Bookmaker Margin Calculator
Enter the odds for every outcome of one market and the calculator shows the sum of implied probabilities, the margin and the odds with the margin taken out. It handles two-way markets, 1X2 and markets with up to 10 outcomes, such as outright betting on a tournament winner.
There are four ways to remove the margin, and each one splits it differently between the favourite and the outsiders. The calculator applies any of them and shows how much markup sits in each outcome, so you can see where the line is most expensive for you. The full-line mode compares the margin across the markets of one match and shows which market lets you back the same view of the game more cheaply.
Work out the margin from the odds of one market
Use odds from one bookmaker, one market and one point in time. A two-way market needs both prices, 1X2 needs the home win, the draw and the away win, and an outright needs every runner.
Inputs
Results update automatically. Decimals can be entered with a point or a comma, and thousands separators are accepted. Enter every outcome of one complete market: leave one out and both the probability sum and the margin come out too low.
Result
Enter the odds and the result appears automatically.
| Outcome | Bookmaker odds | Implied probability | Margin-free probability | Margin-free odds | Margin in outcome |
|---|
Margin across a whole match line: where the bookmaker takes less
Enter the odds for several markets of one match at one bookmaker. The calculator works out the margin of each and sorts them from the cheapest to the most expensive for the player. Empty rows are ignored. The example line is for a match with a clear home favourite.
| Market | Line | Outcome 1 | Outcome 2 | Outcome 3 |
|---|
Markets by margin
| Market | Sum of probabilities | Margin | Bookmaker’s hold |
|---|
Prices derived from the 1 / X / 2 market
Double chance and handicap 0 (Draw No Bet) are fully determined by the match result. Their fair price is calculated from the margin-free 1X2 probabilities (proportional method) and compared with the bookmaker’s price.
| Market | Bookmaker | From margin-free 1X2 | Below fair price by |
|---|
In the example line the match result carries a 4.34% margin, the main total 4.81%, the −1.5 / +1.5 handicap 4.56% and double chance 4.18%. Both teams to score, home team to score, away team to score, odd/even and the second total are already at around 8%, and handicap 0 is at 9.2%. The gap between the cheapest and the most expensive market in a single line is more than five percentage points. Over time, that is the difference between a bet that loses about 4% of turnover on average and one that loses about 8%.
Handicap 0 is the clearest case. Its fair price follows entirely from the match result: the probability of a home win divided by the probability that the match does not end in a draw. From 1.40 / 4.90 / 8.00 you get 1.18 for the home side and 6.71 for the away side, while the bookmaker offers 1.091 and 5.70, which is 7.15% and 15.11% below fair. Double chance in the same line sits 3.8–4.1% below its fair price, roughly the same as the match result itself.
How the bookmaker’s margin is calculated
Each decimal price converts into the probability built into it: pᵢ = 1 / Kᵢ. The probabilities of all outcomes in one complete market are then added up.
S = Σ(1 / Kᵢ)Market margin = (S − 1) × 100%Bookmaker’s hold on a balanced book = (S − 1) / S × 100%If the sum is 106%, the margin under the first formula is 6%. It is a price markup on the whole market, not the probability that a particular bet loses.
The second formula answers a different question: what share of turnover the bookmaker keeps if stakes are spread across the outcomes so that the payout is the same whatever happens. At S = 1.0612 that is 5.76% rather than 6.12%. It is also the player’s average loss per unit staked on such a line. The calculator shows both figures; the result headline and the examples use the first.
How to remove the margin from odds: four methods
Every method brings the sum of probabilities back to 100%, but each decides differently how much markup comes off which outcome.
Proportional: qᵢ = pᵢ / SAdditive (equal shares): qᵢ = pᵢ − (S − 1) / nPower: qᵢ = pᵢ^c, with c chosen so that Σqᵢ = 1Shin model: qᵢ = (√(z² + 4(1 − z) · pᵢ² / S) − z) / (2(1 − z)), with z chosen so that Σqᵢ = 1Margin-free odds = 1 / qᵢwhere n is the number of outcomes and z is the Shin model parameter, read as the share of well-informed bettors in the market.
The proportional method, also known as basic normalisation, is the most widely used and the simplest: it keeps the ratios between the probabilities. The other three take more markup off the outsiders than off the favourite, which accounts for the favourite–longshot bias: prices on unlikely outcomes are usually cut more heavily. In a comparison of methods published in the International Journal of Forecasting in 2014, Shin-model probabilities proved more accurate than basic normalisation for every bookmaker and sport examined.
| Method | 1 (2.20) | X (3.40) | 2 (3.20) |
|---|---|---|---|
| Proportional | 2.33 | 3.61 | 3.40 |
| Additive (equal shares) | 2.30 | 3.65 | 3.42 |
| Power | 2.30 | 3.65 | 3.42 |
| Shin model | 2.31 | 3.64 | 3.42 |
On an ordinary 1X2 market the methods differ by a few hundredths in the odds, but the direction is consistent: the proportional method gives the favourite the highest fair odds and the draw and the outsider the lowest. In two-way markets the Shin model and the additive method give the same result. In markets with a long tail of outsiders the additive method can return a negative probability, and the calculator will warn you when that happens.
