Do you want to know how to calculate probability from odds? Do not worry; this post will help you assess the potential value of a particular market.

Probability and odds are two basic statistical terms to explain the likeliness that an occasion will occur.

Probability is the fraction of the needed results within the context of each possible outcome with a price between 0 and 1, where 0 would be an impossible event, and one would represent an inevitable event. Probabilities are usually given as percentages. [i.e., 50% probability that a coin will land on HEADS.] Odds can have many numbers and can start from zero to infinity, and that they represent a ratio of desired outcomes versus the sphere.

Odds are a ratio and might lean in two ways: odds in favor and against the odds. Odds in favor are odds describing if an occasion will occur, while odds against will tell if an incident will not happen. If you are conversant in gambling, odds against are what Vegas gives as odds. More on it later. For the coin flip, odds in favor of a HEADS outcome is 1:1, not 50%.

Below may be a procedure on the way to calculate probability from odds.

Intuitive calculation of probability

Let us examine the world example. Team A faces Team B on Saturday. Let us consider two complementary events, A and B:

Event A: Team A will keep a clean sheet against Team B.

Event B: Team A will not keep a clean sheet against Team B.

These two events are complimentary. It means at least one of two events will occur. You will or will not be, perfect sheet for Team A in this matchup, and there will be no possible win or the event. And so, the sum of probabilities of occurrence A and event B is 100%.

Denote P(A) as the probability of event A and P(B) as the probability of event B. For complimentary events:

P(A) + P(B) = 100%

Decimal bookies odds of Team A keeping a clean sheet are 6.8, and odds that they will not support a clean sheet are 1.06.

Bookies odds of event A: 6.8

Bookies odds of event B: 1.06.

So bookies favor Team B to get there in a match.

With fundamental calculation, we can convert these numbers into implied probabilities. We invert the percentages. We estimated expectations. Supported this approach, Team A will keep a clean sheet with 14.71 most likely and concede with 94.33 in all likelihood.

However, the matter is apparent. After we sum both probabilities, we do not get 100% when both events are complimentary, and we get a sum of 109.05 %.

P(A) + P(B) = 109.05 % ≠ 100%

This is an enormous downside of this approach that causes inaccuracies in probabilities that are calculated in this manner. Why does it happen?

Downsides of intuitive Conversion Odds to Probabilities

A difference within the results is caused by the margin that bookmakers are using to form profit.

It means bookies are below fair odds (actual odds calculated from accurate probabilities). That is why we get higher chances than we must always, once we only invert odds.

In our case, the margin is:

Margin: 109.05 % – one hundred pc = 9.05 %

If we wish to urge more accurate results, we want to induce probabilities P(A) and P(B) that have 100%. To try and do that, I would like to urge you to prevent the margin from our probabilities.

Now, we’ve Team A keeping a clean sheet with the probability of a 13.49 attempt to concede with 86.51 %. And some of both possibilities are 100%.

Additional Method of Calculating Probability

The method is Margin Weights Proportional to the chances.

Let us denote variables Fair odds of event X as FO(X) and Bookies odds of event X as BO(X).

Fair odds FO(X) are odds after eliminating margin from Bookies odds BO(X). So relationship here is:

FO(X) ≈ BO(X) + margin

Using Margin Weights Proportional to the percentages method, we can calculate Fair odds of event X with the formula:

FO(X) = (n * BO(X))/(n – margin * BO(X)),

where is the number of possible outcomes. In our case, we have 2-way odds (Team A will keep a clean sheet, Team A won’t keep a clean sheet), so n = 2.

For a football match with three possible outcomes (win, draw, lose) n = 3.

Let us continue with our leading example. Using this method, we will calculate fair odds and probability of event A: Team A will keep a clean sheet as:

FO(A): (2 * 6.8)/(2 – 0.0905 * 6.8) = 9.8223

P(A): 1 / 9.8223 = 0.1018 = 10.18 %

Fair odds of event A: Team A will keep a clean sheet are 9.8223. After we invert it, we get the probability of this event. So there is only 10.18 in all likelihood that Team A will keep a clean sheet against Team B.

Similarly, we will calculate fair odds and probability of event B:

FO(B): (2 * 1.06)/(2 – 0.0905 * 1.06) = 1.1134

P(B): 1/1.1134 = 0.8982 = 89.82 %.

It implies that Team A will concede against Team B with 89.82, most likely.

Let us check the sum of both probabilities.

P(A) + P(B) = 10.18 % + 89.82 % = 100%

Conclusions

There is a lot of math on how to calculate probability from odds, and I hope this post will help solve your problem. Your only assignment is to read and follow those steps carefully.