The Kelly Criterion

If you know your win rate and your average reward-to-riskReward-to-riskDistance to target ÷ distance to stop. Minimum workable setups are typically 2:1 or better.Read in glossary → ratio, there is a mathematically optimal bet size that maximizes long-run growth of the account. It's called the Kelly Criterion, developed by Bell Labs physicist John Kelly in 1956 and used by professional gamblers, some hedge funds, and basically no retail traders - because full Kelly produces drawdowns that are emotionally untradeable. Understanding Kelly is nonetheless essential: it sets the theoretical ceiling for sensible bet sizing, and the fraction of Kelly you're running is a useful sanity check on whether you're over- or under-sized for your edge.

The formula

• f* - the optimal fraction of capital to risk per trade
• b - the payoff ratio (if you risk 1 to win 2, b = 2)
• p - probability of winning (e.g., 0.55 for 55% WR)
• q - probability of losing (q = 1 − p)

The formula says: the right fraction to risk depends on both how much you win when right and how often you're right.

Worked examples

Example 1 - coin flip with 2:1 payout

b = 2, p = 0.5, q = 0.5.

f* = (2 × 0.5 − 0.5) ÷ 2 = (1 − 0.5) ÷ 2 = 0.25 = 25%

Kelly says: risk 25% of your bankroll per flip. That's absurdly aggressive - but mathematically optimal for long-run compound growth given these numbers.

Example 2 - a realistic trading strategy

• Win rate: 50%
• Reward-to-risk: 2:1 (so b = 2)
• p = 0.5, q = 0.5

f* = (2 × 0.5 − 0.5) ÷ 2 = 0.25 = 25%

A strategy with 50% WR and 2:1 RR has a full Kelly size of 25% per trade. At that sizing, a 4-loss streak (statistically common) wipes out ~68% of the account.

Example 3 - high-conviction edge

• Win rate: 60%
• Reward-to-risk: 3:1
• p = 0.6, q = 0.4

f* = (3 × 0.6 − 0.4) ÷ 3 = (1.8 − 0.4) ÷ 3 = 1.4 ÷ 3 ≈ 0.467 = 46.7%

Kelly says risk nearly half the account per trade for this edge. Mathematically correct. Practically insane.

Why nobody trades full Kelly

Kelly maximizes expected log-growth - the expected logarithm of wealth over time. That's not the same as what human traders actually want. Three fatal problems:

1. Volatility is brutal

At full Kelly, even profitable strategies endure enormous drawdowns. Simulations show:

• Full Kelly on a 50% WR / 2:1 RR strategy: 50% drawdowns are routine.
• Over long runs: drawdowns exceeding 50% happen with meaningful probability.

Kelly doesn't minimize drawdownDrawdownPeak-to-trough decline in account equity. Resets only at new equity peaks. Recovery math is asymmetric.Read in glossary →. It maximizes growth conditional on surviving. And surviving a 50% drawdown, trade-by-trade, is practically impossible for most humans - even though the math eventually recovers.

2. You don't actually know your edge

Kelly assumes perfect knowledge of p and b. In trading, you estimate these from a sample of past trades. If your "true" win rate is 50% but your estimated win rate from 100 trades is 56% (reasonable variance), full Kelly oversizes you dramatically.

Oversize errors in Kelly are nonlinear. Doubling the Kelly fraction doesn't double the growth - past 2× Kelly, the log-growth turns negative. You actually lose money on a winning strategy if you oversize.

3. It assumes binary outcomes

The standard Kelly formula assumes a trade either wins b× or loses 1. Real trades have distributions - sometimes you win 1.5R, sometimes 4R, sometimes you stop out for 0.8R. The formula needs adaptation for continuous distributions (there are generalized forms), but estimating the full distribution accurately is even harder than estimating win rate.

Bottom line: full Kelly assumes perfect knowledge of outcomes you can't actually measure, in exchange for drawdowns you can't actually survive.

Fractional Kelly - the practical convention

The industry standard fix: use a fraction of Kelly.

• Half Kelly (1/2): still aggressive. Reduces long-run growth ~25% but cuts drawdowns roughly in half.
• Quarter Kelly (1/4): the most common professional size. ~half the drawdown of half-Kelly, ~87% of optimal growth.
• Eighth Kelly (1/8): very conservative. Drawdowns small, growth slow but reliable.

For the 50% WR / 2:1 RR strategy:

• Full Kelly = 25%
• Quarter Kelly = 6.25% per trade

Even quarter-Kelly is far above the 1% rule1% ruleStandard risk policy: never risk more than 1% of account equity on a single trade. The single most protective rule in trading.Read in glossary → most retail traders use. That tells you something: most retail traders are sized well below optimal for their actual edge.

Why 1% is below Kelly (and that's fine)

Work backwards: a 1% trade is what fraction of Kelly, for a typical strategy?

