Understanding Variance

Little is talked about variance when it comes to betting. There are lots of discussions on systems, staking and bankroll size but very few of these ever discuss variance. Variance affects all of these areas of betting and a good understanding will help you to decide whether the system/method is something you would like to bet live and what size stakes and bankroll you will need.

One of the dictionary definitions of variance is ‘A difference between what is expected and what actually occurs.’ As bettors the benefit is that by estimating variance we can determine whether we are going to be happy with the swings in our bankroll and what size stakes we should be using.

If you are a regular betting forum reader you may have heard people discuss the ‘binomial distribution’ more than once. This is the distribution that random events follow. Don’t be worried by the complicated sounding name. It can get very complex but luckily it doesn’t have to be explained that way.

A binomial distribution is a probability distribution that allows us to estimate how often the probability of an event will occur. For example if we have two horses that are exactly the same as each other and continually race under exactly the same circumstances then we would expect them to win 50% of the time. Each horse should win 50 out of 100 races, in reality the chance that each horse is going to win 50 races is just 7.96%.

Rather than a binomial distribution we can use a normal distribution for confidence intervals. These intervals tell us how confident we can be that we are correct. We may be 95% sure that that the horses will win between 40 and 60 of the races or 99% sure that they will win between 38.35 and 61.65 of the races. I shall look at the calculation for normal distribution in another article.

Calculating a binomial distribution can get a bit tricky. Luckily we have an easy method as Excel has a function built in called BINOMDIST which will calculate it for us. Enough talking let us take a look at how we can use it to help us profit in our betting. In fact it is not going to help us profit directly but indirectly, by helping us to manage our risk and calculate the appropriate bankroll size.

If I have selections that give me 1000 selections a year with a 15% strike rate how am I going to calculate my bank size? You could just say that we have 500 units and that covers everything. There is no problem with this except that you will not be growing your bank at the optimum rate. It could take you a long time to double your bank and stake where only 150 units may have been enough.

Using a binomial distribution we can help ourselves calculate what the risk is. We know that we are expecting 15% winners so over the next year we can expect 150 winners from our 1000 selections? Not necessarily!

The above graph shows the binomial distribution for our 15% strike rate over 1000 selections. You can find these in Excel by using the formula ‘=BINOMDIST(150,1000,0.15,false)’ The 150 is where we enter how many selections we expect to win, the 1000 are the amount of selections (trials) that we have, 0.15 is our win rate and we want false in the end so that the results are not cumulative.

What does all this show us that is so important? As you can see from the graph above our estimated 150 winning bets will only occur 3.50% of the time. In fact 3.27% of the time we are going to win less than 130 of our bets.

This can help us to estimate how much risk we are happy with. We may know that at the odds we achieve we need to have a minimum of 130 wins over our 1000 bets to break even. This means that every year there is a 3.50% that we will be in loss to some degree. If we are a cautious bettor who wants to be 99% confident that we our system will produce a profit over the year then we know that this method is not going to work for us. If we are happy only having a 95% confidence and a maximum of 5% risk that we won’t make a profit then we can go ahead and use this system.

As you can see there are many benefits to the use of this simple method of analysis. Later this week I shall take a look at calculating confidence intervals using normal distribution and deciding on your stake size.

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