The Kelly Criterion for Sports Betting (and Why Most Bettors Use a Fraction of It)
How to size a bet from its edge, what happens when you bet too much, and why fractional Kelly is the practical choice.
The Smart Lines teamOctober 20264 min read
What the Kelly criterion is
Finding a good bet is half the job; the other half is deciding how much to stake. The Kelly criterion, a formula from 1956, gives the share of your bankroll that grows it fastest over the long run when you have a real edge. Bet more when your edge is bigger, less when it’s smaller, and nothing when there’s no edge.
The formula
stake as a share of bankroll = (b × p − q) ÷ b
bis your net profit per $1 if the bet wins: decimal odds minus 1 (+150 is 2.50 − 1 = 1.5).pis the chance of winning, ideally a fair, no-vig probability (see no-vig odds).qis the chance of losing: 1 − p.
If the result is zero or negative, the bet has no edge and Kelly says don’t bet.
Example
+150 with a 42% fair chance of winning
- b = 2.50 − 1
- 1.5
- p, q
- 0.42, 0.58
- (1.5 × 0.42 − 0.58) ÷ 1.5
- 3.33% of bankroll
With a $1,000 bankroll, full Kelly says stake $33.33. This bet is +5% EV (see expected value), so Kelly stakes a modest amount even on a clear edge.
What happens if you bet more or less than Kelly
Kelly maximises how fast your bankroll grows over many bets. The table shows the long-run growth per bet for the example above at different stake sizes:
| Stake | Share of bankroll | Long-run growth per bet |
|---|---|---|
| 1/8 Kelly | 0.42% | +0.020% |
| 1/4 Kelly | 0.83% | +0.036% |
| 1/2 Kelly | 1.67% | +0.062% |
| Full Kelly | 3.33% | +0.083% |
| 2× Kelly | 6.67% | +0.001% |
| 3× Kelly | 10.00% | −0.241% |
Two things stand out:
- Half Kelly keeps about three-quarters of the growth with far smaller swings.
- Overbetting is worse than underbetting. At twice Kelly the growth is gone, and at three times Kelly you shrink your bankroll over time even though every bet is +EV.
Why most bettors use fractional Kelly
Full Kelly assumes you know the true probability exactly. You don’t: a fair price is an estimate, and if your edge is smaller than you think, full Kelly is really overbetting. Full Kelly also produces large swings: there’s roughly an even chance your bankroll halves at some point along the way. A fraction of Kelly gives up a little growth in exchange for much more safety.
For example, The Smart Lines’ Strategy mode suggests 1/8 Kelly, capped at 1.5% of bankroll per bet, and recommends keeping each game under 3% and each day under 15% of bankroll. That’s deliberately conservative for prices that are themselves estimates.
The short version
- Kelly stake = (b × p − q) ÷ b, as a share of bankroll.
- It grows a bankroll fastest when your probability is right.
- Overbetting is costly; at twice Kelly the growth disappears.
- Fractional Kelly with caps is the practical choice.
Work out stakes with the Kelly criterion calculator, and check the edge first with the expected value calculator.