How to convert odds to their implied probability

Jun 26th, 2011 - Posted by Andrew_Brocker in Betting Theory

bettingexpert blog editor. Always taking the alternative route to finding the value.

How exactly do you convert odds into their implied probabilites? And how do you convert implied probability into the range of popular odds formats? Andrew walks us through the process.

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 the 3 types of odds to their implied probabilities.

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.

Decimal odds

Decimal odds are a simple reflection of the return you will receive for each single unit placed. In other words, odds of 1.65 means that for every 1.00 you place on a particular outcome, you will receive a profit of 0.65 should that outcome prevail.

To convert these odds to their respective implied probabilities we make a simple calculation.

So for example, our odds of 1.65.

Implied probability = 1 / 1.65

Implied probability = 0.606

Multiplied then by 100 to express as an implied probability percentage of 60.6%.

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, the odds of 5/2 (expressed as 5 to 2) means that for every 2 units that you bet, you will receive 5 back.

To convert fractional odds into their respective probabilities, we make the following calculation.

So in our example of odds of 5/2.

Implied probability = 2 / (5 + 2)

Implied probability = 2 / 7

Implied probability = 0.286

Multiplied then by 100 to express as a implied probability percentage of 28.6%

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 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.

The first are 'minus' moneylines. This is expressed as for example -120. But what does this mean exactly? Well, it is essentially saying that to win 100 you have to make a bet of 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. This means that if you bet 100, you will win 180.

So how do we convert the 'plus' and the 'minus' moneyline odds into their implied probabilities?

For 'minus' moneyline odds, it's the following calculation.

So let's take our example of a moneyline odds offer of -120.

Implied probability = (- (-120) / ((- (-120)) + 100)

Implied probability = 120 / (120 + 100)

Implied probability = 120 / 220

Implied probability = 0.545

Multiplied then by 100, we get the implied probability percentage of 54.5%.

Now the calculation for 'plus' moneyline odds, we make the following calculation:

So let's use our example of moneyline odds offer of +180

Implied probability = 100 / (180 + 100)

Implied probability = 100 / 280

Implied probability = 0.357

Multiplied then by 100, we get the implied probability percentage of 35.7%.

How do we convert one odds format to another?

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.

e.g. Implied probability of 75% would return decimal odds of 1.33.

Decimal odds = 100 / 75

Decimal odds = 1.33

Converting implied probability into fractional odds

So an example of 25% implied probability would be calculated as:

Fractional odds = (100 / 25) – 1

Fractional odds = 4 – 1

Fractional odds = 3, expressed as 3 to 1.

Converting implied probability into moneyline odds

This depends on whether the implied probability is above 50% or below.

If it is above, we make the following calculation.

So for example, the implied probability of 75%.

Moneyline odds = - (probability)/(100 – probability) * 100

Moneyline odds = - (75 / (100 – 75)) * 100

Moneyline odds = - (75 / 25) * 100

Moneyline odds = - 3 * 100

Moneyline odds = - 300.

If the implied probability is below 50%, the calculation is adjusted a little.

So for example, the implied probability of 25%.

Moneyline odds = ((100 - probability)/(probability) * 100)

Moneyline odds = ((75) / (25) * 100)

Moneyline odds = 3 * 100

Moneyline odds = + 300

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.