Implied probability: what the odds say about the chances
ナレッジベース · 公開日 · 読了目安4分
この記事は英語のみです。
Implied probability is the chance of an outcome that is built into a betting price. It lets you compare very different prices on one scale and is the starting point for judging whether a price is fair, too short or too generous.
The basic formula
For decimal odds, the formula is a single division:
- implied probability = 1 / decimal odds
Some examples make the pattern clear.
- 1.50 implies 1 / 1.50 = 66.7%
- 2.00 implies 50%
- 3.00 implies 33.3%
- 5.00 implies 20%
- 10.00 implies 10%
Short prices imply high probabilities and long prices imply low ones. For other formats, convert to decimal first. Fractional odds a/b have an implied probability of b / (a + b), so 3/1 gives 1 / 4 = 25%. American odds of +200 give 100 / 300 = 33.3%, and -200 gives 200 / 300 = 66.7%.
Why the percentages add up to more than 100
In a fair world, the probabilities of all outcomes in one market would add up to exactly 100%. Real prices do not. Take a football match priced at 2.10 for the home side, 3.40 for a draw and 3.50 for the away side.
- Home: 1 / 2.10 = 47.6%
- Draw: 1 / 3.40 = 29.4%
- Away: 1 / 3.50 = 28.6%
The total is 105.6%. The extra 5.6 points are the bookmaker's margin, also called the overround. Because of it, the raw implied probability always slightly overstates each outcome's chance.
Removing the margin
To estimate fair probabilities, divide each implied probability by the total. This simple method is often called normalising or "no-vig" pricing.
- Home: 47.6 / 105.6 = 45.1%
- Draw: 29.4 / 105.6 = 27.8%
- Away: 28.6 / 105.6 = 27.1%
The three now add up to 100%. The fair odds are the inverse: 1 / 0.451 = 2.22 for the home side, and so on. This method spreads the margin evenly across outcomes, which is a simplification. Bookmakers often load more margin onto longshots, so treat the result as an estimate rather than a fact. Our no-vig calculator does the arithmetic for any number of outcomes.
Comparing a price with your own estimate
Suppose you believe a team has a 40% chance to win and the market offers 3.00, which implies 33.3%. Your estimate is higher than the market's, so by your own numbers the price has positive expected value. The expected value per unit staked is:
- EV = probability x odds - 1 = 0.40 x 3.00 - 1 = +0.20
That is an average gain of 0.20 per unit staked if your estimate is right, which is the big if. If the true chance is 30%, the same bet is losing: 0.30 x 3.00 - 1 = -0.10. The method is sound, but it only works as well as the probability estimate you feed into it. Most people overrate their own estimates, so be sceptical of apparent edges, especially large ones.
Break-even probability
The implied probability of a price is also your break-even point. At 2.50 you need to win more than 40% of such bets, over many bets, just to avoid losing money. A bet is only worth considering when you honestly believe the true chance is above that threshold, by enough to cover uncertainty in your estimate.
Where implied probability misleads
- Small samples. A 60% chance still loses four times in ten. A short run of results says very little.
- Margins and prices that move. Prices change with news and money, and the margin differs between providers.
- Wrong sample for your estimate. Form, injuries and schedule matter, and none of them are in the arithmetic.
- Accumulators. Multiplying prices also multiplies margins, so the combined bookmaker advantage grows with every leg.
Key takeaways
Convert odds to a probability with 1 / odds, remove the margin by dividing by the total, and use the result as a yardstick rather than a promise. Implied probability describes what a price assumes. It does not tell you what will happen, and it never guarantees profit.
You must be 18+ to bet. Gamble only with money you can afford to lose, keep to the limits you set, and seek help from a support service if betting stops being fun.