Kelly Criterion — Optimal Position Size from Statistics
How much of your account should you risk per trade when you know win rate and average win/loss ratio? The Kelly criterion gives a mathematical answer: the risk fraction that maximizes long-term logarithmic growth. The Kelly criterion calculator on indicator.trading computes full Kelly, half-Kelly, and quarter-Kelly — so you see what the formula recommends and what is survivable in practice.
Kelly is not a substitute for discipline or chart analysis. It is a statistics tool for traders with documented edge — and a warning against over-optimization. This guide explains the formula, variants, and why most pros deliberately stay below Kelly.
What is the Kelly criterion?
Developed by John L. Kelly Jr. (1956), originally for information theory — later adapted for betting and trading. The core question:
What fraction of capital maximizes expected logarithmic growth over many identical bets?
In trading:
- W = win rate (0–1)
- R = average win ÷ average loss (money or R)
Kelly fraction f = W − (1 − W) / R*
Result as decimal — e.g. 0.15 = 15% account risk per trade per full Kelly.
💡 Nice to Know: Kelly maximizes long-term growth, not short-term comfort. It accepts drawdowns most people cannot handle psychologically.
Calculating Kelly — step by step
Example 1: solid swing system
- Win rate: 45% → W = 0.45
- Avg. win / avg. loss: 2.0 → R = 2
f* = 0.45 − (1 − 0.45) / 2
f* = 0.45 − 0.55 / 2
f* = 0.45 − 0.275 = 0.175 = 17.5%
Full Kelly suggests 17.5% risk per trade — too aggressive for most accounts (see below).
Example 2: high win rate, small R:R
- Win rate: 60% → W = 0.60
- R = 1.0 (wins equal losses on average)
f* = 0.60 − 0.40 / 1.0 = 0.20 = 20%
Even at 60% win rate, full Kelly is high — one loss at 20% risk hurts badly.
Example 3: negative edge
- Win rate: 40%, R = 1.5
f* = 0.40 − 0.60 / 1.5 = 0.40 − 0.40 = 0
Kelly says: do not bet — no positive expectancy at this combination.
The calculator floors negative values at 0 — improve setup or statistics, do not increase size.
🎯 Pro Tip: Take win rate and R from at least 50–100 trades of the same setup — not three weeks or a cost-free backtest.
Kelly formula and expectancy
Kelly > 0 exactly when expectancy is positive:
Expectancy (in R) = W × R − (1 − W)
Positive when W × R > 1 − W, equivalent to W > 1/(1+R) — the break-even win rate from the risk-reward calculator.
Kelly and expectancy are two sides of one coin:
- Expectancy: “Is the system worth it?”
- Kelly: “How much should I risk?”
Full Kelly — why almost nobody uses it
Full Kelly maximizes theoretical growth — with extreme volatility:
- Drawdowns of 50%+ are possible in the Kelly model
- Win rate estimate off by 5% → recommended fraction jumps
- Sequence risk: losing streaks hit large fractions
Professional funds and experienced traders use fractional Kelly — a fraction of the formula.
⚠️ Warning: Full Kelly live is for most a fast path to margin call — not because math is “wrong,” but because inputs are uncertain and humans do not tolerate drawdowns linearly.
Half-Kelly — the practical standard
Half-Kelly = f ÷ 2*
Example: f* = 17.5% → half-Kelly = 8.75%
Half-Kelly gives roughly 75% of Kelly growth with much lower volatility — a common compromise in literature and practice.
Benefits:
- Buffer against misestimated win rate
- More tolerable drawdowns
- Still more aggressive than classic 1% rule
Half-Kelly only makes sense with robust statistics. With uncertain edge, even half-Kelly is too much.
Quarter-Kelly — conservative statistics approach
Quarter-Kelly = f ÷ 4*
Example: f* = 17.5% → quarter-Kelly = 4.375%
Quarter-Kelly sits nearer aggressive retail risk (2–4%) but stays tied to edge. Many quant traders start here and scale only after out-of-sample validation.
Comparison at f* = 20%:
| Variant | Risk per trade | |---------|----------------| | Full Kelly | 20.0% | | Half-Kelly | 10.0% | | Quarter-Kelly | 5.0% | | Classic 1% rule | 1.0% (fixed, not statistics-based) |
The 1% rule is not Kelly — it is a survival thumb rule. Kelly is statistics-based and can be higher or lower.
