How to convert odds into probability

Football odds are simply another way of writing a probability. The probability behind decimal odds (e.g. 2.50) is found with a single division:

probability = 1 ÷ odds

So 2.50 means 40% (1 ÷ 2.50 = 0.40), 1.50 means 66.7% and 4.00 means 25%. Lower odds mean a higher probability; higher odds mean a lower one.

Why do the three outcomes add up to more than 100%?

Convert the home, draw and away odds of a match into probabilities and add them up: you will usually get more than 100%, for example 105% or 110%. The excess is the bookmaker's margin – its built-in profit. To find the true probabilities, the excess has to be removed.

Removing the margin

The simplest method divides each probability by the total. With odds of 2.10 · 3.40 · 3.60 the raw probabilities are 47.6% · 29.4% · 27.8%, totalling 104.8%. Dividing each by 1.048 gives margin-free probabilities of about 45.4% · 28.1% · 26.5%. harbigol does this separately for many bookmakers worldwide and averages the results to capture the market consensus.

Fair odds

The inverse of a margin-free probability (1 ÷ probability) is called the fair odds. In the example above the home side's fair odds are 1 ÷ 0.454 ≈ 2.20 – the price you would see if the bookmaker took no profit.

A probability is an estimate, not a guarantee. An outcome with a 70% probability still fails roughly three times in ten.