Bankroll management — Kelly fractions explained

Find an edge and you've solved half the problem. Size your bets wrong and you can still go broke — even with edge. Bankroll management is what turns a winning strategy into actual money.

This lesson is the Kelly criterion in plain language: what it is, why fractional Kelly is the only practical version, and how Sharp's 5% cap fits.

Why bankroll beats picks

Two bettors place the same set of +3% EV bets across a season. Bettor A varies stake sizes by gut feel — bigger when they "love" a play, smaller when they don't. Bettor B uses a fixed sizing rule. Bettor B finishes ahead almost every time.

The reason: emotional sizing concentrates risk on the wrong bets. The plays you "love" aren't actually higher-edge — they're just more memorable. Meanwhile a perfectly good +EV play gets a small stake because you weren't sure. Variance grinds Bettor A down; Bettor B compounds.

The Kelly criterion

Kelly is a formula for how much to risk on a bet given your edge. The result is the stake that maximizes the long-run growth rate of your bankroll.

For a binary bet (win or lose), the formula simplifies to:

Kelly % = edge / odds

Where "edge" is your estimated edge in decimal (e.g., 0.03 for 3%) and "odds" is the decimal payout minus 1 (e.g., a +110 bet is 1.10).

Example: you find a +110 bet you estimate has 3% EV.

Edge = 0.03
Odds (decimal payout minus 1) = 1.10
Kelly % = 0.03 / 1.10 ≈ 2.7% of bankroll

On a $10,000 bankroll, full Kelly says stake $270.

Why full Kelly is too aggressive

Kelly is mathematically optimal if your edge estimate is exactly correct. In real life, it isn't. You're estimating edge from a noisy model — sometimes you're at +3% when you think you're at +5%, sometimes you've got no edge at all.

Full Kelly punishes that uncertainty brutally. The drawdowns are stomach-turning. A run of bad luck combined with an overestimated edge can wipe out 30% of bankroll fast. Most people quit before the math has time to work.

Fractional Kelly — the practical version

The fix is staking a fraction of what Kelly says. Half-Kelly is the most common, quarter-Kelly is the conservative choice.

Same example:

Full Kelly = 2.7% of bankroll → $270
Half-Kelly = 1.35% → $135
Quarter-Kelly = 0.7% → $70

Why this works: half-Kelly captures about 75% of full-Kelly's long-run growth with a fraction of the volatility. The drawdowns are survivable. You stay in the game long enough for the math to play out.

Fractional Kelly — why ½ beats full almost every time is a deeper look at why ½ specifically tends to beat full almost every time in practice.

Sharp's 5% cap

There's one more rule on top of Kelly: never stake more than 5% of bankroll on a single bet, regardless of what the formula says.

Kelly can occasionally output huge percentages — a 6% edge at +200 odds suggests staking 3% of bankroll, but a 6% edge at -1000 odds suggests far more. The 5% cap protects you from formula errors, edge mis-estimates, and the fat-tail "this should never happen" outcomes that occasionally do.

5% is the Sharp non-negotiable. Every bet, every sport, every "sure thing of the century." The cap stays.

Worked end-to-end

Bankroll: $10,000. Bet you've identified: Lakers +4 at -105, estimated edge +2.5%.

Decimal payout = 1.952 → odds = 0.952
Kelly % = 0.025 / 0.952 ≈ 2.6%
Half-Kelly = 1.3% → $130
5% cap check: 1.3% is well under 5% → fine, stake $130

You bet $130. Win or lose, that's the right size for the edge you had.