full Kelly sizing creates a much larger hole to climb out of than fractional Kelly would.
For these reasons, most professional bettors use Half Kelly (50% of the formula's output) or Quarter Kelly (25%). PropLab's Kelly Calculator shows all three options simultaneously — the recommended default is Half Kelly.
Bankroll safety rule: Never let a single bet exceed 5% of your total bankroll, regardless of what the formula suggests. Large edge estimates are often the result of probability overconfidence, not genuine alpha.
Common Kelly Criterion Mistakes
1. Using full Kelly with uncertain probability estimates: If your win probability estimate is off by even 3-5 percentage points, full Kelly dramatically over-bets. Use fractional Kelly as a safety buffer.
2. Applying Kelly without an edge: Kelly only works when you have a genuine +EV edge. Applying it to -EV bets mathematically tells you not to bet — if Kelly returns a positive fraction for what should be a -EV bet, your probability estimate is wrong.
3. Not adjusting for correlated bets: If you place multiple bets on the same game (e.g., multiple props on one player), the outcomes are correlated. Standard Kelly assumes independent bets. Using Kelly on correlated bets can lead to over-betting.
4. Forgetting to update the bankroll: Kelly fractions are calculated as a percentage of your current bankroll. After wins or losses, recalculate from the new bankroll balance — not the starting amount.
5. Ignoring drawdown limits: Set a maximum loss threshold (e.g., 20-25% drawdown) at which you stop betting and review your process. This protects against extended losing streaks breaking your bankroll before the edge has time to express itself.
Using PropLab's Kelly Calculator
PropLab's Kelly Calculator at /tools/kelly-calculator takes three inputs: - Your odds (American, decimal, or fractional format) - Your estimated win probability - Your current bankroll
It instantly returns: - Full Kelly percentage and dollar amount - Half Kelly percentage and dollar amount (recommended) - Quarter Kelly percentage and dollar amount (conservative) - A "No Bet" signal when there is no edge at the given inputs
Use the Kelly Calculator alongside the EV Calculator in your pre-bet workflow: first confirm the bet is +EV with the EV Calculator, then use the Kelly Calculator to determine appropriate position sizing. Always start with Half or Quarter Kelly until you have validated your probability estimates over a large sample.
Frequently Asked Questions
- What is the Kelly Criterion?
- The Kelly Criterion is a mathematical formula that calculates the optimal fraction of your bankroll to wager based on your edge and odds. Formula: f* = (b × p − q) / b, where b = decimal odds − 1, p = win probability, q = 1 − p. It maximizes long-run bankroll growth when applied correctly.
- Why should I use fractional Kelly instead of full Kelly?
- Full Kelly is theoretically optimal but requires perfectly accurate probability estimates. In practice, even small overestimates of edge lead to significant over-betting and large drawdowns. Half Kelly or Quarter Kelly provides most of the long-run growth benefit with substantially less volatility. Most professionals use Half Kelly as their default.
- What happens if I have no edge at the given odds?
- The Kelly formula returns zero or a negative fraction — meaning do not bet. This is the correct output. Forcing a bet where there is no mathematical edge is a losing strategy that Kelly explicitly rejects.
- Can I apply Kelly to multiple simultaneous bets?
- Standard Kelly assumes each bet is independent. When betting multiple props on the same game or player, outcomes may be correlated, and standard Kelly will over-recommend bet sizes. Use more conservative fractions (Quarter Kelly or smaller) when betting multiple correlated markets.
- How often should I update my bankroll for Kelly calculations?
- Recalculate Kelly fractions from your current bankroll balance regularly — at minimum monthly, ideally weekly or after any significant win/loss. Kelly percentages are relative to current bankroll, not your starting amount.
- What is a safe maximum bet size per prop?
- As a practical rule, most disciplined bettors cap individual bets at 2-5% of bankroll regardless of Kelly output. This protects against catastrophic drawdowns from probability estimation errors. Never bet money you cannot afford to lose.