Implied Probability and Removing the Bookmaker Margin (De-Vig)

Implied probability is one divided by the decimal odds, and removing the bookmaker margin means rescaling those numbers so a market adds up to exactly 100%. A match priced at 2.10, 3.50 and 3.60 implies 104.0% in total, so each raw number is a little too high. After removing the margin, the home win is 45.8% rather than 47.6%. Knowing this difference is the foundation of every sensible accumulator decision.

Step 1: odds to implied probability#

Implied probability = 1 ÷ decimal odds

For fractional odds, convert to decimal first (divide, then add 1). See how acca odds are calculated, or use the odds converter to switch between fractional, decimal and American odds.

Step 2: add up the market#

In a fair market, the probabilities of all possible outcomes sum to 100%. In a bookmaker's market they do not, because the bookmaker has shaded each price.

Worked example, a 1X2 market:

The excess, 4.0%, is the overround. It is the market-wide margin. Pinnacle, a bookmaker known for low margins, publishes guides on how to calculate betting margins, and the same method applies to any bookmaker.

Step 3: remove the margin#

Method 1: proportional (basic normalisation)#

Divide each implied probability by the total.

This is the standard and simplest approach. It assumes the margin is spread across outcomes in proportion to their probability.

Method 2: two-way markets#

For two outcomes, such as Over/Under 2.5 or BTTS, the method is the same. Over 1.80 and Under 2.00 give implied probabilities of 55.6% and 50.0%, a total of 105.6%. Divide each by 1.0556 for fair chances of 52.6% and 47.4%, which are fair odds of 1.90 and 2.11.

Method 3: power and Shin#

Proportional scaling has a known weakness. Research on the favourite-longshot bias suggests that bookmakers tend to shade long shots more heavily than favourites. Two alternatives account for it.

• Power method. Raise each implied probability to a power k (above 1) so the total comes to exactly 100%.
• Shin's method. Based on a model by Hyun Song Shin in which some bettors are better informed, it solves for a share of insider trading and adjusts each price to match. See Shin (1993), Economic Journal.

Here is how the three compare on two markets.

In a balanced market the three methods barely differ. In a lopsided market, they separate by one to two percentage points on the favourite, and about 0.7 to 0.8 points on the outsider. That matters when you are looking for small edges. Štrumbelj (2014) compared methods for converting odds to probabilities in the International Journal of Forecasting and later work on his results reports that Shin-based probabilities predicted outcomes better than basic normalisation, which is why serious modellers do not treat proportional scaling as the last word.

ArtificialAcca uses proportional de-vigging in its engine and says so in its methodology. It is simple, transparent and close to the alternatives for balanced markets. The limitation is that it can understate favourites slightly and overstate long shots.

Step 4: which prices to trust#

A de-vigged price is only as good as the bookmaker behind it. Two practical rules:

1. Prefer sharp prices. Bookmakers that accept big bets and run low margins tend to have prices closer to the market's real view. Pinnacle is commonly used as that benchmark, and ArtificialAcca anchors on it where it quotes the whole market.
2. Otherwise use the middle of the market. Take the de-vigged price from several bookmakers and use the median. One outlier price might be a mistake or a stale line.

Whichever you use, the de-vigged number is a starting point. It does not know about team news released after the price was set.

Step 5: compare with the price you can actually get#

Once you have a fair probability, convert it back to fair odds (1 ÷ probability) and compare with the best price available to you.

Edge = fair probability × offered decimal odds − 1

Example: the home win has a fair probability of 45.8%. The best price you can find is 2.25.

0.458 × 2.25 − 1 = +3.1%

That small positive number is the entire edge, and it relies on the fair probability being right. If you instead used the raw 47.6%, you would calculate 0.476 × 2.25 − 1 = +7.1%, an overstatement of the edge by more than double. That is how people talk themselves into bad bets.

Why this matters for accumulators#

Each leg carries its own margin, and the margin multiplies. If you only look at raw implied probabilities, you will think the acca is better value than it is. At 5% margin per leg, six legs retain about 74.6% of the fair payout, and the maths is in the hidden cost of accumulators. De-vig first, then multiply.

A quick routine#

1. Convert every price in the market to 1 ÷ odds.
2. Add them. The excess over 100% is the overround.
3. Divide each by the total to get fair probabilities.
4. Convert back to fair odds and compare with the best offered price.
5. Multiply fair probabilities across legs for the real chance of the acca.

The ArtificialAcca generator does steps 1 to 5 for you and shows the fair probability beside the odds for each leg. Its Acca of the Day is settled publicly on /results.

Common de-vigging mistakes#

• De-vigging across different markets. The margin belongs to one market. Do not sum a home price from one market with a draw price from another.
• Using stale prices. A price that is hours old may not reflect news, and the de-vigged number inherits that.
• De-vigging a boosted price. A boosted price is a promotion, not the market's view. De-vig the standard price instead.
• Treating fair odds as a target. Fair odds are a reference point. You are paid at the bookmaker's price, so the question is always how far above fair your price is.
• Forgetting double chance has its own margin. A double chance price is not simply the sum of two de-vigged outcomes. Compare it with your own fair number.

Combining several bookmakers#

When you do not have a sharp price, use several bookmakers and take the middle. Here is the home win from three bookmakers, each de-vigged separately:

The median is 45.8%. The mean is 45.9%. They are close here, but if bookmaker C had a stale price at 41%, the mean would drop to 44.6% while the median would stay at 45.8%. The median ignores one odd price, which is why ArtificialAcca uses it when no Pinnacle price is available.

Why this is worth the effort#

It takes a minute to de-vig a market with a calculator or spreadsheet, and the habit changes what you see. Prices that looked like value often turn out to be fair or worse once the margin is out, and the legs that survive the test are the ones worth thinking about. Use the same routine on every leg and you will quickly build a feel for which markets are tightly priced and which are loose.

18+ only. De-vigged probabilities are estimates, and an accumulator still loses if any leg does. Please gamble responsibly. Free support is available at BeGambleAware.org or on 0808 8020 133.