Implied probability: turning horse racing odds into a percentage chance

How do you calculate implied probability from odds?

Convert the price to decimal and divide 1 by it: 3/1 is 4.0, and 1 divided by 4.0 is 0.25, a 25 per cent chance; with fractions, divide the right number by the sum of both numbers, so 3/1 is 1 divided by 4.

The fractional shortcut works for any price. 5/2 is 2 divided by 7, about 28.6 per cent. 4/6 is 6 divided by 10, which is 60 per cent. 10/1 is 1 divided by 11, about 9.1 per cent. For decimal odds, 2.5 gives 1 divided by 2.5, which is 40 per cent.

Implied probability is the market's view expressed as a percentage. It is not the horse's true chance: it includes the bookmaker's margin, and the market can be wrong, especially about horses with little or unusual form.

Why do the implied probabilities in a race add up to more than 100?

The total is above 100 because each price is slightly shorter than a fair price, and the excess is the bookmaker's margin, known as the overround, which is how a bookmaker expects to profit across all outcomes.

In a fair book the implied chances would add up to exactly 100, because one horse must win. A typical bookmaker's win market on a British race adds up to well over that, and the margin grows with the number of runners. Exchange markets usually sit much closer to 100 because backers and layers set the prices and the exchange charges commission instead.

How do you remove the bookmaker margin to get a fair book?

Add up every runner's implied probability to get the book total, then divide each runner's implied probability by that total, which scales the chances back to 100 and gives a fair price.

In the four-runner example below, the prices add up to a 115 per cent book. The 6/4 favourite's 40 per cent becomes about 34.8 per cent once the margin is removed, which converts back to a fair decimal price of about 2.88, roughly 15/8. This simple proportional method spreads the margin evenly; in practice bookmakers tend to load more margin onto outsiders, so the fair chance of longer-priced horses is often smaller still.

How often do horses win compared with their implied probability?

Across ten seasons of British and Irish racing, runners starting at 5/1 won 14% of 37,169 runs against an implied chance of about 16.7 per cent, and the chart on this page shows the same comparison for every price to 10/1.

At most prices, horses win a little less often than their starting price implies, which is the margin showing through in real results. The gap is usually smaller for favourites and wider for outsiders, a pattern known as the favourite-longshot bias. The chart covers ten seasons, and the full tables draw on 1,201,143 runs across Flat and jumps.

What is the difference between implied probability and a horse's true chance?

Implied probability is the market's price turned into a percentage, margin included, while a horse's true chance is unknown and can only be estimated from form, conditions and the betting.

Anyone assessing a race is really comparing their own estimate of each horse's chance with the implied probability. If you think a horse has a one in four chance and it is priced at 5/1, your view and the market's differ. Whether you are right is another matter: the market is often efficient, and the evidence behind an estimate has to be stronger than the crowd's to justify disagreeing with it.

Racing records

Public racing records and results from Britain and Ireland.

below 1.00 means less.

• Expected winners = the sum of each runner's margin-free chance
• Above 1.00: won more often than the prices suggested
• Below 1.00: won less often than the prices suggested
• Small samples swing widely, so check the number of runs

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