Implied probability - Revision history

Vincent: /* Converting odds formats */

2020-01-15T20:32:57Z

Converting odds formats

Vincent: /* Fractional */

2020-01-15T20:06:37Z

Fractional

Vincent: /* Decimal */

2020-01-15T17:44:12Z

Decimal

Vincent: /* Converting odds formats */

2020-01-15T17:38:17Z

Converting odds formats

Vincent: /* Fractional */

2020-01-15T04:24:13Z

Fractional

Vincent: Created page with "In sports betting '''implied probability''' is the conversion of betting odds into percentages. This calculation takes into account the bookmaker's vigorish, and reveals h..."

2020-01-15T04:21:50Z

Created page with "In sports betting '''implied probability''' is the conversion of betting odds into percentages. This calculation takes into account the bookmaker's vigorish, and reveals h..."

New page

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).

{| class="wikitable" style="text-align: center; margin: auto;"
|- style="background-color:#eaecf0;"
|colspan="2"|'''Team'''
|'''Spread'''
|'''Total'''
|'''Moneyline'''
|-
|[[File:Packers.png|25px]]
|Green Bay Packers
| -3.5 (-110)
| Over 48.5 (-110)
| -180
|-
|[[File:Seahawks.png|25px]]
|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):

{| class="wikitable" style="text-align: center; margin: auto;"
|- style="background-color:#eaecf0;"
|colspan="2"|'''Bet'''
|'''Odds'''
|'''Initial risk'''
|'''Total return'''
|'''Implied probability'''
|-
|[[File:Packers.png|25px]]
|Green Bay -3.5
| -110
| $110
| $210
| $100 / $210 = 0.5238 or 52.38%
|-
|[[File:Seahawks.png|25px]]
|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 format]]s.

=== American ===

[[American odds]]

=== 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.

=== Decimal ===

[[Decimal odds]]

@@ Line 58: / Line 58: @@
 === American ===
-[[American odds]]
+[[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.
 === Fractional ===
-Total profit relative to initial risk is represented through [[fractional odds]]. Odds are represented by a fraction; an initial risk of the amount in the denominator will yield the amount in the numerator. Since implied probability is calculated by dividing stake by total return fractional odds can be converted into percentages by dividing the numerator by the sum of the numerator and denominator.
+[[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 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;"
@@ Line 82: / Line 124: @@
 | Under 217.5 (10/11)
 | 6/1
 |}

@@ Line 62: / Line 62: @@
 === 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).
+Total profit relative to initial risk is represented through [[fractional odds]]. Odds are represented by a fraction; an initial risk of the amount in the denominator will yield the amount in the numerator. Since implied probability is calculated by dividing stake by total return fractional odds can be converted into percentages by dividing the numerator by the sum of the numerator and denominator.
 {| class="wikitable" style="text-align: center; margin: auto;"

← Older revision		Revision as of 17:44, 15 January 2020
Line 108:		Line 108:
	\|}		\|}

−	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:	+	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%
		+	\|}

@@ Line 54: / Line 54: @@
 == 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 format]]s.
+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 format]]s into percentages.
 === American ===
@@ Line 62: / Line 62: @@
 === Fractional ===
-Potential profit is calculated by multiplying initial risk by the [[fractional odds]]. This makes it an easy format to convert to implied probability. Flip the numerator and denominator of the fractional odds to reveal the implied probability.
+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).
 === Decimal ===
-[[Decimal odds]]
+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.