What a half point is actually worth

The fair price of half a point equals the probability of the game landing exactly on the whole number underneath it. In the NFL, three points occurs in close to one game in seven, so buying from −3.5 to −3 is buying about a nine per cent chance of a refund.

Every half point either creates or removes a push, and a push is a refund. So the value is not about being 'closer to right' — it is the price of an option on one specific final margin, and margins are not uniformly likely.

In basketball the distribution is smooth and every half point is worth roughly the same small amount, which is why this market is worth studying in football and is close to pure arithmetic in the NBA.

Which is where it goes wrong. Paying the standard rate at a number where the underlying margin is rare is a straight transfer to the book with no upside attached. The rate being standard is the problem, not the price.

What to do with it. Only buy points through key numbers, and only when the quoted rate is below what the underlying margin frequency justifies.