Kelly vs. fixed percentage risk
| Approach | Advantage | Disadvantage | |----------|-----------|--------------| | Fixed 1% | Simple, robust, beginner-friendly | Ignores edge strength | | Kelly | Scales with proven edge | Sensitive to estimate error | | Half/quarter-Kelly | Balance growth/stability | Needs good data |
Recommendation for most:
- Start at 0.5–1% fixed (position size calculator)
- After 100+ trades: calculate Kelly
- If f* > 0: use quarter-Kelly as upper bound, not full Kelly
- Never above 2% without institutional risk framework
More background in position sizing.
Measuring win rate and R:R for Kelly
Win rate (W)
- Only trades of one setup
- Same rules as backtest
- Exclude rule-break losses or track separately
R (avg. win / avg. loss)
Kelly uses average wins and losses in money — not planned R:R.
Difference:
- Planned R:R: 1:3
- Realized: winners closed early → avg. win / avg. loss maybe 1:1.2
Kelly with planned 1:3 overstates f* if live execution is worse. Use realized journal values.
Outliers
One 10R win skews avg. win. Median variants exist — for starters, mark outliers and test sensitivity (Kelly with and without top trade).
Practical examples through the calculator
Trend-following system
- W = 38%, R = 2.5
- f* = 0.38 − 0.62/2.5 = 0.38 − 0.248 = 0.132 → 13.2%
- Half-Kelly: 6.6%
- Quarter-Kelly: 3.3%
Quarter-Kelly fits experienced aggressive trading — full Kelly would be suicide on a losing streak.
Scalping system
- W = 58%, R = 0.9
- f* = 0.58 − 0.42/0.9 = 0.58 − 0.467 = 0.113 → 11.3%
Positive Kelly despite R < 1 — because win rate is high enough. Still bake spread and slippage into R or f* is too high.
No edge
- W = 35%, R = 1.2
- f* = 0.35 − 0.65/1.2 ≈ −0.19 → 0
Do not trade the system — no matter how good the chart looks.
Kelly and drawdown recovery
High Kelly fractions cause deep drawdowns — and drawdowns need disproportionate recovery (see drawdown recovery calculator).
Example: 10% risk per trade, ten losses → can exceed −50% → +100%+ recovery needed.
Kelly without drawdown awareness is dangerous. Fractional Kelly exists to stay below the theoretical optimum — not above it.
Common Kelly mistakes
Backtest win rate as truth
Overfitting: 65% in backtest, 42% live → Kelly was too high.
Planned vs. realized R:R
Systematically overstates f*.
Kelly on total net worth
Only trading capital — not rent, emergency fund, retirement.
Kelly on correlated trades
Kelly often assumes independent bets. Five simultaneous EUR pairs are not five times Kelly risk — they are highly correlated. Cap portfolio risk.
Full Kelly “because the formula says so”
The formula maximizes log growth — not your nerves.
Kelly and multiple open positions
Multivariate Kelly exists for uncorrelated setups — impractical for retail. Practical rule:
- Quarter-Kelly per setup
- Cap sum of simultaneous risk (e.g. max 3% total)
The position size calculator works per trade — you aggregate in journal or head.
How to use the Kelly criterion calculator
- Win rate (%) from journal or validated backtest
- Avg. win / avg. loss — realized, not wish R:R
- Read full Kelly — theoretical ceiling
- Read half-Kelly and quarter-Kelly as practical band
- Convert with position size calculator to lots/shares
If Kelly is 0 → improve strategy, not size.
If quarter-Kelly > 2% → recheck statistics — such aggression is rarely justified.
Kelly in your trading plan context
Kelly does not answer:
- Where entry and stop go
- Whether the market fits your setup today
- Whether you are psychologically stable
Kelly answers one question: given my historical edge — what risk fraction is mathematically optimal?
The answer is often above 1% — and that is exactly why you should stay below Kelly. Half-Kelly and quarter-Kelly are not weakness; they recognize:
- Win rate is estimated, not known
- Drawdowns are expensive
- Survival is prerequisite for compounding
Conclusion: Kelly as compass, not accelerator
The Kelly criterion connects risk-reward and position sizing with hard statistics. Full Kelly is theory — fractional Kelly is practice.
Enter honest numbers. If f* is positive and quarter-Kelly is 2–3%, you may have real edge — scale slowly. If f* is 25%, the formula is not permission for 25% risk; it is a hint to reconcile statistics with live reality.
Math maximizes growth. Good trading maximizes the time you stay in the market.