Przewodnik Kelly Criterion

For a bet with decimal odds O and true probability p of winning, the Kelly fraction is f = (p × (O − 1) − (1 − p)) / (O − 1). In words: 'edge divided by odds-minus-one'. For a bet at 2.00 with a true probability of 55%, Kelly says stake f = (0.55 × 1 − 0.45) / 1 = 0.10, or 10% of your bankroll. That's an aggressive number - most recreational bettors are horrified by it.

The formula scales naturally: a smaller edge produces a smaller stake. A 52% probability at 2.00 gives f = 0.04 (4% of bankroll). A 65% probability at 2.00 gives f = 0.30 (30% of bankroll - terrifying). A 51% probability at 2.00 gives f = 0.02. And any negative-edge bet gives a negative f, which Kelly correctly interprets as 'don't bet'.

The mathematical guarantee is that no other sizing strategy beats Kelly in the long run for maximising compound growth. Flat staking underperforms Kelly asymptotically; doubling up after losses (Martingale) dramatically underperforms and eventually bankrupts you. Kelly is provably optimal - under the assumption that you know your true edge, which is where the practical problems start.

Full Kelly is optimal only if you know your true probability exactly. In reality, you estimate it, and the estimate is noisy. If you think your edge is 5% but it's actually 2%, full Kelly will size you as if you're twice as good as you are - which leads to dramatic drawdowns. The math is unforgiving: a model that's 10% off on its edge estimate will experience roughly 4× the drawdown of a model that's perfectly calibrated.

The second issue is psychological. Full Kelly assumes you can handle 40% drawdowns without flinching. Very few humans can. A run of bad variance that takes your bankroll from €10,000 to €6,000 will make most people panic, scale down, or quit - and that emotional response wipes out any theoretical edge Kelly was supposed to deliver.

The standard professional adjustment is fractional Kelly: bet some fraction (usually 0.25 or 0.5) of what the formula says. Half-Kelly delivers ~75% of the long-run growth of full Kelly with ~50% of the variance. Quarter-Kelly gives you ~43% of the growth with ~25% of the variance. Most professional syndicates sit in the 0.2–0.4 range for this exact tradeoff.

Pure Kelly assumes one bet at a time, but football bettors often place multiple bets on the same day or weekend. If the bets are uncorrelated (different leagues, different markets), you can scale them independently using their individual Kelly fractions - with one important caveat: the sum of all fractions should never exceed 1, or you risk running out of bankroll before all the bets settle.

If the bets are correlated (three Premier League matches on the same Saturday - all influenced by general Premier League variance that weekend), pure Kelly over-allocates because it double-counts the risk. The correct move is to size down proportionally, or to use a constrained-Kelly optimisation that respects the correlation matrix.

BetsPlug member tools ship a built-in multi-bet Kelly calculator that accounts for correlation between simultaneous fixtures. For the free preview, the confidence score is the raw signal - if you want to sizing-size yourself, divide by 4 (quarter-Kelly) and you'll be close to a safe baseline without needing the correlation math.

Let's say you have a bankroll of €2,000 and BetsPlug's ensemble gives you a 58% probability on a match where the bookmaker price is 2.10. Your edge is 0.58 − (1 / 2.10) = 0.58 − 0.476 = 0.104 (10.4%). Full Kelly f = (0.58 × 1.10 − 0.42) / 1.10 = 0.1945, or 19.45% of bankroll. That's €389 on a single bet - a terrifying number.

Half-Kelly would stake €194, quarter-Kelly €97. The difference in long-run growth between these three options is much smaller than the difference in variance, so most professionals take quarter-Kelly on fresh picks and scale up only after the model has proven itself on a large sample.

Notice how sensitive this is to the probability estimate. If the true probability was 54% instead of 58% (a 4-point overestimate), the real edge drops to 6.4%, real full Kelly becomes 11.6%, and quarter-Kelly falls to 2.9% - a third of the stake you would have placed based on the 58% estimate. This is exactly the kind of mis-sizing that sinks overconfident models. Always quarter-Kelly until you've validated the model on at least 500 out-of-sample picks.