In our previews for Fantasy Premier League or Fantasy Champions League gameweeks, we are often mentioning converting bookies odds to probabilities. Especially, when we talk about clean sheets. But how are those calculations done? How we can get the most accurate estimations of probabilities from bookmakers odds?
We reveal that in this article. We also programmed our own odds to probability calculator that is very simple and easy to use. Feel free to use it anytime when you want to convert bookies odds into probabilities.
It can help you with your decision-making process about your fantasy team. For example, it can help you compare and asses clean sheet odds or goal scorer odds. Or when you need to calculate more complex predictions that are based on probabilities.
Calculator can also help you with your betting strategies, especially with value betting, where you need to find out fair odds. But our main focus is to use it on fantasy football.
Guide for Odds to Probability Calculator
1. The Odds to Probability Calculator
If you are familiar with this article or with the problematic of converting bookies odds to probabilities, you can use our calculator right away. However, if you are reading this for the first time, please, read the case study and how to use calculator sections first in order to understand the math behind calculations and upsides and downsides of selected methods.
Three-way odds converter
- Insert three-way decimal odds into input fields.
- All three fields must be filled.
- You can use it, for example, for football match with three possible outputs (win, draw, lose).
2. Case study
In order to better understand the problematic of odds to probability conversion, we prepared a case study that explains problems in conversion and how to eliminate them.
If you have knowledge from the field of statistics, you have probably intuitively tried to convert bookies odds to probabilities.
And you have found out that margin distorts the results. But more about that latter. We start our case study with simple and very intiutive calculation of probabilities from bookmakers odds.
2.1 Intuitive calculation of probability
Let’s look at real life example. West Bromwich face Chelsea on Saturday. Let’s consider two complementary events A and B:
- Event A: West Brom will keep a clean sheet against Chelsea
- Event B: West Brom will not keep a clean sheet against Chelsea
These two events are complementary (more about complementary events on page 7 of Probability and Statistics). It means that one of those two events will happen. There will be or there will not be a clean sheet for West Brom in that match. There is no third event, no third possible output. So sum of probabilities of event A and event B is 100 %.
Denote P(A) as probability of event A, and P(B) as probability of event B. For complementary events:
- P(A) + P(B) = 100 %
Decimal bookies odds of West Brom keeping a clean sheet are 6.8 and odds that they won’t keep a clean sheet are 1.06.
- Bookies odds of event A: 6.8
- Bookies odds of event B: 1.06
So bookies really favor Chelsea to score in that match.
With very basic calculation, we can convert these numbers into implied probabilities. We just invert the odds and we get:
- P(A): 1 / 6.8 = 0.1471= 14.71 %
- P(B): 1 / 1.06 = 0.9433 = 94.33 %
We estimated probabilities. Based on this aproach, West Brom will keep a clean sheet with 14.71 % probability and concede with 94.33 % probability.
However, the problem is obvious. When we sum both probabilities, we do not get 100 % as we should, when both events are complementary. We get sum of 109.05 %.
- P(A) + P(B) = 109.05 % ≠ 100 %
This is a big downside of this aproach that causes inaccuracies in probabilities that are calculated this way. Why it happens?
2.2 Downsides of intuitive conversion odds to probabilities
A difference in the result is caused by the margin that bookmakers are using to make profit.
It means that bookies odds are lower than fair odds (real odds calculated from real probabilitites). That is why we get higher probabilitites than we should, when we only invert odds.
In our case the margin is:
- Margin: 109.05 % – 100 % = 9.05 %
If we want to get more accurate results, we need to get probabilities P(A) and P(B) that have sum of 100 %. In oder to do that, we need to get rid of the margin from our probabilities. And that is really a tricky part of this calculation. Let’s dive in.
2.3 More accurate probability and getting rid of margin
Now, we know that we have to get rid of the margin from our probabilities. Let’s begin with another intuitive approach.
This approach can give us better results, but not as accurate as we would like. However, it is good for very quick assessment of probability. We simply decrease calculated probabilities by the margin.
- P(A): 14.71 % / 109.05 % = 0.1349 = 13.49 %
- P(B): 94.33 % / 109.05 % = 0.8651 = 86.51 %
- P(A) + P(B) = 13.49 % + 86.51 % = 100 %
Now, we have West Brom keeping a clean sheet with the probability of 13.49 % and conceding with the probability of 86.51 %. And sum of both probabilities is 100 %.
Great, but not really. If you start to dig deeper into this method, you realize that this approach is good, when both odds are on similar level, like 1.8 and 1.8. On the other hand, it is very inaccurate when one odds are very low and the other very high (just as in our example).
So there is one more method (the last, I promise), that will finally give us satisfying resluts.
2.4 The final method of calculating true odds
Clearly, if we knew, how bookmakers create odds and how they calculate the margin, it would solve our situation. However, we don’t. Thankfully, there are some methods that can help us.
Our most favourite method is Margin Weights Proportional to the Odds.
Firstly, let’s denote variables Fair odds of event X as FO(X) and Bookies odds of event X as BO(X).
Basically, Fair odds FO(X) are odds after we get rid of margin from Bookies odds BO(X). So relationship here is:
- FO(X) ≈ BO(X) + margin
Using Margin Weights Proportional to the Odds method we can calculate Fair odds of event X with formula:
- FO(X) = (n * BO(X))/(n – margin * BO(X)),
where n is the number of possible outcomes. In our case, we have 2-way odds (West Brom will keep a clean sheet, West Brom will not keep a clean sheet), so n = 2.
For football match with three possible outcomes (win, draw, lose) n = 3.
Let’s continue to our main example. Using this method we can calculate fair odds and probability of event A: West Brom will keep 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: West Brom will keep a clean sheet are 9.8223. When we invert it, we get probability of this event. So there is only 10.18 % probability that West Brom will keep a clean sheet against Chelsea.
Similarly, we can 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 means that West Brom will concede against Chelsea with 89.82 % probability.
At the end, let’s check the sum of both probabilitites.
- P(A) + P(B) = 10.18 % + 89.82 % = 100 %
3. How to use the calculator [documentation]
Step 1: Put decimal odds into fields of the calculator
In the picture below, we put in odds from our case study of West Brom keeping a clean sheet (6.8) and West Brom not keeping a clean sheet (1.06). These events are complementary, so make sure you are putting in odds for complementary events. In case of 3-way possible output (like win, draw, lose) use Three-way calculator.
Step 2: Click Convert odds and see the results.
Calculator calculates the margin from bookies odds and then calculates fair odds (odds without the influence of margin). At the end, fair odds are converted into probabilities. In the picture below, the result is the same as the result of our case study.
Ing. Matej Šuľan
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