Bet Sizing: Translating Predicted Probabilities into Positions

A signal tells you which direction to trade; bet sizing tells you how much. Getting the direction right but sizing the position wrong can turn a profitable strategy into a losing one: a trader who makes 60% correct calls but bets 10× more on the 40% of losses than on the 60% of wins will still lose money. Conversely, optimal sizing of a signal with modest accuracy can compound wealth geometrically.

This note covers the translation from predicted probability to position size: the Kelly criterion as the theoretical optimum, fractional Kelly as the practical compromise, and the probability-to-bet-size mapping from López de Prado that handles multi-class and meta-labeling settings. The connection to the S-score signal is direct: the S-score is a continuous signal, not a binary one, and its translation into a graded position size is exactly the bet-sizing problem.

• state the Kelly criterion and derive the optimal fraction for binary bets;
• explain why fractional Kelly (e.g. half-Kelly) is preferred in practice;
• translate a predicted probability $p$ into a bet size $m \in [-1, 1]$ using the z-score mapping;
• describe meta-labeling as a two-stage bet-sizing framework;
• connect the S-score to a graded position size through the Normal CDF.

1. 1. The Kelly criterion
2. 1. Fractional Kelly and the case for conservatism
3. 1. Probability-to-bet-size mapping
4. 1. Meta-labeling: decoupling side from size