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. Betting odds directly or indirectly indicate potential payout relative to stake and can therefore be used to derive formulas for calculating implied probability. Below are formulas used to convert popular odds formats into percentages.

American

American odds

Fractional

Total return can be directly calculated by multiplying initial risk by fractional odds. This makes it an easy format to convert into implied probability. Percentage is calculated by dividing 1 by the fractional odds (taking the reciprocal of the fraction).

Team		Spread	Total	Moneyline
	Los Angeles Lakers	-11.5 (10/11)	Over 217.5 (10/11)	1/9
	Memphis Grizzlies	+11.5 (10/11)	Under 217.5 (10/11)	6/1

Decimal

Total return relative to initial risk is indicated through decimal odds. Because implied probability is calculated by dividing the stake by the total return this makes it an easy odds format to convert into percentage. Divide 1 by the decimal odds to convert it to implied probability.

Team		Puck line	Total	Moneyline
	Montreal Canadiens	-1.5 (2.70)	Over 6.5 (1.91)	1.66
	Toronto Maple Leafs	+1.5 (1.50)	Under 6.5 (1.91)	2.30

Consider the moneyline market in the example above. Montreal is favored and has 1.66 odds to win the match. As the underdog Toronto has 2.30 odds. Dividing 1 by these decimal odds will convert them to implied probability.

Bet		Odds	Calculation	Implied probability
	Montreal ML	1.66	1 / 1.66 = 0.6024	60.24%
	Toronto ML	2.30	1 / 2.30 = 0.4348	43.48%