Coming to grips with the betting odds?

The big game is about to begin, you have done your research and backed the home team at 7/4; you grab a beer and take it easy waiting for the beginning. While you wait, do you ever question exactly what those betting odds mean?

If not, maybe you should, it can throw a lot of interesting light on what your chances of winning the bet actually are. In the case above they're saying that should this same match be played eleven times then the home team will win four times and not win seven times. A different way of looking at it is thru probability, which tells us that the home team has a 36% probability of winning and a 64% chance of not winning.

Betting odds and probability are often confused by novice and inexperienced punters, and most appear to believe they're the same thing. They're not, they are tight related, but they're different.

Probability is a real number between 0 and 1, where 0 represents 0%, that is, there's no chance of the event happening, and 1 represents 100%, that is, the event will happen, nothing can stop it. Betting 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 boring 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 2 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 since the die has six sides and 100 divided by six equals 16.66. Put differently we have a 1 in 6 chance of rolling the number we want. Expressed as odds this is 5/1.

So how do we calculate the probability when we only have the odds?

Well it depends in what format your odds are written. The two most widely applied means of expressing odds are fractional and decimal. Fractional odds have been around in the United Kingdom since betting started, while decimal is the method used by most European countries, though it's acquiring in popularity in the UK since the introduction of betting exchanges and most internet bookies now offer the choice. Given the choice, decimal is now my favored option, it's 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%
A couple more examples:

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 couple of 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 as well gives us the ability to see exactly how much of a profit the bookmaker is really making. To do this we need to convert all the odds on an event into percentages and then add them together. Any sum over 100% is the profit that the bookmaker is making on that event.

Taking match betting odds on a football match as an example, there are 3 potential 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 final result of an event can only be 100%, but we can see here that by adding up the probabilities (in brackets) we in reality arrive at a total of 111.35% this extra 11.35% is called the overround, it's the profit that the bookie is anticipating to make on this result and is generated by offering worse odds on the event than the factual true odds.