01
How to convert odds to implied probability
Odds and probability are the same information written two ways. Each odds format has its own formula, and all three give the same answer for the same odds.
American odds
Minus odds: the odds ÷ (the odds + 100), ignoring the sign. Plus odds: 100 ÷ (the odds + 100).
-150 → 150 ÷ 250 = 60.0%
+200 → 100 ÷ 300 = 33.3%
Decimal odds
1 ÷ the odds.
2.50 → 1 ÷ 2.50 = 40.0%
Fractional odds
The second number ÷ the two numbers added together.
5/2 → 2 ÷ (5 + 2) = 28.6%
02
Odds to probability conversion table
The same odds in each format, with the probability they imply.
| American odds | Decimal odds | Fractional odds | Implied probability |
|---|---|---|---|
| -500 | 1.20 | 1/5 | 83.3% |
| -400 | 1.25 | 1/4 | 80.0% |
| -300 | 1.33 | 1/3 | 75.0% |
| -250 | 1.40 | 2/5 | 71.4% |
| -200 | 1.50 | 1/2 | 66.7% |
| -150 | 1.67 | 2/3 | 60.0% |
| -120 | 1.83 | 5/6 | 54.5% |
| -110 | 1.91 | 10/11 | 52.4% |
| +100 | 2.00 | 1/1 (evens) | 50.0% |
| +110 | 2.10 | 11/10 | 47.6% |
| +120 | 2.20 | 6/5 | 45.5% |
| +150 | 2.50 | 3/2 | 40.0% |
| +200 | 3.00 | 2/1 | 33.3% |
| +250 | 3.50 | 5/2 | 28.6% |
| +300 | 4.00 | 3/1 | 25.0% |
| +400 | 5.00 | 4/1 | 20.0% |
| +500 | 6.00 | 5/1 | 16.7% |
| +1000 | 11.00 | 10/1 | 9.1% |
03
Why the percentages add up to more than 100%
A bookmaker's odds on every outcome of a game imply probabilities that add up to more than 100%. The amount over 100% is the bookmaker's margin, also called the overround or the vig.
Two teams both listed at -110 imply 52.4% each: 104.8% in total, a margin of 4.8%. To take the margin out, divide each implied probability by the total. Here that gives 50.0% for each team.
With a draw there are three outcomes. Odds of 2.10, 3.40 and 3.60 imply 47.6%, 29.4% and 27.8%, which is 104.8% in total. With the margin removed they are 45.4%, 28.1% and 26.5%. The “Remove the margin” tab above does this for any two or three outcomes.
04
What implied probability does not tell you
Implied probability is the break-even rate of the odds. It is not a forecast. To judge odds you need your own estimate of the same outcome: the model comparison calculator puts an estimate and the odds side by side.
On Goalorithm's game pages the bookmakers' percentages are shown with the margin already removed, so they can be read against the model's probability for the same outcome. See today's games, or read implied probability explained for the longer version.
05
Questions about implied probability
What is implied probability?
- Implied probability is the win rate at which odds break even, written as a percentage. Odds of 2.00 (+100, or evens) pay back double the stake, so they break even when the outcome happens half the time: an implied probability of 50%. Shorter odds imply a higher probability, longer odds a lower one.
How do I convert American odds to implied probability?
- For minus odds, divide the number without its sign by itself plus 100: -150 is 150 ÷ 250 = 60.0%. For plus odds, divide 100 by the number plus 100: +200 is 100 ÷ 300 = 33.3%.
What is the implied probability of -110?
- 52.4%: 110 ÷ (110 + 100). When both sides of a game are listed at -110 the two percentages add up to 104.8%. The extra 4.8% is the bookmaker's margin, and with it removed each side is 50.0%.
How do I convert decimal or fractional odds?
- Decimal odds: divide 1 by the odds, so 2.50 is 1 ÷ 2.50 = 40.0%. Fractional odds: divide the second number by the two numbers added together, so 5/2 is 2 ÷ (5 + 2) = 28.6%.
How do I turn a probability back into odds?
- Divide 100 by the percentage to get decimal odds: 40% is 100 ÷ 40 = 2.50, which is +150 in American odds and 3/2 in fractional odds. Odds worked out this way have no margin in them, which is why they are sometimes called fair odds.
Is implied probability the real chance of winning?
- No. It is what the odds say, and listed odds include the bookmaker's margin, so the implied probabilities of every outcome of a game add up to more than 100%. Taking the margin out gives the bookmaker's view of the game. Whether that view is right is a separate question.
Is an implied odds calculator the same thing?
- For sports, yes: people who look for an implied odds calculator want the probability that the odds imply, which is what this page works out. In poker the phrase means something different: the money a hand could still win in later rounds.