Implied Probability and the Bookmaker's Margin

Every price implies a probability. Add up the implied probabilities for all outcomes and the total is more than 100 percent. The excess is the margin.

From price to probability

With decimal odds, implied probability is one divided by the odds. A price of 2.00 implies 50 percent. A price of 4.00 implies 25 percent.

A two-way example

Suppose both sides of an even contest are priced at 1.91.

• 1 / 1.91 = 52.4 percent for each side.
• Together: 104.7 percent.

The true probabilities must sum to 100. The extra 4.7 points is the bookmaker's margin, sometimes called the overround. It is how the business is paid regardless of the result. The mathematics are set out in Wikipedia's article on the mathematics of bookmaking.

Removing the margin

To estimate the probabilities the prices really reflect, divide each implied probability by the total. In the example, 52.4 / 104.7 gives 50 percent each.

What this is useful for

• Comparing markets. A market that sums to 102 percent is cheaper to bet into than one that sums to 108.
• Checking a hunch. A bet is only reasonable if you believe the true chance is higher than the implied one. Most hunches do not survive being written as a percentage.
• Seeing the cost. The margin is paid on every bet, win or lose, in the form of a slightly worse price.

A limit worth stating

Stripping out the margin gives the market's estimate, not the truth. Markets are often accurate and are sometimes wrong, and knowing which is the hard part.