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Implied probability in one minute

Every price is a probability in disguise. One division converts it, and once you can do that in your head the whole board starts saying something readable.

BAI8 ResearchResearch desk
1 min read

A decimal price of 4.00 is the claim that something happens about a quarter of the time. One divided by four is 0.25. That is the entire conversion, and it is the single most useful thing anybody who looks at a betting board can learn.

The three formats, one idea

Decimal is the easy one: divide 1 by the price. 2.50 is 40%, 1.50 is 66.7%, 10.00 is 10%.

Fractional is decimal with the stake removed, so add one before dividing. 3/1 is a decimal of 4.00, which is 25%.

American is two rules wearing one coat. A positive number is how much you win from 100, so +150 is 100 divided by 250, which is 40%. A negative number is how much you must stake to win 100, so -150 is 150 divided by 250, which is 60%.

They are three ways of writing the same sentence. The reason this product lets you pick one is that a reader in Ohio and a reader in Lyon read the same number differently, not that the numbers differ.

What to do with it

Once every price on a board is a percentage, the board becomes a forecast you can argue with. You can add the outcomes up and see the margin. You can compare one book's number to another's on the same footing. And you can put your own estimate next to it, which is the only way an edge can be identified at all.

What this does not tell you

The implied probability is not the market's honest opinion. It is the market's opinion plus a fee, and on a three-way market that fee can be several percentage points. Stripping it out properly is its own piece of arithmetic, and the naive method of dividing everything by the total is good enough for a glance and wrong for a decision.

Common questions

How do I convert decimal odds to a probability?

Divide 1 by the decimal price. A price of 4.00 implies 1 divided by 4, which is 25%.

How do I convert American odds to a probability?

For a positive number, 100 divided by the number plus 100. For a negative number, the number divided by the number plus 100, ignoring the minus sign.

Does the implied probability equal the real probability?

No. It includes the bookmaker's margin, so the implied figures across a market always add up to more than 100%.

Sources

  1. Odds and implied probabilityen.wikipedia.org
  • implied probability
  • pricing
  • odds
  • margin

Part of

Betting basics2 minWhat a positive edge actually meansAn edge is the gap between our number and the bookmaker's price. Here is how that gap is worked out, and the three things it does not tell you.

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