Odds are just probabilities written in a different way. Once you can switch between the two, a lot of betting maths stops being mysterious: you can see how much the bookmaker is charging you, work out a fair price, and tell whether a bet is worth taking at all.
This guide covers implied probability, the bookmaker margin (also called the overround or the vig), how to remove it, and why player props make that last step awkward.
01What is implied probability?#
Implied probability is the chance of an outcome that the odds suggest. With decimal odds the formula is as simple as it gets:
implied probability = 1 / decimal odds
So odds of 2.00 imply 50%, odds of 4.00 imply 25%, and odds of 1.25 imply 80%.
If you use other formats, convert first:
| Format | Example | To decimal |
|---|---|---|
| Fractional | 3/1 | 3 / 1 + 1 = 4.00 |
| Fractional | 4/6 | 4 / 6 + 1 = about 1.67 |
| American, positive | +150 | 150 / 100 + 1 = 2.50 |
| American, negative | -200 | 100 / 200 + 1 = 1.50 |
Implied probability includes the bookmaker's margin, so it isn't the bookmaker's honest estimate of the chance. It's the chance you'd need for the bet to break even.
02What is the bookmaker margin?#
If you add up the implied probabilities of every outcome in a market, you'd expect 100%. With a bookmaker it's always more. The extra is the margin.
Example (hypothetical match odds):
| Outcome | Odds | Implied probability |
|---|---|---|
| Home | 2.10 | 47.62% |
| Draw | 3.40 | 29.41% |
| Away | 3.60 | 27.78% |
| Total | 104.81% |
The book adds up to 104.81%, so the overround is 4.81%. You'll also see this expressed as a payout percentage: 1 / 1.0481, about 95.4%. In other words, if you spread your money across all three outcomes in the right proportions, you'd get back about 95.4% of it whatever happens.
Different sites quote "margin" in slightly different ways (4.81% as the overround above, or about 4.6% as 100% minus the payout). They describe the same thing, so just be consistent when you compare bookmakers.
03How to remove the margin and get fair odds#
Removing the margin (people call it "de-vigging") gives you the bookmaker's underlying view without the charge on top. The simplest method is proportional: divide each implied probability by the total.
Using the hypothetical match above:
| Outcome | Implied | Fair probability | Fair odd |
|---|---|---|---|
| Home | 47.62% | 47.62 / 104.81 = 45.43% | 2.20 |
| Draw | 29.41% | 28.06% | 3.56 |
| Away | 27.78% | 26.50% | 3.77 |
Those fair probabilities add up to 100%. The fair odd is just 1 divided by the fair probability.
The proportional method assumes the bookmaker spreads the margin evenly. In practice books often put more margin on longshots than on favourites, which is why people also use other methods (additive, power, or Shin's method). They give slightly different fair odds, especially for big prices. For most purposes, proportional is a sensible starting point, and the gap between methods is a useful reminder that a fair odd is an estimate, not a fact.
04Why player props are harder#
Here's the catch. To de-vig a market you need every outcome. In a 1X2 market you have all three. In many player props you only see one side.
Take an anytime goalscorer price of 2.50. The implied probability is 40%, but there's usually no "not to score" price next to it, so you can't tell how much of that 40% is margin. You could add up every player's price in the match, but that doesn't work cleanly either, because more than one player can score (or nobody can).
Some prop markets do come as a pair. Shots on target are sometimes offered as over and under 0.5:
Example (hypothetical two-way line):
- Over 0.5 shots on target at 1.50: implied 66.67%
- Under 0.5 at 2.40: implied 41.67%
- Total 108.33%, so the overround is 8.33%
- Fair probability for over: 66.67 / 108.33 = 61.54%, fair odd 1.625
That's a much bigger margin than the match odds example, and it's typical of how props compare with main markets. For one-sided markets, the honest alternative is to build your own fair odd from player data, which is what JOPP does. I explain how bookmakers build theirs in how bookmakers price player props.
05From fair odds to value#
Once you have a fair odd from anywhere (a de-vigged sharp price, your own model, or a tool), finding value is one comparison:
EV% = (bookmaker odd / fair odd - 1) x 100
If your fair odd for a player is 2.20 and a bookmaker offers 2.40, EV is (2.40 / 2.20 - 1) x 100, about +9.1% (hypothetical). If the bookmaker offers 2.00, it's about -9.1%. The full walkthrough is in what is expected value in betting.
06Common mistakes with implied probability#
- Treating implied probability as the real chance. It includes the margin, so it overstates every outcome a little.
- Comparing margins across different market types. A 5% book on match odds and an 8% book on a two-way prop aren't the same "expensive". Compare like with like.
- Forgetting that bet builders multiply margins. Every leg carries its own margin, so a three-leg builder can be far more expensive than any single leg. More in bet builder tips.
- Ignoring the rules. Two prices on the same player can imply different things if one bookmaker voids non-starters and the other doesn't.
07Frequently asked questions#
How do you calculate implied probability from odds?#
Divide 1 by the decimal odds. Odds of 2.50 imply 1 / 2.50 = 40%. For fractional odds, convert to decimal first by dividing the two numbers and adding 1, so 3/2 becomes 2.50.
What is a normal bookmaker margin in football?#
It depends on the market and the bookmaker. Main match markets in big leagues tend to carry the smallest margins, while player props and niche markets carry bigger ones. Work it out yourself by adding the implied probabilities of every outcome in the market.
What's the difference between overround, margin and vig?#
They all describe the bookmaker's built-in edge. Overround is usually the amount the book sums above 100%. Margin and vig (short for vigorish, also called juice) are used for the same idea, sometimes calculated as 100% minus the payout percentage. The numbers differ slightly depending on the convention.
How do I remove the vig from player prop odds?#
If the market has two sides, like over and under 0.5 shots on target, divide each side's implied probability by the total. If only the "yes" side is offered, you can't de-vig it properly from that price alone, so you need a fair odd from another source such as a model.
Is implied probability the same as fair odds?#
No. Implied probability comes straight from the bookmaker's odds, margin included. Fair odds are what the price would be with no margin, based on the true chance as best you can estimate it.