Twelve bets on one evening's slate are not twelve bets. They share weather, pace, injury news and a referee, and everything they share makes them a smaller number of larger positions than the count suggests.
The arithmetic is exact once you have a correlation. For n bets with
average pairwise correlation ρ, the number of independent bets you are
really holding is n / (1 + (n-1)ρ):
| Positions | At ρ = 0.15 | At ρ = 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 |
At 0.45, twelve positions are 2.0 independent bets. Doubling them to twenty gets you to 2.1. That is the part worth sitting with: past a handful of correlated bets, adding more stops buying diversification almost entirely, and only adds stake.
What it does to sizing
A single-bet cap of 5% of bankroll is right for someone holding nothing. On a 20,000 bankroll that is 1,000.00. Holding eleven correlated bets already, the same cap should be 409.96 — the difference is the shrink factor the correlation implies, and it is not a rounding adjustment.
Measure it, do not assume it
ρ can be measured from your own settled record: group bets that resolved together, and read the correlation off how much their combined results swing against what independence predicts. It needs 30 settled bets and 20 multi-bet groups before it is worth anything, and below that the honest answer is a labelled prior rather than a number.