How to Turn Betting Odds Into Probability and Remove the Margin

Step 1: a decimal price becomes an implied probability

Decimal odds tell you the total return on a stake of one. A price of 4.00 returns four, so it breaks even if the outcome happens one time in four. That gives the first formula, and it is the easy one.

implied probability p = 1 / decimal odds 1.90 -> 1 / 1.90 = 0.5263 = 52.63 % 3.60 -> 1 / 3.60 = 0.2778 = 27.78 % 4.20 -> 1 / 4.20 = 0.2381 = 23.81 %

So far so good. Now add them up.

Step 2: the sum gives away the margin

Those three numbers come to 104.22 percent. Exactly one of the three outcomes has to happen, so a set of honest probabilities would come to 100. The extra 4.22 percentage points are the bookmaker's margin, usually called the overround or the vig.

overround R = p_home + p_draw + p_away = 0.5263 + 0.2778 + 0.2381 = 1.0422 margin = 4.22 %

Every price in the list is inflated. That is not a trick, it is how the business works: the margin is the fee for taking the other side. But it means the raw implied probabilities are systematically too high, and if you read 52.63 percent off a price of 1.90 you have quietly overstated that team.

Step 3: divide the margin back out

The simplest correction, and the one used in this project, is the proportional method: divide each implied probability by the sum. The result is three numbers that add to exactly 100 percent and keep the same ratios to each other.

fair probability q_i = p_i / R home 0.5263 / 1.0422 = 0.5050 = 50.5 % draw 0.2778 / 1.0422 = 0.2665 = 26.7 % away 0.2381 / 1.0422 = 0.2285 = 22.8 % ------ 100.0 %

The favourite dropped from 52.6 to 50.5 percent. Two percentage points sounds small until you build a scoreline model on top of it, at which point the error travels into every number the model produces.

Step 4: one bookmaker is not a market

A single book has its own liabilities and its own view. The fix is unglamorous: run steps one to three separately for every bookmaker that quotes the match, then average the margin free results outcome by outcome. Averaging after removing the margin, rather than before, matters, because books do not all charge the same margin and the wider ones would otherwise pull the average around.

for each bookmaker b: q_b = devig(prices of b) consensus Q = mean over all b of q_b

That consensus is what the app calls the market. It is the aggregate view of everyone who has money at stake, which is a strong public signal, and it is why the numbers move when the market moves rather than when somebody changes their mind.

Two-way markets work the same way

The over and under 2.5 goals market has two outcomes rather than three, and nothing else changes. Convert both prices, add them, divide each by the sum. This project keeps only the fair over probability, because under is one minus over. What that number is used for is covered in goal markets explained.

What proportional devigging does not fix

It is honest to name the limits of a method you rely on.

The margin is not spread evenly. Bookmakers tend to load more of their cut onto long shots than onto favourites, an effect known as the favourite and long shot bias. Proportional devigging assumes the margin is spread in proportion to price, which is a simplification. Other methods, such as the multiplicative or Shin approaches, distribute it differently.
A consensus is not the truth. It is the average opinion of a well informed crowd. Crowds are usually close and occasionally badly wrong.
It says nothing about what to do. A fair probability is a description, not a recommendation.

What the numbers looked like across a whole tournament

Applied to all 104 matches of the 2026 World Cup, the fair consensus put the average draw probability at 22.2 percent, with a range from 5.8 percent in the most one-sided fixture to 34.1 percent in the tightest. That is a useful sanity check on any model you build: a football draw is rarely worth less than one chance in twenty, and almost never worth more than one in three.

How to turn betting odds into probability