Implied Probability Explained: American Odds to Percent
American odds look like prices, but they also encode a probability. Turning odds such as -110 or +150 into a percentage lets you compare a price with a hit rate, compare books with each other, and see how often a bet must win just to break even. This guide shows the formulas and works through several examples.
The two formulas
American odds come in two forms.
Negative odds (the favorite side) show how much you must stake to win 100.
Implied probability = odds without the minus sign / (odds without the minus sign + 100)
Positive odds (the underdog side) show how much you win on a 100 stake.
Implied probability = 100 / (odds + 100)
Examples
- -110: 110 / 210 = 52.38%
- -115: 115 / 215 = 53.49%
- -200: 200 / 300 = 66.67%
- -300: 300 / 400 = 75.00%
- +100: 100 / 200 = 50.00%
- +150: 100 / 250 = 40.00%
- +250: 100 / 350 = 28.57%
The pattern: the more negative the number, the higher the implied chance, and the larger the positive number, the lower. At +100 (also called even money) the implied chance is exactly 50%.
Why it is a break-even number
Implied probability tells you how often you must win for the price to be a wash over many repeats.
Take -110. You risk 110 to win 100. If you place 100 such bets and win 52.38 of them on average:
- Winnings: 52.38 x 100 = 5,238
- Losses: 47.62 x 110 = 5,238
Equal, so you break even. At 55 wins in 100 you would have 55 x 100 - 45 x 110 = 5,500 - 4,950 = +550 on 11,000 risked (100 bets of 110), a gain of 5%. At 52 wins you would have 5,200 - 48 x 110 = 5,200 - 5,280 = -80, a small loss of under 1%. These illustrate the arithmetic. They are not predictions about any real outcome.
The practical point is that -110 sets a hurdle of 52.38%, not 50%. That gap is the sportsbook's margin, covered in the no-vig price article.
Going the other way: probability to odds
Sometimes you have a percentage and want the odds.
- If the probability p is above 50%: odds = -100 x p / (1 - p)
- If p is below 50%: odds = +100 x (1 - p) / p
Examples:
- 60%: -100 x 0.60 / 0.40 = -150
- 40%: +100 x 0.60 / 0.40 = +150
- 25%: +100 x 0.75 / 0.25 = +300
You can also work in decimal odds, where the implied probability is 1 divided by the decimal price. -110 is 1.909 in decimal (100/110 + 1), and 1 / 1.909 = 52.38%, matching the American formula. +150 is 2.50 in decimal, and 1 / 2.50 = 40.00%. The odds converter moves between American, decimal and fractional formats, and the implied probability calculator gives the percentage directly.
Comparing a price with a hit rate
This is where implied probability becomes useful in prop research. Suppose a player has cleared a 64.5-yard line in 7 of his last 10 games, a 70% L10 hit rate, and the over is priced at -115 (53.49% implied).
It is tempting to say 70% beats 53.49%, so the over looks good. That conclusion skips three things:
- The sample is small. If the line were truly a coin flip, 7 or more hits in 10 games happens about 17% of the time by chance alone. See how to read a hit rate.
- The line moves with the player. A line set at 64.5 already reflects recent form. A history of beating older, lower lines is not the same as beating this one.
- The price includes margin. 53.49% is not the market's fair view. The no-vig number, about 51% if the under is -105, is closer to what the book thinks.
A hit rate and an implied probability are two different kinds of number. One is a count from history; the other is a statement about a price. Putting them side by side is a reasonable first look, not a conclusion.
Implied probability is not true probability
An implied probability is what the price needs, or what a market is asking you to believe. It is not a measurement of how likely the event really is. Three reasons it can differ:
- Margin. Both sides of a market sum to more than 100%.
- Mispricing. Books make mistakes, especially in thin prop markets.
- Timing. A price reflects what was known when it was posted, and the line may have moved since.
When you see a "chance" on any betting site, ask whether it is margin-free, where it came from and when it was captured. ArchivePicks describes how its own figures are built on the methodology page, and the glossary defines the terms used here.
Common mistakes
Adding probabilities across independent bets. If two props are each 50%, the chance of both is not 100%. For separate events you multiply: 0.5 x 0.5 = 25%. The parlay article takes this further.
Ignoring the other side. An over at -110 has an implied 52.38%, but the under at -110 has 52.38% as well. Together that is 104.76%, so neither number alone is the whole story.
Confusing odds length with confidence. A +300 price implies 25%. That does not mean the book is 25% sure of anything; it means the price pays 3 to 1 and the break-even point is one win in four.
Quick reference
| American odds | Implied probability |
|---|---|
| -300 | 75.00% |
| -200 | 66.67% |
| -150 | 60.00% |
| -115 | 53.49% |
| -110 | 52.38% |
| +100 | 50.00% |
| +120 | 45.45% |
| +150 | 40.00% |
| +300 | 25.00% |
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