Kelly Criterion Calculator

The Kelly Criterion is a math formula that figures out the optimal position size for maximum long-term portfolio growth with minimal risk of blowing your account. It's named after John L. Kelly Jr., and it tells you what percentage of your account to risk on each trade based on your historical win rate and profit/loss ratio.

At its core, it's a simple idea: risk more on your best trades and less on the worse ones. But getting it right takes care. The formula factors in your win probability and the relationship between average wins and losses.

Unlike fixed position sizing where you risk the same amount every time, Kelly adapts to your actual trading stats. If you've got a 60% win rate at 1:1 risk/reward, it'll suggest a different size than 40% win rate at 2:1.

Key point: Full Kelly can be aggressive and risky. Most pros use fractional Kelly (like 25% of full) to cut down volatility and drawdowns while still getting solid growth.

The Kelly formula:

f = (bp - q) / b

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Breakdown: Imagine you've got a system with a 55% win rate. Winning trades average 2:1 (you make $2 for every $1 risked), and losses are 1:1.

Calculation:

f = (2 × 0.55 - 0.45) / 2

f = (1.1 - 0.45) / 2

f = 0.65 / 2 f = 0.325 = 32.5%

That means risk 32.5% of your account per trade for max growth. In practice, most folks use half Kelly (16.25%) or quarter (8.1%) for safety and a smoother equity curve.

Why it matters: The formula mathematically shows that optimal bet size depends on BOTH win rate AND profit/loss ratio. 55% at 1:1 is nothing like 55% at 3:1.

To get the Kelly Criterion, let's look at how it plays out with real numbers. Here are some realistic trading scenarios:

Example 1: Day Trader with a Positive Edge

Scenario: John is a day trader who's been tracking his trades for 6 months. He trades ES (S&P 500 futures) consistently. 58% win rate, average win $150, average loss $100.

Step-by-Step Calculation: Step 1: Win rate = 58% / 100 = 0.58 Step 2: Loss rate = 1 - 0.58 = 0.42 Step 3: Expected value per trade = (0.58 × $150) - (0.42 × $100) = $87 - $42 = $45 Step 4: Apply Kelly formula = (0.58 × $150 - 0.42 × $100) / $150 = $45 / $150 = 0.30

Result: John's Kelly is 30%, so risk 30% of his account per trade. With a $10,000 account, that's $3,000 per trade.

Real Outcome: But John went with fractional Kelly at 33% (about 10% real risk) instead of full. Over 12 months, his account grew from $10,000 to $28,500 - 185% return. Thanks to the fraction, growth was steady, drawdowns smaller.

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Example 2: Swing Trader with Borderline Win Rate

Scenario: Sarah is a swing trader with 200+ trades in a year. She uses a breakout strategy with a 48% win rate (under 50%!), but wins are bigger than losses. Average win $250, loss $100.

Step-by-Step Calculation: Step 1: Win rate = 0.48 Step 2: Loss rate = 1 - 0.48 = 0.52 Step 3: Expected value = (0.48 × $250) - (0.52 × $100) = $120 - $52 = $68 per trade Step 4: Kelly formula = ($120 - $52) / $250 = $68 / $250 = 0.272

Result: Sarah's Kelly is 27.2%, even with <50% win rate. Because her wins outweigh losses.

Real Outcome: Sarah uses 25% Kelly (close to the calc) for conservatism. With $15,000 account, risks $625 per trade. Over 18 months, account hit $47,300 - 216% return. She proves you don't need >50% win rate if average wins beat losses.

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Example 3: Conservative Trader Using Fractional Kelly

Scenario: David is a cautious options trader with 52% win rate, average win $500, loss $600. Calculated full Kelly but took 1/4 due to risk tolerance.

Step-by-Step Calculation: Step 1: Win rate = 0.52 Step 2: Loss rate = 0.48 Step 3: Expected value = (0.52 × $500) - (0.48 × $600) = $260 - $288 = -$28

Result: Negative Kelly (-$28) - the system has negative expectancy. Losses slightly bigger than wins, formula says don't trade (0% size).

