The Kelly Criterion: Optimal Bankroll Management for Sports Bettors

What is the Kelly Criterion?

The Kelly Criterion is a mathematical formula that calculates the optimal percentage of your bankroll to bet on a given wager, given your edge and the payout odds. It was developed by John L. Kelly Jr. at Bell Labs in 1956, originally for information theory — and later adopted by gamblers and investors as the gold standard for growth-optimal bet sizing.

The full Kelly formula is:

f = (bp − q) / b

Where:

• f = fraction of bankroll to bet
• b = net odds received (decimal odds minus 1)
• p = probability of winning (our model's estimate)
• q = probability of losing (1 − p)

A concrete example

You want to bet on a team at −110 odds. Our model says they have a 56% chance of winning.

• Decimal odds = 1.909, so b = 0.909
• p = 0.56, q = 0.44
• Full Kelly: (0.909 × 0.56 − 0.44) / 0.909 = (0.509 − 0.44) / 0.909 = 7.6% of bankroll

On a $1,000 bankroll that is $76 per bet — aggressive for most bettors.

Why SherlockPicks uses fractional Kelly

The full Kelly formula is mathematically optimal for maximising bankroll growth in the long run, but it assumes your edge estimate is perfectly accurate. In practice, model probabilities are approximations. Overestimating your edge can lead to overbetting and severe drawdowns.

SherlockPicks applies a 25% fractional Kelly: we take the full Kelly bet size and multiply it by 0.25. This approach:

• Reduces variance significantly without sacrificing much of the growth rate
• Acts as a safety margin for model estimation error
• Keeps individual bets in a range most bettors find comfortable (typically 0.3–1.5 units)

Additional caps: maximum 1.5 units per bet and 5 units per day, regardless of what Kelly suggests.

Kelly and unit management

Rather than treating Kelly as an absolute dollar figure, it is best understood as a relative guide. If Kelly says 5% and you use fractional Kelly at 25%, that is 1.25% of bankroll — roughly 0.6 units if you define 1 unit as 2% of bankroll. This is the connection between the Kelly formula and the "units" system: Kelly determines the relative weighting, units translate that into a standard bet size.

The compounding effect

The power of Kelly — even fractional Kelly — is that it automatically adjusts bet sizes as your bankroll changes. A winning streak grows your unit size proportionally. A losing streak shrinks it, protecting against ruin. This is the single biggest advantage of percentage-based betting over flat dollar betting.

Over a full NBA regular season of consistent +5% EV betting at fractional Kelly, a $1,000 bankroll typically grows to $1,100–$1,400 depending on variance. Flat betting the same amount every game produces similar profits but with a higher risk of significant drawdown periods.