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Maths · the arithmetic behind a price

Maths

The overround, and why prices never add to 100

Add the implied probabilities of every outcome in a market. A fair market sums to 100 per cent; a real one sums to more, and the excess is the bookmaker's margin. Two sides at −110 sum to 104.8, so the overround is 4.8 points.

The margin has to live somewhere, and building it into the prices is far more effective than charging a fee, because it is invisible. Nobody sees a line item. They see two numbers that look like a fair coin flip and are not one.

Same game, two books Book A: −110 / −110, summing to 104.8%. Book B: −105 / −115, summing to 104.9%. Almost identical overrounds, very different bets — if your opinion is the −105 side, Book B is materially better, and if it is the other side, materially worse.

A low overround is not generosity. It usually appears on markets the book is most confident it prices better than you do, which is why the tightest prices on any board are on the most heavily modelled events.

Here is the catch. Comparing books by their headline price on one side tells you nothing about their margin. A book can be best on favourites and worst on underdogs across its whole card, and most are.

What to do with it. Compare overrounds to judge a book, and compare individual prices to judge a bet. They are different questions and the same two numbers answer both.

Add the implied probabilities from the bet calculator and whatever they exceed 100 by is the margin you are paying.

Work it out. The no-vig calculator takes both sides of a market and returns the margin and the fair price of each.

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