Real Outcome: David saw the signal and paused the system. If he'd ignored it, account would drop 1.8% per trade, 83% drawdown over 100 trades. Instead, he tweaked the strategy, bumped average win to $700, recalculated Kelly to 7.5% - now trades with a small positive edge.

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Example 4: Aggressive Trader (Full Kelly Warning)

Scenario: Mike is an experienced trader with 60% win rate, average win $200, loss $100. Calculated 40% and went full Kelly.

Step-by-Step Calculation: Step 1: Kelly % = (0.60 × $200 - 0.40 × $100) / $200 = ($120 - $40) / $200 = 0.40

Result: Full Kelly 40% - risk 40% of account per trade.

Real Outcome: Win rate held at 60% initially, but an 8-month streak of 4 losses slashed his account from $20,000 to $8,400 - 58% drawdown. Account survived thanks to edge, but stress was huge. After, Mike switched to 25% Kelly (1/4 size) - smoother growth, strong progress.

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Example 5: Crypto Trader with High Win Rate but Low Profit Factor

Scenario: Emily is a crypto scalper with an impressive 75% win rate, average win $50, but losses $200. Wins often, but big losses hurt.

Step-by-Step Calculation: Step 1: Kelly % = (0.75 × $50 - 0.25 × $200) / $50 = ($37.50 - $50) / $50 = -0.25

Result: -25% Kelly - negative expectancy, despite high win rate.

Real Outcome: Emily realized frequent small wins don't cover rare big losses. Don't trade the system. She adjusted: either boost average win or tighten stops. When losses dropped to $80, Kelly turned positive at 8.75% - now trades safely.

This table shows how different win rates and risk/reward ratios lead to various Kelly percentages:

What it shows:

1. Win rate matters less than you think - 50% at 2:1 gives positive Kelly
2. Risk/reward is crucial - Better ratios let you risk more safely
3. No one uses full Kelly - 40-56% is theoretical max; real traders take half or quarter
4. Negative Kelly is clear - If negative, the system is statistically losing
5. Fractional is safer - 25-50% of calculated cuts drawdowns big time

Mistake #1: Full Kelly Without Testing

A lot of traders calculate the percentage and jump straight to 100%. The issue: Historical data doesn't guarantee the future. That 60% in backtest might drop to 50% live due to slippage, missed fills, or market changes.

Why it fails: Full Kelly leaves no margin. One bad month - big drawdown. Many quit the system right then - locking in losses.

How to avoid: Always use fractional (quarter or half) live, even if backtest justifies full. Example: If 24%, take 12% or 6%.

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Mistake #2: Calculating on Small Data

Trader with 15 wins and 10 losses (60%) runs Kelly. Problem: 25 trades is way too few. Small samples are ruled by variance - the percentage isn't reliable.

Why it fails: Luck can skew it. That 60% might be fluke at true 50%. Kelly needs accurate probabilities - small sample doesn't give them.

How to avoid: Gather at least 100, ideally 200+ before calculating. Update every 50-100. Even better - out-of-sample (test on 100 fresh trades, not whole history).

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Mistake #3: Ignoring Risk Costs

Trader calculates 20% per trade. But skips market microstructure: slippage, commissions - and they're already baked into average win/loss.

Why it fails: Live slippage can be 50-200% worse than backtest. 20% on optimistic P&L amps ruin risk beyond predicted.

How to avoid: Backtest with conservative prices. Or half Kelly as default - buffers hidden costs.

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Mistake #4: Rare Recalculations

Trader calculates on 200 trades, uses it 2 years without update. Second year market shifts - win rate to 45%.

Why it fails: Kelly is accurate for tested conditions. Markets evolve - edges fade. No recalc means risking big on lost edge.

How to avoid: Recalculate every 50-100. Track win rate and ratio. If Kelly dips below 5%, review the system - edge is gone.

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Mistake #5: Mixing Average Win with Expected Value

Trader averages: $2,000 win, $1,500 loss. Plugs into Kelly. But expected per trade ($2,000 × 0.55) - ($1,500 × 0.45) = $1,100 - $675 = $425. Comparing wrong otherwise.

