Understanding The Maths Behind Value

The third part in our sports betting value series looks at the mathematics. You can read the first part here and the second part here if you have not yet had the opportunity to.

I warn you, there will be some maths today, but I will do my best to make it as simple and easy to understand as possible. If you have any questions on it then you can leave me a comment at the bottom.

There are lots of complex mathematical explanations of value around, and that, as you know is not what I want to do. There is no point in baffling you with mathematical expertise, what is important is that you understand how the maths work so that you can see that the only way to make a profit from horse racing, or indeed any form of sports betting, is by finding value. Whether you do this through planned value or default value is not important.

I am going to explain the maths using two examples. We already know that the general betting public create an accurate probability of a horses chance of winning. However if we bet on the most likely horse to win the race we are going to lose money! Let’s look at why this happens.

In order to show you this example I have taken a sample of data from my database. These are the favourites that have raced in the first few days of May 2012. I have removed all those horses who were non-runners or didn’t finish the race.

[membership_downloads_box title=”Your Downloads”]You may need to right-click the following links and select Save Link As to download the file to your computer[membership_download_item_txt link=”” + target=”_self”]Favourites Data[/membership_download_item_txt][/membership_downloads_box]

There are 174 favourites in this sample, and the first thing to note is that you would have made a loss of -20.63 units if you had bet all of them. This is not unexpected of course.

Remember when looking at this file that the odds are the same as probabilities. Odds not only tell us what we will be paid out but they also tell us what chance of winning the general betting public think we will get. Read that a few times before moving on.

The reason that we are losing when we bet on favourites is because there is no edge, if we are winning the same or less than the general betting public think we should be then we will not be making a profit.

If you look at the Average Probability that the general betting public give for these runners you will notice it is 0.35 or 35%. Just below that figure is our strike rate, which is 0.32 or 32%.

The general betting public are giving us odds based on the horses winning an average of 35% of the time, however, we are only winning 32% of the time. This is the reason that we are losing our money if we bet on the favourites.

In order to make a profit we need to be winning more often than the average probability we are being given by the publics odds. In this sample we would need to be winning 35% of the time to theoretically break even and anything above would result in a profit. I say theoretical because if you are betting on exchanges you have commission to take into account which makes the calculations slightly more complicated.

When we are winning more than the average probability of the odds we have been given, then we are finding value bets and making a profit. Without this value we cannot possibly make a profit.

Now, this sample is a small sample but it is a good example and you will see it proven in much larger samples as well.

One of the questions that has come up the most is…

‘Why do you care about averages, it is only important whether a horse wins or loses because each race is independent?’

Each race is independent, but as bettors we cannot look at independent races. It is impossible to accurately say the chances of a horse winning a race as there is no way of proving that our assessment was accurate.

The only way that we can prove that the general betting public’s odds are accurate is by taking them over a period of time and analysing them to find out that in fact the horse that they think will win most often does. We have no way of saying that this is the case in an individual race.

For this reason we must also monitor our betting over a period of time and selections. All we need to make a profit is to be right more often than the general betting public. This is the reason for using averages. If on average we are better than the general betting public then we will make a profit.

If you have any questions then don’t hesitate to put them in the comments below and I shall get back to you.

Michael Wilding

Michael started the Race Advisor in 2009 to help bettors become long-term profitable. After writing hundreds of articles I started to build software that contained my personal ratings. The Race Advisor has more factors for UK horse racing than any other site, and we pride ourselves on creating tools and strategies that are unique, and allow you to make a long-term profit without the need for tipsters. You can also check out my personal blog or my personal Instagram account.


  1. The stumbling-block for me is: “How, how, how can I be right more often than the general betting public?”

    1. That is an excellent question and one that requires a more detailed answer than I can give in this space. I shall write a detailed article answering it but it revolves around measuring using averages being a necessity and the runners in the publics averages may not be the same that are in yours.

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