Implied vs fair probability

Lesson 1 of 6 · 4 min read

In Reading odds you turned a price into a percentage. That number is useful, but it isn't the book's honest opinion, because the vig is baked into it. Every price carries two chances, and value starts with knowing which is which.

Implied: what the price charges

A price's implied probability is the chance you need just to break even at that price. −150 implies 60%, so a bet at −150 has to win more than 60% of the time to make money. It is the bar your bet must clear, and it includes the book's fee.

You can see the fee by adding both sides. A fair market adds up to exactly 100%. Bears −150 and Lions +130 add up to 103.48%, about 103.5%. Those extra 3.48 points are the overround from the vig lesson: the book's cushion, charged across both sides. Measured as a share of the money bet, the book's margin is a little smaller, about 3.4% (1 − 1 ÷ 1.0348); that is the figure the calculator below shows.

Fair: what the market thinks

Take the cushion out and you get each side's fair probability: the market's own estimate of the real chance, with no fee in it. The fair chances of the two sides always add up to exactly 100%. Turn a fair chance back into a price and you have the fair odds, the price the bet would carry if the book charged nothing.

Taking the vig out is called de-vigging. The simplest way is to divide each side by the sum of both. A more careful way, the Shin method, allows for books charging longshots more of their margin than favorites. On a bet with two sides, Shin works out the same as taking half the extra off each side, and that is what the example below does. Dividing gives the favorite a little less: 58.0% instead of 58.3%, and the gap grows as prices get more lopsided.

Why you need both numbers

• Implied is your cost. It comes from the price you would actually take, at the book you would actually use.
• Fair is the market's opinion. It is the best single starting guess at the real chance, because it already reflects what the books and their bettors know.

At any one book, the fair chance of a side is always below that book's implied chance; the vig sits in between. So agreeing with the market is not enough to beat the same book's price. You need a better price somewhere else, or a good reason to think the real chance is higher than the market says. The first is line shopping, two lessons on. The second takes real evidence, because the market is usually close to right.

How Consensus Edge uses it

We de-vig each book's prices separately, then blend them into one fair chance. We let the lower-vig books count for more in our blend (inverse-vig weighting), a rule of thumb rather than proof of a better price; sharpness is about who leads the market (see Steam and market makers). That blend is Square, one of the three sources behind our consensus, alongside our own model (Sharp) and prediction markets (Crowd).

Try it: put any two prices into the calculator below to see each side's implied and fair chance.

Terms in this lesson

Implied ProbabilityFair ProbabilityFair OddsOverroundVigShin MethodInverse-Vig WeightingSquareLine Shopping