Why it fails: Kelly is on ratios (win size to loss), not absolutes. Mixing dollars with ratios is nonsense. You could calc $3,000 risk when it's 2% of $100,000 ($2,000).

How to avoid: Always use ratios in formula: Risk $1,000, average win $2,000, loss $1,000 - 2:1. No dollars in calc; just for size after percentage.

Full Kelly (100%) is mathematically optimal, but psychologically brutal. Successful traders tweak it for tolerance and account size.

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Half Kelly (50% of calculated)

Most common among pros.

Example: Sarah's System Sarah day trades EUR/USD on 4h with breakouts. Stats:

• Win rate: 58%
• Average win: $320
• Average loss: $200
• Account: $15,000
• Kelly: 38%
• Half: 19%

Risk per trade: $15,000 × 0.19 = $2,850 Stop $200 - 14 lots.

What Sarah did: Checked in Position Size Calculator: EUR/USD 1.0850, stop 1.0830 (20 pips = $200), 14 lots × $10/pip = $140/pip × 20 = $2,800 risk. ✓ Matches.

Result over 50 trades at 58%:

• Start: $15,000
• After: $18,200 (21% gain)
• Max drawdown: 8% (psychologically manageable)
• Full Kelly: 15% drawdown (she'd probably quit)

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Quarter Kelly (25%)

For beginners or volatile markets.

Example: Mike's Learning Phase Mike is new to crypto, 45 trades. Promising stats (52% win rate, 1.8:1), but unsure.

• Kelly: 18%
• Quarter: 4.5%
• Account: $5,000
• Risk: $5,000 × 0.045 = $225

What Mike did: In Position Size Calculator for BTC $44,000, stop $900 - 0.25 BTC ($11,000 gross, $225 risk = quarter).

Result over 100:

• Start: $5,000
• After: $5,940 (18.8%)
• Max drawdown: 2.1% (no doubts)
• Builds confidence: After proving system on 2 markets, switched to half

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Three-Quarter Kelly (75%)

For aggressive with proven edge.

Example: John's Confidence Level John has 2 years, 500 trades. ES strategy:

• Win rate: 62%
• Win: $480
• Loss: $320
• Account: $50,000
• Kelly: 44%
• Three-quarter: 33%
• Risk: $50,000 × 0.33 = $16,500

What John did: In Position Size Calculator, 1 ES = 50 points × $50 = $2,500/point. Stop 16.5 points - 4 contracts ($50 × 4 × 16.5 = $33,000 gross, protected $16,500).

Result over 3 months (60 trades):

• Start: $50,000
• After: $59,800 (19.6%)
• Max drawdown: 14% (handles it)
• Yearly projection: 78%

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How to Pick a Fraction:

1. Calculate full using the formula
2. Choose comfort:
   • BEGINNER? Quarter (4-7%)
   • INTERMEDIATE? Half (10-15%)
   • PRO 2+ years? Three-quarter or full
3. Position size via Position Size Calculator
4. Track 50-100 trades
5. Sleeping easy and following? Increase fraction
6. Stressing out? Decrease

Pro secret: Almost no one takes 100%. The most successful use 25-50%, balancing math and psychology.

After calculating optimal size with the Kelly Criterion Calculator, these related tools expand your framework:

Position Size Calculator - With your Kelly percentage, figure exact size based on account, stop distance, and risk. Kelly gives %; this turns it into shares or contracts.

Risk/Reward Ratio Calculator - Kelly shines with win rate and ratio. Monitor this. Check your actual ratio from trades. If you thought 2:1 but it's 1.5:1 - Kelly % drops hard.

Profit/Loss Calculator - When executing Kelly-optimized sizes, track real P&L. Wrong average win/loss kills the calc.

Maximum Drawdown Calculator - Kelly predicts max drawdown from edge. Compare to historical. If real is 2x bigger - assessment off.

Margin Call Calculator - With leverage (margin), sizes change. Kelly is on risk, not gross. This helps with borrowed capital.