Effective bets calculator
how many bets am i really making if they are correlated?
Stake spread across correlated bets is not spread. Effective bets is the count a book is really holding: n divided by one plus n minus one times rho, where rho is the average pairwise correlation between positions. Independent bets give n_eff equal to n. Everything else gives less.
The correlation used as a starting point here is a prior, not a measurement: rho of 0.15. The measured figure on this book is 0.45. Same bet counts, two columns.
| Bets | Effective at prior rho 0.15 | Effective at measured rho 0.45 |
|---|---|---|
| 2 | 1.7 | 1.4 |
| 4 | 2.8 | 1.7 |
| 8 | 3.9 | 1.9 |
| 12 | 4.5 | 2.0 |
| 20 | 5.2 | 2.1 |
Read the measured column down. From 2 bets to 20 bets, the effective count crawls from 1.4 to 2.1. Past a handful of correlated positions, adding another buys no diversification. It only adds stake.
That is what a staking rule has to see. A max single of 5% on a bankroll of 20000 caps a lone bet at 1000. The same rule, applied to a book already loaded with correlated exposure, caps it at 409.96. Competitors print the first figure and call the portfolio diversified. They are counting tickets — and tickets are not independent.
Where the number comes from
Everything above was computed by the same engine that prices bets, at the moment this page was built — not typed into a template. The build fails if a figure appears here and not in the engine's own output.