How To Convert Odds To Their Implied Probability

How exactly do you convert odds into their implied probabilities? And how do you convert implied probability into the range of popular odds formats? Use our odds conversion calculator or learn the formulas behind.
Knowing how to convert betting odds can be very helpful. In fact, if you don't know how to convert betting odds into their respective implied probabilities, you're not helping your chances of coming away as a long term winner in the competitive world of sports betting. Understanding the implied probability behind the odds on offer is key to assessing the potential value in a particular betting market. And it is just as important when assessing the value that exists with regards to specific odds on a particular outcome. If the implied probability is less than your own assessed probability of a particular outcome occurring, that outcome represents a value betting opportunity.
Converting Odds To Implied Probability
Typically, there are three kinds of odds you will come across in the sports betting landscape.
 Decimal odds: represented as 1.65 or 2.95 etc.
 Fractional odds: represented as 5/2 or 3 to 2 'on' etc.
 Moneyline odds: represented as 120 or +140 etc.
They all reflect the same thing, the return you will receive on a given amount of money placed on a bet. To convert your odds to implied probabilities or an implied probability to odds, you can either use our odds conversion calculator or do it by hand with the formulas provided below the calculator.
Odds Conversion Calculator
Converting Decimal Odds
Decimal odds are a simple reflection of the return you will receive for each single unit placed. For example, let's say bookmaker Matchbook is offering odds of 1.65 for Manchester United to win. This means that for every 1.00 you bet on that particular outcome, you will receive a profit of 0.65 should Manchester United win.
To convert these odds to their respective implied probabilities we make a simple calculation.
Converting decimal odds to implied probability formula:
Implied probability  =  1 / decimal odds 
Let's look at an example, in which Diego Costa to get a yellow card is odds 1.65.
Example: How to convert decimal odds to its implied probability
1 / 1.65  =  0.606  =  60.6% 
Multiplied then by 100 to express as an implied probability percentage of 60.6%.
Converting Fractional odds
Fractional odds are generally the most traditional form of expressing betting odds. They are a simple reflection of the return you will receive for a particular amount bet.
So for example, let's say bookmaker Ladbrokes is offering odds of 5/2 for a particular hose to win an upcoming race. The odds of 5/2 (expressed as "5 to 2") means that for every 2 units that you bet, you will receive 5 back as profit. So if you bet €200 on that horse, you would have received €500 profit in return plus your original stake of €200.
Converting fractional odds into implied probability formula:
Implied probability  =  denominator / denominator + numerator 
Let's look at an example, in which Diego Costa to get a yellow card is odds 5/2.
Example: How to convert fractional odds to its implied probability
5 / 2  =  2 / (5 + 2)  =  2 / 7  =  0.286  =  28.6% 
Multiplied then by 100 to express as a implied probability percentage of 28.6%
Converting Moneyline Odds
Moneyline odds, also known as 'American odds' are probably the most foreign odds format to those of us outside of North America. And at first they appear a little confusing. But it is helpful to understand what these odds represent especially when listening to Americans speaking about gambling odds in sports broadcasts or podcasts. So, let's see how we can convert Moneyline odds into their respective implied probabilities.
There are two instances of Moneyline odds: 'minus' moneylines and 'plus' moneylines.
The first are 'minus' moneylines. This is expressed as for example, 120. But what does this mean exactly? Well, let's say bookmaker bet365 are offering odds of 120 for the Los Angeles Lakers to win a game. This is essentially saying that to win $100 you have to bet $120. In other words, if you place $120 on that outcome, you will receive a profit of $100.
The other instance are 'plus' moneylines. This is expressed as for example +180. In this case, let's say bookmaker Winner Sports have offered odds of +180 for the New York Yankees to win a game. This simply means that if you bet $100, you will win $180.
So how do we convert the the 'minus' and the 'plus' moneyline odds into their implied probabilities? Let's start out with the 'minus' moneyline conversion:
Converting 'minus' moneyline odds into implied probability formula:
Implied probability  =  (  ( 'minus' moneyline odds ) ) / (  ( 'minus' moneyline odds ) ) + 100 
So let's take an example, in which Titanbet offers the following bet: San Diego Chargers to win against New England Patriots at odds 120.
