📈 Sharp Money

Kelly Criterion: The Math Behind Optimal Bet Sizing

📅 December 2025 ⏱️ 8 min read 📈 Sharp Money

The Kelly Criterion is a mathematical formula that tells you the optimal percentage of your bankroll to bet based on your edge. Used correctly, it maximizes long-term growth. Used incorrectly, it can blow up your bankroll. Here's how it works.

The Kelly Formula

f* = (bp - q) / b

f* = fraction of bankroll to bet

b = decimal odds - 1 (or American odds converted)

p = probability of winning

q = probability of losing (1 - p)

A Real Example

Let's say you believe a bet at +110 odds has a 55% chance of winning. Here's how to calculate the Kelly stake:

Example: +110 with 55% Win Probability

Odds (b) 1.10 (from +110)
Win probability (p) 0.55
Loss probability (q) 0.45
Kelly formula (1.10 × 0.55 - 0.45) / 1.10
Result 4.5% of bankroll

Kelly says to bet 4.5% of your bankroll on this wager. That's aggressive—which is why most professionals use fractional Kelly.

Why Full Kelly Is Dangerous

The Kelly Criterion assumes you know your exact edge. In sports betting, you never do. Your "55% probability" is an estimate, not a certainty.

Problems with full Kelly:

⚠️ The Edge Estimation Problem

Kelly requires knowing your true win probability. But in sports betting, you're always estimating. A slight overestimate of your edge leads to dramatically overbetting. This is why full Kelly often leads to ruin.

Fractional Kelly: The Practical Approach

Most successful bettors use fractional Kelly—typically 25% to 50% of the full Kelly recommendation:

Kelly Fraction Bet Size (from 4.5% example) Trade-off
Full Kelly (100%) 4.5% Maximum growth, maximum variance
Half Kelly (50%) 2.25% Good growth, manageable variance
Quarter Kelly (25%) 1.1% Slower growth, smooth ride
Flat 1% 1% Simple, ignores edge sizing

Half Kelly is a common choice among professionals. It captures most of the growth potential while dramatically reducing variance. Quarter Kelly is even more conservative and approximates the flat 1% rule we recommend for most bettors.

When Kelly Makes Sense

Kelly is most useful when you have:

  1. A proven edge: Tracked over 500+ bets with positive CLV
  2. Quantifiable probability estimates: A model, not gut feel
  3. Patience: Ability to weather drawdowns without panicking
  4. Multiple simultaneous bets: Kelly works best when diversifying across many edges

If you're new to betting or don't have a tracked edge, Kelly is premature. Stick with flat staking until you've proven yourself profitable over a large sample.

Kelly vs. Flat Betting

Factor Kelly Flat 1%
Requires edge estimate Yes (can be wrong) No
Complexity High Simple
Long-term growth Optimal (if edge is known) Sub-optimal but steady
Variance High Low
Ruin probability Higher if edge overestimated Very low
📊 The Professional Reality

Even sharp bettors with proven models often use quarter Kelly or less. The theoretical maximum growth isn't worth the emotional and practical costs of full Kelly variance. Survival matters more than optimization.

Common Kelly Mistakes

1. Using Kelly Without a Proven Edge

If you don't have a tracked, statistically significant edge, Kelly gives you nothing. Garbage in, garbage out.

2. Ignoring Correlation

Kelly assumes independent bets. If you're betting multiple correlated outcomes (same game, related markets), you need to adjust down.

3. Not Adjusting for Limits

Kelly might say bet $500, but the book limits you to $200. Real-world constraints matter.

4. Emotional Sabotage

After a 30% drawdown, most bettors panic and abandon their system. If you can't handle the swings, use smaller stakes.

Our Recommendation

For most Ohio bettors, the 1% flat staking rule is superior to Kelly. It's simple, protects your bankroll, and doesn't require accurate edge estimation.

Consider fractional Kelly (quarter to half) only if:

The best system is the one you'll actually follow. For most people, that's flat staking.

Start With the Basics

Master flat staking before moving to Kelly.

The 1% Rule →