Getting to grips with the odds?
The big game is about to start, you've done your research and backed the home team at 7/4; you grab a beer and sit back waiting for the kick-off. As you wait, do you ever wonder exactly what those odds mean?
If not, perhaps you should, it can throw some interesting light on what your chances of winning the bet really are. In the case above they are saying that should this same match be played 11 times then the home team will win 4 times and not win 7 times. Another way of looking at it is via probability, which tells us that the home team has a 36% chance of winning and a 64% chance of not winning.
Odds and probability are often confused by novice and inexperienced punters, and most seem to think they are the same thing. They are not, they are closely related, but they are different.
Probability is a real number between 0 and 1, where 0 represents 0%, that is, there is no chance of the event happening, and 1 represents 100%, that is, the event will happen, nothing can stop it. Odds, on the other hand are used to express the ratio of the probability of the event happening against the probability of it not happening. It sounds a bit tedious put like that, but let's look at a simple example to make it clearer.
Assuming an honest coin, when flipping that coin the probability of it coming up heads or tails is exactly 50% as these are the only two outcomes possible. It means we have a 1 in 2 chance of getting the result we want. Expressing this in Odds we would get 1/1 or even money.
To roll a six on a six-sided die, assuming the die is honest, gives us a probability of 16.66%. This is because the die has six sides and 100 divided by six equals 16.66. In other words we have a 1 in 6 chance of rolling the number we want. Expressed as odds this is 5/1.
So how do we work out the probability when we only have the odds?
Well it depends in what format your odds are written. The two most widely used means of expressing odds are fractional and decimal. Fractional odds have been around in the UK since betting began, while decimal is the method used by most European countries, though it is gaining in popularity in the UK since the introduction of betting exchanges and most on-line bookies now offer the choice. Given the choice, decimal is now my preferred option, it is so much easier to work with.
When converting fractional odds to probability we need to divide the right hand side of the fraction by the sum of the left and right hand sides and multiply the answer by 100. When written like that it looks complicated, but it really isn't. Let's do an example:
Odds of 7/4 converted to probability.
7/4 becomes 4/(7+4) which is 4/11 = .3636
Multiply by 100 and the answer is 36.36 so our probability is 36.36%
5/4 = 4/(5+4) = 4/9 = .4444 = 44.44%
4/1 = 1/(1+4) = 1/5 = .20 = 20%
When converting decimal odds to probability things get really simple, all we have to do is divide 100 by the decimal odds.
So faced with decimal odds of 5.0 we simply divide 100 by 5 as follows:
100/5 = 20 so the probability is 20%
A few more examples of decimals to probability:
1.25 = 100/1.25 = 80%
1.90 = 100/1.90 = 52.63%
Not only is it easier to see what chance the bet has as a percentage, but it also gives us the ability to see just how much of a profit the bookmaker is actually making. To do this we need to convert all the odds on an event into percentages and then add them together. Any amount over 100% is the profit that the bookmaker is making on that event.
Taking match odds on a football match as an example, there are three possible results home win, away win or draw. Assuming the game is priced as follows:
Home win = 1.75 (57.14%)
Away win = 3.9 (25.64%)
Draw = 3.5 (28.57%)
Logically the result of an event can only be 100%, but we can see here that by adding up the probabilities (in brackets) we actually arrive at a total of 111.35% this extra 11.35% is called the overround, it is the profit that the bookmaker is expecting to make on this event and is generated by offering worse odds on the event than the actual true odds.
For those who like their life a little easier I have included a table which shows fractional odds, decimal equivalents and probabilities. Click Here to get the Odds Probability Chart
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