What Is the Kelly Criterion?
The Kelly Criterion is a formula developed by John L. Kelly Jr. at Bell Labs in 1956 that determines the optimal fraction of your bankroll to wager when you have an edge. It maximizes the long-term geometric growth rate of your bankroll, balancing the desire to capitalize on an edge against the risk of ruin from overbetting.
The formula is: f* = (bp - q) / b, where b is the net odds (decimal odds minus 1), p is your estimated probability of winning, and q is the probability of losing (1 - p). When the result is positive, you have an edge worth betting. When it is negative or zero, the math says to pass.
Most professionals use fractional Kelly (typically quarter or half Kelly) to reduce variance and protect against probability estimation errors. Read the full Kelly Criterion guide for detailed strategy, worked examples, and the mathematics behind fractional Kelly.
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Formula Breakdown
Edge Detected
Unit Sizing Reference Table
Kelly percentages map to a standardized unit system for practical bankroll management. This table shows how Olympus Bets converts Kelly output to unit recommendations using half Kelly:
| Kelly % | Unit Size | Confidence Level | $10K Bankroll (Half Kelly) |
|---|---|---|---|
| 0 - 1% | 0.5 units | Minimum threshold | $25 - $50 |
| 1 - 3% | 1.0 unit | Standard play | $50 - $150 |
| 3 - 6% | 1.5 units | Above average edge | $150 - $300 |
| 6 - 10% | 2.0 units | Strong edge | $300 - $500 |
| 10 - 15% | 2.5 units | Very strong edge | $500 - $750 |
| 15%+ | 3.0 units | Maximum (capped) | $750+ |
League-specific caps apply on top of this table. For example, soccer bets are capped at 2.0 units regardless of Kelly output, because low-scoring sports have inherently higher variance that model probabilities cannot fully capture.
| League | Max Units | Rationale |
|---|---|---|
| NBA / NFL / MLB | 3.0u | Deep data, high possession/at-bat counts |
| CBB / NHL | 2.5u | Higher variance environments |
| Soccer | 2.0u | Very low scoring, draws common |
How Olympus Bets Uses Kelly
At Olympus Bets, the Kelly Criterion is never applied to raw model output. Every probability estimate goes through a multi-layer calibration pipeline before reaching the Kelly formula:
- Monte Carlo simulation produces raw win/cover/total probabilities from 10,000+ iterations per game
- Bayesian calibration applies 15% shrinkage toward 50%, then Platt scaling, to correct for model overconfidence
- Ensemble stacking blends the calibrated model probability with market-implied probability and contextual signals
- Kelly sizing converts the calibrated edge into a unit recommendation
- League caps enforce sport-specific maximums to account for inherent variance differences
- Profitability zone gating blocks or boosts bets based on 15-dimensional historical performance analysis
This pipeline ensures that every unit recommendation reflects a genuine, calibrated edge rather than raw model overconfidence. The result: sustainable bankroll growth with manageable drawdowns.
Further Reading
- Kelly Criterion for Sports Betting: Full Guide — complete formula breakdown, fractional Kelly strategy, and common mistakes
- Monte Carlo Simulation in Sports Betting — how the probability estimates that feed Kelly are generated
- Bayesian Probability Calibration — why raw probabilities must be calibrated before Kelly sizing
- Our Methodology — full technical overview of the Olympus Bets platform