Changes

Implied probability can always be calculated by dividing the initial risk by the total return. Formulas Betting odds directly or indirectly indicate potential payout relative to stake and can therefore be used to directly convert odds into percentagesderive formulas for calculating implied probability. Below are the formulas used to calculate implied probability using convert popular [[odds format]]sinto percentages.

[[American odds]]represent betting prices through positive and negative numbers relative to a 100 unit base figure. Negative American odds require a risk of that amount in order to profit $100. Positive American odds yield a profit of that amount for an initial stake of $100. Converting positive and negative American odds to implied probability require separate formulas. {| class="wikitable" style="text-align: center; margin: auto;"|- style="background-color:#eaecf0;"|colspan="2"|'''Team'''|'''Spread'''|'''Total'''|'''Moneyline'''|-|[[File:Patriots.png|25px]]|New England Patriots| -3.5 (-110)| Over 44.5 (-110)| -180|-|[[File:Ravens.png|25px]]|Baltimore Ravens| +3.5 (-110)| Under 44.5 (-110)| +160|} In the NFL match above the New England Patriots are favored with -180 odds to win outright. Implied probability is calculated by dividing initial risk by total return. Since a bet on a market with -180 odds requires a risk of $180 in order to profit $100, it is converted into a percentage by diving the odds (180) by the odds augmented by 100 (180 + 100 = 280). The Baltimore Ravens are the underdog with +160 odds to win outright. An initial stake of $100 would yield $160 profit and a return of $260. Converting positive American odds into implied probability is done by dividing the odds (160) by the odds augmented by 100 (160 + 100 = 260). {| class="wikitable" style="text-align: center; margin: auto;"|- style="background-color:#eaecf0;"|colspan="2"|'''Bet'''|'''Odds'''|'''Calculation'''|'''Implied probability'''|-|[[File:Patriots.png|25px]]|Patriots ML| -180| 180 / (180 + 100) = 0.6429| 64.29%|-|[[File:Ravens.png|25px]]|Ravens ML| +160| 100 / (160 + 100) = 0.3846| 38.46%|}

Potential [[Fractional odds]] represent profit relative to initial risk. Odds are represented by a fraction. Betting the amount in the fraction's denominator will profit the amount in the numerator. Since implied probability is calculated by multiplying dividing initial risk by total return fractional odds can be converted into percentages by dividing the denominator by the sum of the numerator and denominator: {| class="wikitable" style="text-align: center; margin: auto;"|- style="background-color:#eaecf0;"|colspan="2"|'''Team'''|'''Spread'''|'''Total'''|'''Moneyline'''|-|[[fractional oddsFile:Lakers.png|25px]]|Los Angeles Lakers| -11.5 (10/11)| Over 217.5 (10/11)| 1/9|-|[[File:Grizzlies.png|20px]]|Memphis Grizzlies| +11.5 (10/11)| Under 217.5 (10/11)| 6/1|} Consider the moneyline market in the NBA game above. This makes it an easy format to convert to implied probabilityThe Los Angeles Lakers are favored and have 1/9 fractional odds of winning the match outright. Flip The Memphis Grizzlies are the numerator underdog and are priced at 6/1. Implied probability is calculated by dividing the denominator by the sum of the fractional odds to reveal the implied numerator and denominator. {| class="wikitable" style="text-align: center; margin: auto;"|- style="background-color:#eaecf0;"|colspan="2"|'''Bet'''|'''Odds'''|'''Calculation'''|'''Implied probability'''|-|[[File:Lakers.png|25px]]|Lakers ML| 1/9| 9 / (1 + 9) = 9/10 = 0.90| 90.00%|-|[[File:Grizzlies.png|20px]]|Grizzlies ML| 6/1| 1 / (6 + 1) = 1/7 = 0.1428| 14.28%|}

Total return relative to initial risk is indicated through [[Decimal 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. {| class="wikitable" style="text-align: center; margin: auto;"|- style="background-color:#eaecf0;"|colspan="2"|'''Team'''|'''[[Puck line]]'''|'''[[Total]]'''|'''[[Moneyline]]'''|-|[[File:Canadiens.png|25px]]|Montreal Canadiens| -1.5 (2.70)| Over 6.5 (1.91)| 1.66|-|[[File:MapleLeafs.png|20px]]|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. {| class="wikitable" style="text-align: center; margin: auto;"|- style="background-color:#eaecf0;"|colspan="2"|'''Bet'''|'''Odds'''|'''Calculation'''|'''Implied probability'''|-|[[File:Canadiens.png|25px]]|Montreal ML| 1.66| 1 / 1.66 = 0.6024| 60.24%|-|[[File:MapleLeafs.png|25px]]|Toronto ML| 2.30| 1 / 2.30 = 0.4348| 43.48%|}