Kelly Criterion (Bet Sizing)

Kelly Math (Core)

For decimal odds O, define b = O − 1. With win probability p and loss probability q = 1 − p, the **full-Kelly fraction** of bankroll is:

f* = (b·p − q) / b

• If f* ≤ 0 → the bet is **not** +EV; pass.
• Stake = f* × Bankroll (for full Kelly).

Fractional Kelly

Because p is estimated (noisy), **fractional Kelly** reduces variance:

• Half-Kelly stake = 0.5 × f* × Bankroll
• Quarter-Kelly stake = 0.25 × f* × Bankroll

Tradeoff: smaller growth rate vs. smoother equity curve and lower drawdowns.

Practical Workflow

1. Price the market (model) to get p, compute Fair = 1/p.
2. Verify **value**: only proceed if Book > Fair (EV+).
3. Compute f* and apply fractional multiplier.
4. Respect hard caps (e.g., max 2% per bet; max 5–10% total on one match).
5. Log entry/close prices and results; review CLV and volatility weekly.

Worked Examples

Example — Side Market

Book O=2.30, model p=0.46 → b=1.30, q=0.54, f*=(1.30×0.46−0.54)/1.30≈0.0246 ⇒ 2.46% (full). Half-Kelly ≈ 1.23% of bankroll.

Example — Thin Edge

O=1.95, p=0.52 → b=0.95, q=0.48, f*≈0.0105 ⇒ 1.05% (full). Consider quarter-Kelly if league variance is high.

Risks & Drawdowns

• Edge error: If your p is overestimated, Kelly oversizes; use fractional multipliers and caps.
• Correlation: Multiple bets on the same match/round increase portfolio heat.
• Psychology: Drawdowns are inevitable; pre-define stop rules and review cadence.