Where the margin hides: outcome by outcome
The margin in an outcome is how far the bookmaker’s odds sit below the margin-free odds: fair odds / bookmaker odds − 1.
| Outcome | Bookmaker odds | Markup: proportional | Shin model: margin-free | Markup: Shin model |
|---|---|---|---|---|
| 1 | 2.20 | 6.12% | 2.31 | 5.06% |
| X | 3.40 | 6.12% | 3.64 | 7.10% |
| 2 | 3.20 | 6.12% | 3.42 | 6.76% |
By construction, the proportional method puts the same markup on every outcome: 6.12%, the same as the market as a whole. The Shin model spreads it differently, and in this line a bet on the draw costs almost two percentage points more than a bet on the favourite. If the model describes the market correctly, these are the outcomes where you pay the bookmaker the most.
Why you cannot remove the margin from a single price
A single price only gives you the probability built into that price. To estimate the margin and strip it out, you need the probability sum of all mutually exclusive outcomes in the market. If all you want is to turn one price into a percentage, use the odds to probability converter.
Worked examples
| Market | Odds | Sum of probabilities | Margin | Bookmaker’s hold |
|---|---|---|---|---|
| Two outcomes | 1.72 / 2.10 | 105.76% | 5.76% | 5.45% |
| Football 1X2 | 2.20 / 3.40 / 3.20 | 106.12% | 6.12% | 5.76% |
| Symmetrical market | 1.95 / 1.95 | 102.56% | 2.56% | 2.50% |
| Tournament winner, 6 runners | 2.75 / 3.75 / 5.00 / 7.00 / 10.00 / 13.00 | 115.01% | 15.01% | 13.05% |
The last row shows why outright margins cannot be compared with the margin on a single match: there are more outcomes, and the markup builds up across all of them. The difference between removal methods is especially visible on a line like this; try it in the calculator with the “tournament winner” preset.
How to compare different lines
Compare the same market at the same point in time. A smaller positive margin means a smaller price markup, but there is no universal threshold such as “good below 3%, bad above 6%” that holds for every sport and market.
Liquidity, the competition, the type of market, the time left before the event and the operator’s own rules all move the margin noticeably. That makes the figure more useful for comparing several lines than as a standalone verdict on a bookmaker.
What a negative margin means
If the probability sum is below 100%, the calculator shows a negative value. For one bookmaker’s prices on one complete market, this is a reason to recheck your input: most often an outcome is missing.
If the prices come from different bookmakers, a sum below 100% may point to an arbitrage, or surebet: a combination where bets on every outcome make a profit whatever the result. Splitting the stake between the outcomes is a job for an arbitrage calculator; bear in mind that many operators restrict accounts that bet arbitrages systematically.
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Frequently asked questions
What is a bookmaker’s margin?
For a complete market, it is how far the sum of the probabilities implied by the odds exceeds 100%. A sum of 105% corresponds to a 5% margin. On a balanced book the bookmaker keeps 5 / 105 = 4.76% of turnover.
How do you remove the margin from odds?
Enter the odds for all outcomes in the market and choose a method. The proportional method is the simplest: the probabilities are divided by their sum and converted back into odds. The Shin model and the other two methods also allow for the fact that bookmakers usually build more markup into the outsiders.
Which margin removal method should I choose?
Proportional is enough for a quick estimate. If accurate probabilities matter, for example when you compare them with your own model, choose the Shin model: in the published comparison it was more accurate than basic normalisation. In a two-way market the Shin model and the additive method give the same answer.
Are margin-free odds the true odds?
No. They are the output of the removal method you chose. They are useful as an estimate of the price without the bookmaker’s markup, but they do not prove the real probability of an event: different methods give different values, especially for outsiders.
What counts as a normal margin?
There is no universal norm. The main outcomes of popular matches usually carry a lower margin than secondary markets and outrights with many outcomes. It is fairer to compare the same market across several operators at the same time than to judge the number on its own.
Which market in a match has the lowest margin?
Usually the main ones: the match result, the main total and the main handicap, where most money is staked and bookmakers compete hardest. On secondary markets (both teams to score, odd/even, team totals, extreme total lines) it is often twice as high. You can check a specific line in the full-line mode, which sorts the markets by margin.
Can you work out the margin from a single price?
No. The margin needs the full set of mutually exclusive outcomes in the market.
Why is the sum of probabilities above 100%?
Because published odds include the bookmaker’s price markup. When you convert every outcome into a probability, that markup shows up as a sum above 100%.
What does a margin below 0% mean?
First check that you have entered all outcomes of the market. If the odds come from different bookmakers, a sum below 100% may mean an arbitrage.
Sources
- Štrumbelj E. On determining probability forecasts from betting odds. International Journal of Forecasting, 2014, vol. 30, pp. 934–943 — a comparison of margin removal methods, including the Shin model