9th January 2017
Hi ,
Today I want to look at what standard deviation is. This is something you see often in articles to do with betting and it's important to know what it means.
The definition of standard deviation (SD) is:
"In probability theory and statistics, standard deviation is a measure of the variability or dispersion of a population, a data set, or a probability distribution."
Please don’t run off in fear, it isn’t really all that complicated it just sounds it and I'm hoping that this article will make those of you with a dislike of math understand the value that using it can have in your betting.
What SD tells us in horse racing (or investments in general) is the volatility of an investment in the past. I'm going to show you how to calculate it and use it in just a moment.
This helps us to predict the likely volatility in the future. Knowing how volatile your selections, profit or a multitude of ratings is likely to be is important when deciding bankrolls, staking and many other factors.
You may have heard the term ‘normal distribution’ in some forums when people are discussing betting. A normal distribution (also known as a bell curve) very simply says that most of the results are around the average for the data while only a few are at the extremes.
Let us take an example of a group of horses racing on six furlong standard surfaces in the last 6 years.
We look at all of these horses who have speed ratings and take the average, which is 41.
If most of the horses speed ratings in our sample are around the average of 41 with just a few higher or lower, then would be called a normal distribution.
To calculate the standard deviation we perform a very simple sum:
We already have the average for our sample of speed ratings which is 41.
We then want to subtract this number from each speed rating to determine how much each rating differs from this average.
Next we square the result of each number from the previous step.
We add all these squared numbers (from the previous step) together which gives us 5873969.
We divide 5873969 by the number of ratings, 15273 ratings, minus 1. This gives 384.62
The SD is simply the square root of this number or 19.61
This is quite a high deviation and shows that the horses speed ratings in these races could be plus or minus 19.61. In other words, they are quite unpredictable or volatile.
So how can this help us?
Imagine if we had decided to just look at all of the winners of the six furlong races on standard surfaces. We would now begin to have an idea how volatile the speed is for the winners in this type of race. Maybe they are very volatile and we choose to skip these races but in seven furlongs they are much more stable!
There are also confidence intervals that we can use to help our analysis. For our purposes a confidence interval tells us how likely a horse is to have a rating between certain values in our data. If we had looked at the winners of the races, then as well as being able to tell how volatile the winners speed ratings are we would be able to say that with 90% confidence the winners will be within a specific range of speed ratings, with 95% confidence in a slightly bigger range and with 99% confidence in a slightly bigger range again. You can of course use any level of confidence but these are the most common.
This knowledge can help us to narrow down a field and make our selections.
How do we calculate these confidence levels?
Well, we use the SD that we've already worked out!
If you are looking for a 95% confidence level then you would be looking at +-1.97 SD from the average, a 99% confidence level is +-2.33 SD from the average. It is as simple as that.
Using our example above, if a horse had a rating of 100 and we wanted to know what range of rating we would expect it to achieve with a 95% confidence we know that we need to use +-1.97 standard deviations. Our standard deviation was 20, rounded up, so we multiple this by 1.97 to give 39. That means our horses rating could be expected to be anywhere between 61 and 139 but it's most likely to be in 100.
Now, if you do this for all the runners in the race you get a very different picture of how far ahead/behind horses actually are!
Best Wishes,
Michael Wilding
