NBA Props Kelly Criterion: Optimal Bet Sizing
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PropStarz – Alex Selesnick – achieved a 490-353 record on NBA prop bets over two seasons, generating 75.73 units of profit. Those numbers represent elite performance, but they also raise a question that haunts every profitable bettor: how much should you stake on each wager to maximise long-term growth without risking ruin? The Kelly Criterion provides a mathematical answer, though applying it to props betting requires understanding both its power and its limitations.
I discovered Kelly Criterion early in my props career and initially implemented it too aggressively. The formula suggested stakes that felt enormous, and variance quickly taught me humility. Nine years later, I use a modified version that captures Kelly’s insights while protecting against the estimation errors that make pure Kelly dangerous in practice.
The Kelly Formula Explained
Kelly Criterion calculates the optimal fraction of your bankroll to bet based on your edge and the odds offered. The formula is: Kelly % = (bp – q) / b, where b is the decimal odds minus 1, p is your probability of winning, and q is your probability of losing (which equals 1 – p).
Let me work through an example. You estimate 58% probability of winning a prop at 1.91 decimal odds. Here, b = 0.91 (decimal odds minus 1), p = 0.58, and q = 0.42. Kelly % = (0.91 x 0.58 – 0.42) / 0.91 = (0.528 – 0.42) / 0.91 = 0.108 / 0.91 = 0.119 or roughly 12% of bankroll.
That 12% stake feels aggressive, and it should. Kelly optimises for maximum bankroll growth rate, not for minimising variance or psychological comfort. Betting 12% of your bankroll on a single prop means dramatic swings – a few losses in a row and you have lost significant capital even if your long-term edge remains intact.
The formula assumes you know your true edge with certainty. This assumption fails immediately in props betting. Your 58% probability estimate might be wrong. Maybe the true probability is 54% or 62%. Kelly’s recommendation changes dramatically based on edge estimates, and small errors compound into large differences in suggested stakes.
Fractional Kelly for Real-World Betting
Virtually no serious bettor uses full Kelly. The standard practice is fractional Kelly – betting some fraction of the Kelly-optimal stake, typically one-quarter to one-half. This approach sacrifices some theoretical growth rate in exchange for reduced variance and protection against estimation errors.
Half Kelly means betting 50% of whatever the formula recommends. In the earlier example where full Kelly suggested 12%, half Kelly would be 6%. Quarter Kelly drops it to 3%. These reduced stakes produce smoother equity curves with fewer gut-wrenching drawdowns while still capturing most of the formula’s bankroll-growing benefits.
I default to quarter Kelly for most props bets. The reasoning is simple: my probability estimates are imperfect. I might be 58% confident in a bet but the true probability could be anywhere from 52% to 64%. Quarter Kelly provides a buffer that keeps me in the game when my estimates miss while still sizing up meaningfully when I have genuine edges.
The fraction you choose reflects your confidence in your edge estimates. Bettors with rigorous models and long track records verifying their accuracy might justify half Kelly. Beginners or those using informal analysis should lean toward quarter Kelly or even less until they have evidence their estimates are reliable.
Applying Kelly to Props Specifically
Props betting presents challenges that Kelly’s original context – horse racing with well-defined probabilities – did not face. The variance inherent in player props means even correct probability estimates produce wildly different outcomes game to game. A player prop with 58% true probability might hit at 50% over a 30-bet sample purely through variance.
I adjust Kelly stakes based on prop type variance. High-variance props like three-pointers made or steals get additional haircuts beyond my standard fractional Kelly. If half Kelly suggests 5% for a points prop, I might use 3% for an equivalent-edge steals prop. The mathematical edge might be identical, but the path to realising that edge differs enormously.
Correlation between bets complicates Kelly calculations. If you bet three props in the same game, their outcomes are not independent – a blowout affecting one likely affects the others. Pure Kelly assumes independent bets. When props are correlated, you should reduce combined exposure beyond what individual Kelly calculations suggest.
Daily volume affects practical implementation. Some nights offer five strong betting opportunities; others offer one. Kelly technically should be recalculated after each bet as your bankroll changes. In practice, I calculate stakes at the start of each day based on my current bankroll and treat that as fixed for the night’s bets.
Practical Limits and Considerations
Research shows gambling addiction correlates with lower credit scores, higher bankruptcy rates, and increased overdraft fees – consequences that Kelly cannot protect against if you bet money you cannot afford to lose. The formula optimises bankroll growth, not financial wellbeing. Only apply Kelly to a betting bankroll entirely separate from living expenses.
Maximum stake caps provide additional safety beyond fractional Kelly. I never bet more than 3% of my bankroll on a single prop regardless of what the formula suggests. This ceiling protects against both estimation errors and the psychological damage of large individual losses. Even with a massive edge, one unlucky streak could devastate both bankroll and confidence.
Minimum stakes create a practical floor. Kelly might suggest 0.5% on a marginal edge, but minimum bet sizes on most platforms mean you cannot bet that little without effectively over-betting. When Kelly suggests stakes below your minimum practical bet, either pass on the wager or accept that you are over-Kelly for that specific bet.
Bankroll tracking enables proper Kelly implementation. You need to know your current bankroll precisely to calculate appropriate stakes. This seems obvious but many bettors estimate rather than track. A spreadsheet recording every bet, win, and loss lets you apply Kelly correctly to your actual situation rather than a guess.
Kelly Criterion Props FAQ
What is Kelly Criterion for betting?
Kelly Criterion is a mathematical formula that calculates the optimal stake size based on your edge and the odds offered. It maximises long-term bankroll growth rate by betting more when edges are larger and less when edges are smaller. The formula assumes you know your true winning probability, which makes it sensitive to estimation errors in practice.
Should I use full or fractional Kelly?
Use fractional Kelly – typically quarter to half of the formula’s recommendation. Full Kelly produces optimal growth mathematically but assumes perfect probability estimates, which no bettor has. Fractional Kelly sacrifices some growth rate for reduced variance and protection against estimation errors. Most professionals use quarter to half Kelly.
Is Kelly Criterion good for props?
Kelly provides useful guidance for props bet sizing but requires modification for this context. Props carry higher variance than Kelly’s original applications, and probability estimates are inherently uncertain. Use fractional Kelly, apply additional haircuts for high-variance prop types, and cap maximum stakes regardless of what the formula suggests.
From Formula to Practice
Kelly Criterion transformed my bet sizing from guesswork to system. Before Kelly, I sized bets based on confidence feelings that did not correspond to actual edge. A bet I felt great about might have the same mathematical edge as one I felt uncertain about. The formula forces quantification of that edge and translates it into appropriate stakes.
But formulas are tools, not masters. Kelly tells you what to bet given your inputs; it cannot tell you whether your inputs are correct. The work of props betting remains identifying genuine edges. Kelly simply ensures that when you find them, you capitalise appropriately without risking ruin. Use it as one component of a complete betting system, not as a replacement for the analytical skill that creates edges in the first place.
Prepared by the nba Bets Props editorial staff.
