Implied probability
In sports betting implied probability is the conversion of betting odds into percentages. This calculation takes into account the bookmaker's vigorish, and reveals how often a given bet must win to break even. Wagers that are believed to win more often than the implied probability are said to have positive expected value and are used to generate long term profit.
House advantage
Sportsbook house advantage exists through the implied probabilities of events summing to more than 100%. The greater the sum the larger the bookmaker's edge. Implied probability is calculated by dividing the initial risk by the potential return (which includes both risk and profit).
| Team | Spread | Total | Moneyline | |
|
Green Bay Packers | -3.5 (-110) | Over 48.5 (-110) | -180 |
|
Seattle Seahawks | +3.5 (-110) | Under 48.5 (-110) | +160 |
Consider the spread market in the example above. Green Bay -3.5 and Seattle +3.5 both have the same odds at -110. An initial risk of $110 on either side would yield $100 profit for a total return of $210. Implied probability is calculated by dividing the initial stake ($110) by the potential return ($210):
| Bet | Odds | Initial risk | Total return | Implied probability | |
|
|
Green Bay -3.5 | -110 | $110 | $210 | $100 / $210 = 0.5238 or 52.38% |
|
|
Seattle +3.5 | -110 | $110 | $210 | $100 / $210 = 0.5238 or 52.38% |
Both sides of the market have an implied probability of 52.38% which sum to 104.76%. Given that a fair market would sum to 100% this reveals a house advantage of 4.76%. To generate a profit over a large sample size bettors need to win more than 52.38% of their wagers at -110 odds.
Converting odds formats
Implied probability can always be calculated by dividing the initial risk by the total return. Formulas can be used to directly convert odds into percentages. Below are the formulas to calculate implied probability using popular odds formats.
American
Fractional
Fractional odds display potential profit relative to a one unit risk. This makes it one of the easier odds formats to convert to implied probability.