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Odds into Implied Probabilities

It’s advisable for anyone interested in betting to learn and master the method of converting odds into their implied probabilities. We’ll look into the conversion of 3 most talked about odds formats throughout the world – the American format, fractional format and the decimal format, into their respective implied probabilities.

Introduction to conversion of odds
You must keep in mind certain basic steps when converting odds into their implied probabilities. Let’s start by giving you an example, if you have decimal odds of 2 .5, which have an implied probability of 40%, they can be converted back into fractional odds of 3 / 2 .

As mentioned earlier, you’ll come across 3 different types of odds formats in the sports betting world:
Fractional odds – These are represented in the form of 3 / 2 or 3 to 2 etc.
Decimal odds – These are represented in the form of 1.5, 2 .8 etc.
Money line odds – These are represented in the form of + 110, - 130 etc.

All different odds tell the same thing, which is the returns you’ll receive by wagering money on a certain possible event. Let’s now look into the method of converting these odds into their respective implied probabilities.

Conversion of decimal odds
These odds are simply a reflection of the returns you’ll get for every single unit of bet placed on a particular outcome. For instance, let’s say that Bet365 is offering you odds of 1.4 for Liverpool to win a soccer game. It implies that for every £ 1 that you bet on that particular possibility, you’ll get a profit of £ 0.4 if Liverpool indeed comes out as a winner.
To convert these odds of 1.4 into their implied probability, you need to make the following simple calculation:
Implied probability = 1 / decimal odds

So, in the above mentioned example,
Implied probability = 1 / 1.4 = 0.714 = 71.4%
Please note, the arrived at implied probability figure needs to be multiplied by 100 to give it an expression in the percentage format.

Conversion of fractional odds
These type of odds are considered the most conventional way of expressing the betting odds. They’re simply a reflection of the exact return you’ll get for a particular bet amount. So, for instance, let’s say that Bet365 is providing odds of 4 / 2 for the possibility of a certain horse winning an upcoming race. Also referred to as ‘4 to 2 ,’ these odds imply that for every £ 2 that you bet on that particular horse, you’ll get back £ 4 as profit. So, if you were to bet £ 200 on a horse, you’d be taking back a profit of £ 400 if that horse indeed wins the race. Please note, that £ 400 would be over and above your original stake of one hundred pounds. So, in total you’d be getting £ 600!

Following is the formula used for conversion of fractional odds into their implied probability:
Implied probability = denominator / (denominator + numerator)

So, if the odds of Manchester United winning a particular soccer game are 7 / 2, the implied probability of these odds would be calculated as follows:
Implied probability = 2 / (2 + 7) = 2 / 9 = 0. 2222 = 22 . 22%

As also shown above, multiplying the arrived at implied probability by 100, gives it an expression in the percentage format (22 . 22%).

Conversion of money line odds
Also commonly referred to as the American odds, money line odds are the most commonly used ones in the northern American betting places. They might seem quite confusing initially, but are pretty easy to understand once you learn the basics. Let’s now look at the conversion of money line odds into their respective implied probabilities.

Money line odds can be either plus money lines or minus money lines.

For instance, minus money lines may be expressed like – 130. What this means is that if Bet365 were offering -130 odds on LA Lakers to win a particular game, it would mean that you’d need to bet £ 130 to win £ 100.

In case of plus money line bets, let’s say that Bet365 is offering money line odds of +160 for New York Yankees to win a particular game. It means that you’d need to bet £ 100 to win £ 160 if you’re confident about that probability.

Conversion of minus money line odds into their implied probabilities:
Implied probability = ( - (minus money line odds)) / (( - (minus money line odds)) + 100)

So, for the above example, the implied probability of LA Lakers to win the game would be:
( - (-130)) / (( - (-130)) + 100) = 130 / 230 = 0.565 = 56.5%

Conversion of plus money line odds into their implied probabilities:
Implied probability = 100 / (plus money line odds + 100)

So, for the above example of New York Yankees game, we’d calculate the implied probability in the following way:
(100 / (+160 +100)) = 100 / 260 = 0.384 = 38.4%