Why do we want to know what standard deviation is? 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 am hoping that this post 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. 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 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 6 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 this is 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 are quite unpredictable or volatile. So how can this help us? Using this example it can’t really but I just wanted to show you the calculation.
Imagine though if we had decided to just look at all of the winners of the 6 furlong races on standard surfaces. We would now begin to have an idea how volatile the speed is of the winners in this type of race. Maybe they are very volatile and we choose to skip these races but in 7 furlongs they are much more stable!
There are also confidence intervals that we could look at 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 in this range of speed ratings, with 95% confidence in this range and with 99% confidence in a different range. You can of course use any level of confidence but these are the most common.
It would be very useful to be able to know this information, whether it helps us narrow down the field or make our selections. How do we calculate these confidence levels? We use the SD that we have 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. You now have plenty to look at with the ratings that you use and your past results, have a look to see how volatile they are in different races.
Keep an eye out this week for the latest part in our Race Advisor system build and my first look at the Cheltenham Festival.
Tags: Advisor, analysis, bankroll, bell curve, bet, betting, calculate, course, data, dispersion, extremes, furlong, group of horses, horse, Horse Racing, horses, information, multitude, normal distribution, post, probability theory, profit, racing, rating, ratings, selections, speed, speed rating, speed ratings, square root, squared numbers, staking, standard deviation, surfaces, system, type, value, variability, volatility, Week, win
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