Implied Probability

Implied probability is the conversion of betting odds into the win probability they represent, as priced by the bookmaker. For decimal odds the formula is: implied probability = 1 / decimal odds x 100. For American odds the calculation differs by sign. For -110, it is 110 / (110 + 100) x 100 = 52.38%; for a positive price such as +150, it is 100 / (150 + 100) x 100 = 40%. Worked example: a match has both sides priced at 1.90 in decimal. Each implies 1 / 1.90 x 100 = 52.63%. Add the two together and you get 105.26%, not 100%. That excess of 5.26 percentage points is the overround (also called the vig or juice) — the bookmaker's built-in margin. The two outcomes cannot both be more likely than a coin flip, so the surplus is the edge the book charges for taking the bet. Why it matters: implied probability is the yardstick for spotting value. If your own assessment of a team's chance is 60% but the price implies only 52%, the bet has positive expected value. To compare odds fairly you should strip out the margin to find the no-vig, or fair, probability, dividing each implied figure by the total overround. A frequent mistake is to treat the raw implied probability as the bookmaker's honest estimate of the true chance; it is always inflated by the margin, so the real estimate sits slightly lower. See also overround, value bet and decimal odds.