The Kelly Criterion for Greyhound Betting

29 May 2026betting-strategy · kelly · staking

The Kelly Criterion is the standard tool for sizing a bet when you have a positive expected value. It was derived by John Kelly at Bell Labs in 1956 to solve a communication-channel problem, and it turns out to maximise the long-run geometric growth rate of your bankroll. This article explains the formula, walks through a greyhound example, and shows why TrapStats uses a fractional Kelly in practice.

The formula

For a single binary bet at decimal odds O with your estimated win probability p:

f* = (b·p − q) / b

where b = O − 1 (net odds), q = 1 − p, and f* is the fraction of your bankroll to stake. f* > 0 means the bet has positive expected value and you should stake f* × bankroll; f* ≤ 0 means skip.

The same formula written more intuitively: you're betting your edge (b·p − q) divided by your net odds. Bigger edge → bigger stake. Bigger payoff multiple → smaller stake (because the variance is wider).

A worked example

Suppose TrapStats predicts a dog at trap 5 has a 35% win probability and the forecast price is 4.0:

  • p = 0.35, O = 4.0, b = 3.0, q = 0.65.
  • Expected value per unit: p·O − 1 = 0.35 × 4 − 1 = +0.40 (i.e. +40% edge).
  • Full Kelly: f* = (3 × 0.35 − 0.65) / 3 = 0.40 / 3 ≈ 13.3% of bankroll.

If your bankroll is £100, full Kelly says stake £13.30. That's an enormous bet, and as we'll see, it's almost never the right choice in practice.

Why fractional Kelly

The Kelly formula assumes your probability estimate p is exactly right. Reality has two problems:

  1. Your p is an estimate, not a truth. Even a well-calibrated model has noise. If you overestimate by 5pp, Kelly massively over-bets.
  2. Returns compound through losses too. A full-Kelly bettor with the correct p still experiences ~50% drawdowns regularly. That's mathematically expected but psychologically (and financially) ruinous.

The standard fix is fractional Kelly: stake α × f* where α is something like 0.25 (quarter-Kelly) or 0.5 (half-Kelly). The growth rate is α(2 − α) times the full-Kelly growth rate — so quarter-Kelly gives you 7/16 ≈ 44% of the full growth with about 1/16 the volatility. The trade-off is excellent.

In our example: quarter-Kelly on the 35% / 4.0 dog would stake £3.30, not £13.30.

How TrapStats applies it

The Denis live tracker uses a percentage-tiered staking scheme (not pure Kelly) for three reasons:

  • Shrinkage: model probabilities are shrunk toward the market-implied probability (pw_eff = (1 − λ)·prob_win + λ·(1/price), λ=0.30) before EV is computed. This is a defence against the well-documented model overconfidence on the selection arm.
  • EV bands: stakes scale 1% / 2% / 3% of bankroll based on the shrunk EV bucket — not on full Kelly. This caps any single bet's blast radius regardless of how excited the model is.
  • Hard caps: a max-EV guardrail (denis_safety_max_ev=0.50) rejects implausibly high EV outputs as a model-overconfidence flag, and a max-price guardrail (denis_safety_max_sp=6.0) rejects long-shot phantom edges. The price floor (denis_safety_min_price=3.5) skips short-price favourites because the 4-week analysis showed those segments lose at the empirical ~28% flat win rate.

The result is a more conservative regime than full Kelly, with explicit constraints that protect against probability mis-estimation.

Common Kelly mistakes

  • Treating the model's probability as truth. Even calibrated, it's an estimate. Use fractional Kelly always.
  • Compounding through a drawdown. If your bankroll halves, your Kelly stake halves too. That's correct — it's not a sign to "make it back" with bigger bets.
  • Ignoring correlation. Two bets in the same race aren't independent. Kelly assumes independence, so adjust down when betting multiple runners in one race.
  • Confusing edge with hit rate. A 28% hit rate at average price 5.0 is profitable; a 50% hit rate at average price 1.8 is not. Kelly cares about the edge b·p − q, not the win rate alone.

Want the maths in one line?

The Kelly stake is (edge / payoff) where edge is what you expect to win on average per £1 and payoff is the net decimal odds. If those numbers don't make sense for the bet, the Kelly stake won't either. When TrapStats shows an EV of +35% at price 4.0, that's edge = 0.35, payoff = 3.0, full-Kelly = ~11.7%. We will recommend less than that — by design.

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