Example: How to convert 'minus' moneyline odds to its implied probability
( (120) / ( ( (120) ) + 100)  =  120 / 220  =  0.545  =  54.5% 
Multiplied then by 100, we get the implied probability percentage of 54.5%.
Converting a 'plus' moneyline is a bit different. Calculating the implied probabilities on these look like this:
Converting 'plus' moneyline odds into implied probability formula:
Implied probability  =  100 / ( 'plus' moneyline odds + 100 ) 
So let's take an example, in which Paddy Power offers odds +180 for Los Angeles Lakers to beat Miami Heat.
Example: How to convert 'plus' moneyline odds to its implied probability
( 100 / 180 + 100 )  =  100 / 280  =  0.357  =  35.7% 
Multiplied then by 100, we get the implied probability percentage of 35.7%.
How Do We Convert Implied Probability Into Odds?
Knowing how to convert one form of odds to another can be helpful, especially if you have come into possession of a large amount of betting data that has odds formatted in an unfamiliar way.
To do this, we first need to convert any odds format to their implied probability. Once we have done this, the calculations are fairly straight forward.
Converting Implied Probability Into Decimal Odds
Converting implied probability into decimal odds formula:
Decimal odds  =  100 / implied probability 
Let's take an example. In this example we think that Arsenal has a 75 % probability of defeating Stoke. To calcluate our decimal odds target, we want to covert 75 % into odds:
Example: How to calculate implied probability to decimal odds:
100 / 75  =  1.33 
Implied probability of 75% would return decimal odds of 1.33.
Converting Implied Probability Into Fractional Odds
Convert implied probability into fractional odds formula:
Fractional odds  =  ( 100 / implied probability ) 1 
Let's look at an example, where we think Wayne Rooney has 25% probability of scoring a goal. In this example, the fractional odds target will be calculated as:
Example: How to convert implied probability to fractional odds:
(100 / 25)  1  =  4  1  =  3 
The outcome of this formula is 3, meaning we will express the odds as fractional odds = 3 to 1.
Converting Implied Probability Into Moneyline Odds
Converting implied probability into moneyline is a bit more complicated than converting it into decimal or fractional odds. The calculation depends on whether the implied probability is above 50% or below.
When the implied probability is above 50%, we make the following calculation.
Convert implied probability (50% and above) into moneyline odds formula:
Moneyline Odds  =   ( implied probability / 100  implied probability ) x 100 
Let's look at an example, where we think Lionel Messi has a 75 % chance of scoring against Levante. In this example, the moneyline odds target will be calculated as:
Example: How to convert implied probability (50% and higher) to moneyline odds:
 (75 / (100 – 75)) x100  =   (75 / 25) x 100  =   3 x 100  =   300 
Moneyline odds =  300.
When the implied probability is below 50%, the calculation is adjusted a little.
Convert implied probability (below 50%) into moneyline odds formula:
Moneyline odds  =  (100  implied probability / implied probability ) x 100 
Let's look at an example, where we think Niclas Bendtner has a 25 % chance of scoring against VfB Stuttgart. In this example, the moneyline odds target will be calculated as:
Example: How to convert implied probability (below 50%) to moneyline odds:
((100  probability)/(probability) x 100)  =  ((75) / (25) x 100)  =  3 x 100  =  300 
Moneyline odds = + 300.
Odds Conversion Table
Bookmaker Odds Settings
Most online bookmakers now offer alternative display options for their odds. Below you can see the odds options available at bet365. Simply check your preferred odds format and all odds in all markets offered by bet365 will appear in that format.
Concluding Thoughts
While there are many tools on the web that will help you convert odds to their implied probabilities and convert odds to other formats, it is still a good practise to understand the calculations behind these conversions. This will only help you better understand what the odds represent in terms of value as well as exercising your betting brain to think instinctively in terms of implied probabilities when odds are presented to you.
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Tags: Betting Theory