Quarter-Kelly Bet Sizing

The Kelly criterion (Kelly 1956) gives the bet size that maximizes the long-run logarithmic growth of bankroll, assuming you can correctly estimate the probability of winning. For a single bet with probability p and decimal payout b, full Kelly is:

f* = (p * b - (1 - p)) / b

This is the same numerator as the expected-value formula, scaled by the payout. The output is the optimal fraction of bankroll to wager.

Why quarter-Kelly

Full Kelly is mathematically optimal under perfect knowledge of p. In practice, no one knows p exactly. If your probability estimate is even slightly biased, full Kelly compounds that bias into bankroll volatility large enough to eclipse the expected growth rate. MacLean & Ziemba (1992) showed that fractional Kelly captures roughly half of full Kelly's long-run growth at a quarter of the variance. Most disciplined bettors size at quarter-Kelly or lower as a result.

BaseCase reports kelly_pct as a quarter-Kelly figure on every detected edge. It appears in the Edge Finder under the ¼ Kelly column, gated to Sharp tier and above.

Worked example

Suppose BaseCase estimates a 56% true probability and the book is offering +120 (b = 1.2). Full Kelly:

f* = (0.56 * 1.2 - 0.44) / 1.2 = (0.672 - 0.44) / 1.2 ≈ 0.193

Full Kelly says risk 19.3% of bankroll. Quarter-Kelly says risk 4.8%. Most active bettors run materially below even that — closer to 1-2% — because the practical estimation error in p is larger than most analysts admit.

Uncertainty-adjusted Kelly

BaseCase applies an additional confidence adjustment to the quarter-Kelly figure (Baker & McHale 2013). The intuition: when sportsbooks disagree more, the true probability is less certain, and bet sizing should scale down. The pipeline measures cross-book dispersion at the moment of detection and applies a multiplicative confidence factor before reporting kelly_pct. Edges with tight cross-book agreement and confirmed line movement carry the largest sizing recommendations; edges with wide dispersion or unconfirmed moves are scaled down or floored.

This conservative posture is intentional. The largest source of bet-sizing error is not the choice of fraction, it is the calibration of the underlying probability estimate. BaseCase's research roadmap includes ongoing refinement of the dispersion-to-confidence mapping, and Kelly outputs should be treated as guidance scaled to your own conviction rather than as a fixed prescription.

How BaseCase displays it

The ¼ Kelly column shows the fraction directly as a percentage of bankroll. A row reading 0.6% means BaseCase recommends 0.6% of bankroll on that bet. Rows where the underlying confidence multiplier zeros out display an em-dash rather than a number.

Caveats

Kelly assumes single-bet, sequential resolution and a fixed bankroll. Same-game correlated bets violate this assumption — staking quarter-Kelly on three correlated edges in the same game is not equivalent to staking quarter-Kelly once. BaseCase's pipeline includes a per-game best-edge filter (is_best_in_game) that visually demotes duplicate edges on the same game; treat the is_best_in_game = true row as the primary sizing reference and sum your exposure across games rather than rows.

Kelly also assumes log-utility — you maximize the geometric growth rate of bankroll. If your utility function is closer to linear (you care about absolute dollar return more than long-run growth), Kelly oversizes; if it's closer to constant relative risk aversion above 1, Kelly undersizes. Most professional sports bettors approximate log-utility well enough that quarter-Kelly is the sensible default.

Quarter-Kelly is the practical compromise between mathematical optimality and the certainty that you don't know your edge as precisely as you think.

Further reading

• Expected value — the prerequisite signal that Kelly sizes
• Why fair value beats consensus — where the p Kelly relies on actually comes from