Finding an edge is only half the job. The other half is deciding how much to actually bet — and this is where most traders either leave money on the table or blow up their bankroll. Kelly sizing solves this problem with math instead of gut feel, and fractional Kelly makes it safe enough to use in the real world.
What the Kelly Criterion Does
The Kelly Criterion answers one question: If you have the edge and the odds are being offered, what percentage of your bankroll will give you the greatest growth? The formula for a binary market is:
f = (bp − q) / b
Where:
- f = fraction of your bankroll to bet
- b = net odds received (payout per $1 risked, minus 1)
- p = your estimated probability of winning
- q = probability of losing (1 − p)
If a “yes” contract trades at $0.40 and you believe the true probability is 55%, buying it pays out $1 for a $0.40 cost — so b = 1.50. Plugging in: f = (1.50 × 0.55 − 0.45) / 1.50 ≈ 0.25, or 25% of your bankroll. Full Kelly is already telling you something useful here — but for almost everyone, betting full Kelly is a mistake.
Why Fractional Kelly, Not Full Kelly
Full Kelly assumes your probability estimate is exactly correct. In practice, base rate estimates are always a bit noisy — you might genuinely believe 55%, but the true number could be 50% or 60%. Full Kelly sizing punishes that uncertainty severely: a slightly overconfident estimate can lead to wild bankroll swings or catastrophic drawdowns.
This is why most disciplined traders use half-Kelly (50% of the full formula) or quarter-Kelly (25%). Using the example above, quarter-Kelly would mean betting about 6.25% of your bankroll instead of 25%. You give up some theoretical growth rate, but you cut variance dramatically and protect against the reality that your “edge” might be smaller than you think — or might not exist at all.
Applying the Fractional Adjustment
Once you’ve calculated full Kelly, applying the fraction is a simple multiplication — but choosing which fraction to use should depend on how confident you actually are in your estimate:
- Quarter-Kelly (0.25×) — the standard default for most prediction market bets. Use this when your estimate is based on a solid reference class but still carries real uncertainty, which is true of almost every market.
- Half-Kelly (0.50×) — reserve this for cases where your edge is unusually well-supported: a deep, reliable reference class, a resolution you’re certain will be clean, and no reason to think the market is mispriced on purpose.
- Eighth-Kelly (0.125×) or lower — appropriate when your estimate is more of an educated guess than a rigorous base rate, or when you’re testing a new type of market you haven’t traded before.
The mechanics are always the same: take your full Kelly percentage, multiply it by your chosen fraction, and that’s your position size as a percentage of bankroll.
A Worked Example
Say your bankroll is $2,000. You estimate a market’s true probability at 65%, while the market is pricing it at 55%. Net odds (b) come out to about 0.818 (payout of $1 for $0.55 risked). Full Kelly gives roughly f = (0.818 × 0.65 − 0.35) / 0.818 ≈ 0.226, or 22.6% of the bankroll ($452). At quarter-Kelly, that shrinks to about 5.6%, or roughly $113 — a far more survivable position size if your 65% estimate turns out to be too optimistic.
Practical Rules for Sizing in Real Markets
- Cap single-position size regardless of what the formula says — many traders set a hard ceiling (e.g., 5–10% of bankroll) no matter how large the calculated edge appears.
- Re-check your estimate, not just the math. A large Kelly output is often a sign your probability estimate needs a second look, not a green light to size up.
- Account for resolution risk and liquidity. Kelly assumes clean, guaranteed payouts — ambiguous resolution criteria or thin order books mean your effective edge is smaller than the formula suggests.
- Reduce your fraction further for correlated bets. If you’re holding several positions tied to the same underlying event (say, multiple Fed-related markets), size each one down since they aren’t truly independent.
The Takeaway
Fractional Kelly turns “how much should I bet” from a gut call into a repeatable process: estimate your edge, run the formula, then deliberately scale it down to account for the uncertainty in your own estimate. It won’t guarantee any single trade wins — but it’s what keeps a real edge from turning into a blown bankroll.
