The Kelly Criterion: Sizing for Compounding
The Kelly Criterion is the optimal bet-sizing formula. It tells you what fraction of your bankroll to risk on a single trade to maximize long-term geometric growth. Bet too little and you leave money on the table. Bet too much and a single bad streak wipes you out. Kelly is the math that threads that needle.
The Formula
For a binary bet:
f* = (b × p − q) / b
Where:
- •f* = optimal fraction of your bankroll to risk
- •b = the net odds you receive (profit per $1 risked)
- •p = your estimated probability of winning
- •q = 1 − p (probability of losing)
If f* is negative, the bet has negative EV — don't take it.
Working a Numerical Example
Back to our "Fed cuts rates" market. Your estimate: 55% probability. Market price: $0.40 for Yes.
If Yes wins, you receive $1.00 for your $0.40 share — profit $0.60 per $0.40 risked = 1.5x net odds.
So b = 1.5, p = 0.55, q = 0.45.
f* = (1.5 × 0.55 − 0.45) / 1.5 = (0.825 − 0.45) / 1.5 = 0.375 / 1.5 = 0.25
Kelly says to risk 25% of your bankroll on this trade. With a $1000 bankroll, that's $250 — and notice this is a very aggressive sizing for a market that's only slightly favored.
Why "Full Kelly" Is Almost Always Too Much
Full-Kelly sizing assumes:
- Your probability estimate is exactly right.
- You can rebalance instantly after each trade.
- You can stomach 50%+ drawdowns without changing your strategy.
In practice, none of these hold. Your estimate is approximate (real probability could be 50% or 60%, not exactly 55%). You can't rebalance perfectly. And drawdowns mess with your judgment.
Almost every serious bankroll-management text recommends fractional Kelly: bet a fraction (often 1/2, 1/4, or 1/5) of what Kelly recommends.
- •Half Kelly: bet 12.5% of bankroll instead of 25%. About 75% of the geometric growth, but only half the drawdown risk.
- •Quarter Kelly: 6.25%. About 50% of the growth, but very smooth equity curve.
- •Eighth Kelly: 3.1%. Even smoother. Almost no risk of ruin even with bad estimates.
For a beginner, quarter Kelly is a reasonable default. Once you have 100+ resolved trades to validate your edge, you can scale up gradually.
A Critical Failure Mode: Overestimating Your Edge
The single most dangerous Kelly mistake: thinking your edge is bigger than it actually is.
If you believe you have a 55% probability when the true probability is 50%, you'll bet aggressively on what's actually a coinflip. Over enough trades, you'll lose money — even though Kelly recommends a big position size.
How to protect against this:
- •Use Predite's AI estimate as a starting point, then adjust down. Models are calibrated, but no model is perfect. Apply a conservative haircut to its confidence (e.g., if AI says 55%, treat it as 53%).
- •Never use full Kelly with an unproven edge. Quarter Kelly is the floor until you have 100+ resolved trades.
- •Track your win rate vs. predicted win rate. If your model predicts 60% winners and you're only hitting 55%, your model is mis-calibrated. Trade smaller until you fix it.
Position Size Caps (Beyond Kelly)
Kelly recommends a percentage of bankroll. In practice, you also want absolute caps:
- •Max 25% of bankroll in any single market, regardless of what Kelly says. One unexpected resolution shouldn't wipe you out.
- •Max 50% of bankroll exposed to correlated markets. If three markets all resolve on the same Fed decision, treat them as one bet.
- •Max 5-10% in highly illiquid markets ($10k or less daily volume). You may not be able to exit at the price you expect.
Kelly Across Multiple Simultaneous Trades
If you have several +EV opportunities at once, you can't just add up the Kelly sizes — that would over-leverage you. The simple approximation:
- •Compute each trade's Kelly fraction.
- •Sum them.
- •If the sum exceeds your "max exposure" (say 50% of bankroll), scale each one proportionally.
So if you have three trades each suggesting 20% Kelly = 60% total, scale all three down to ~17% each so the sum hits your 50% cap.
A more sophisticated approach considers correlation between trades, but for most retail traders the simple proportional scaling is enough.
Practical Kelly Workflow in Predite
The Predite Position Size Calculator does the math for you:
- •Go to Dashboard → Kelly Calculator.
- •Enter the market price and your estimated probability.
- •Enter your bankroll and your preferred Kelly fraction (default: 0.25 = quarter Kelly).
- •The calculator outputs your suggested USD position size and the expected geometric growth rate.
For automated bots, the bot configuration page lets you specify a Kelly fraction directly, and the bot sizes each trade according to that fraction of available capital.
What Kelly Doesn't Tell You
Kelly is about sizing, not about which trades to take. It assumes you've already identified a +EV opportunity. The work of figuring out whether your edge estimate is correct — that's the part Predite focuses on. Once you have an estimate, Kelly tells you how big to go.
Also worth noting: Kelly maximizes long-term geometric growth, not short-term EV. For very long-tail bets (like "1% probability paying out 1000:1"), Kelly will recommend a vanishingly small fraction, even though the EV per dollar is huge. This is correct math — even a small chance of losing your bankroll has catastrophic geometric cost.
Common Kelly Pitfalls to Avoid
- •Doubling up after losses. This is "anti-Kelly" — it increases position size right when your effective bankroll has decreased. Lethal over a long enough series.
- •Skipping the Kelly calc because the edge looks small. A 3pp edge on a 50/50 market still implies a real (positive) Kelly fraction. Take small bites consistently.
- •Confusing position size with conviction. Your subjective confidence is already in the probability estimate. Don't double-count by sizing up beyond what Kelly says just because you "feel sure".
- •Recomputing the bankroll only quarterly. Kelly is dynamic — your bankroll changes after every trade. Predite recomputes automatically on every trade for bots; for manual trading, refresh your bankroll number monthly at minimum.