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Maths · the arithmetic behind a price

Maths

Why correlated legs are restricted

When one leg makes another more likely, multiplying their independent prices understates the true combined chance. A team winning by twenty and the game going over are not independent events, so the naive parlay price would be too generous.

Books forbid or reprice the obvious combinations because the multiplication that makes parlays profitable for them assumes independence. Remove the assumption and the arithmetic flips, which is why same-game markets are priced by a correlation model rather than by multiplication.

The classic banned pair A heavy favourite to cover −14 and the game to go over. If the favourite wins by twenty the total is very likely high, so the two outcomes travel together — and pricing them as independent would sell a joint outcome at a discount.

Correlation also runs negatively. A low total and a large margin pull against each other, and combining them is a worse bet than the independent price suggests rather than a better one.

What follows from that is less comfortable. Where a correlated combination IS offered, it is offered because the book's model says the correlation runs the other way from what it looks like, or because the price already carries it.

What to do with it. Before taking any multi-leg bet from one game, ask whether the legs help each other. If they do and the price is a simple multiplication, look again at why it is available.

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