For 50% WR / 2:1 RR:

• Full Kelly = 25%
• 1% of account = 1 / 25 = 4% of Kelly, or ~1/25 Kelly

For 40% WR / 3:1 RR:

• Full Kelly = (3 × 0.4 − 0.6) ÷ 3 = 0.2 = 20%
• 1% of account = 1/20 Kelly = 5% of Kelly

The 1% rule is running at roughly 1/20 to 1/25 Kelly - way below even conservative professional sizing.

This is good. It means:

• Your drawdowns are tiny compared to optimal (typically 5-15% instead of 50%+).
• You give up some growth rate in exchange for massive survivability.
• Estimation errors don't kill you.

For most retail traders, 1% is correct because it's a tiny fraction of Kelly. The marginMarginBorrowed capital used to increase position size. Amplifies both gains and losses proportionally.Read in glossary → is what you're paying for survival.

When to think about Kelly

Most of the time, you don't. The 1% rule is derived from psychology and survival math, not Kelly math, and it's almost always the correct choice.

Three situations where Kelly matters:

1. Scaling up from 1% to 1.5% or 2%

After 200-500 tracked trades with proven positive expectancyExpectancyExpected R-multiple per trade: (WinRate × AvgWinR) − (LossRate × AvgLossR). Positive = edge. Negative = bleed.Read in glossary →, some traders move from 1% → 1.5% or 2% risk. Kelly sanity check: compute full Kelly from your data. If 2% is still less than 10% of full Kelly, you're safely under-sized. If 2% is approaching half-Kelly, you're in aggressive territory.

2. Multi-strategy allocation

If you run 3 strategies simultaneously with different edges, Kelly math helps allocate capital between them. Higher-edge strategies get more capital within the fractional-Kelly budget.

3. Conviction-based sizing (rare)

Some discretionary traders size up on their highest-conviction setups (e.g., 2% on A+ setups, 1% on B setups). Kelly can guide the ratio - but only if you have tracked data showing the A+ setup actually has higher expectancy. Without data, "conviction" is just storytelling.

A worked comparison - same strategy, different sizings

Strategy: 50% WR, 2:1 RR. Expected growth per trade = +0.25R.

Simulating 500 trades at different sizes on a $10,000 starting account:

The table tells the story:

• 1% rule produces solid compounding with tolerable drawdown.
• Bigger sizing produces bigger expected returns but bigger drawdowns.
• Full Kelly produces the best theoretical median outcome but with routine 90% drawdowns.
• Past 2× Kelly, log-growth goes negative. You lose money on a winning strategy from oversizing alone.

The real-world Kelly hierarchy

Here's how practitioners actually think about bet sizing:

1. Start at 0.5% per trade - below Kelly by a huge margin, but appropriate for learning.
2. Move to 1% once you have 100+ tracked trades showing positive expectancy.
3. Cap at 2% unless you have 500+ trades and understand your Kelly fraction.
4. Never exceed half-Kelly even with a proven edge - the drawdown profile becomes untradeable.
5. If you compute 5%+ per trade as "optimal," the math is probably right but the trader rarely is.

Common questions

Is Kelly the same as "maximum edge" sizing? Kelly maximizes long-run compound growth. Different than maximum single-trade expectancy. At sizes above Kelly, each trade's expectancy is still positive but growth declines and eventually goes negative - because the compounding arithmetic of percentage losses dominates.

Should I recompute Kelly as my strategy evolves? Yes. Kelly depends on your current measured WR and RR. If your edge changes (better execution → higher WR, tighter stops → better RR), the optimal fraction changes. Recompute every 100+ trades.

What about "Kelly for continuous distributions"? For traders whose R-multipleR-multipleThe dollar amount risked on a trade. Every outcome is measured in R: a 2R winner made twice the risked amount.Read in glossary → distribution is continuous (e.g., variable winners and losers), the generalized Kelly formula uses the full P&L distribution. In practice, computing it is complex and the answer usually differs from simple Kelly by less than 20%. Simple Kelly with fractional caps is the pragmatic choice.

Can I Kelly-size different setups at different fractions? Yes, and this is one of Kelly's useful applications. If one setup has 60% WR at 3:1 and another has 40% WR at 2:1, Kelly gives you the relative weighting. But you need tracked data on each setup separately - "I think this one is better" doesn't count.

Key takeaways

• Kelly Criterion = the optimal bet fraction for maximum long-run growth: f = (bp − q) / b*.
• For typical trading strategies, full Kelly = 15-40% per trade. That's mathematically optimal but emotionally untradeable.
• Fractional Kelly (quarter-Kelly = 25% of full Kelly) is the professional convention.
• The 1% rule is typically 4-5% of full Kelly - very conservative, and that's the point.
• At 2× Kelly, log-growth goes negative. Oversizing destroys a winning edge.
• Kelly is most useful as a ceiling check on your current sizing, not as the sizing itself.
• You cannot run Kelly without honest data on your strategy. "I feel like it's 60% WR" is not data.

Up next: Risk of RuinRisk of RuinThe probability of blowing up an account given sizing, edge, and number of trades. Nonlinear in per-trade size.Read in glossary → and Losing Streak Math - the probability of blowing up given your sizing, and why 7-loss streaks are statistically guaranteed long before they feel normal.