Win money with standard deviations

Relying to firmly on averages when betting can be unwise, because averages can be sharply influenced by outliers that will skew our perception. An inherent problem with the average is its inability to show the dispersion within a set of numbers.

beattheoddsSeveral methods have been developed to measure dispersion, and one of them is standard deviation. In statistics, standard deviation (SD) is a measure that is used to quantify the amount of variation or dispersion of a set of data values. Standard deviation is represented by the Greek letter sigma: σ.

A standard deviation close to zero indicates that the data points tend to be very close to the mean (also known as the expected value) of the set. Conversely, a high standard deviation indicates that the data points are spread out over a wide range of values.

Mathematically speaking, the standard deviation of a data set is the square root of its variance. If you need something more robust, use average absolute deviation instead.

Standard deviation is commonly utilized to measure confidence in statistical conclusions. In this sense, it can be extremely useful for anyone trying to do sports betting predictions.

Average absolute deviation

The average absolute deviation of a data set is the average of the absolute deviations from a central point. The central point chosen is usually the mean, the median or the mode.

The average absolute deviation is a summary statistic of statistical dispersion.

Maximum absolute deviation

The maximum absolute deviation around an arbitrary point is the maximum of the absolute deviations of a sample from that point. It is important to understand that this is not a measure of central tendency and that it can not be less than half the range.

Poisson vs. normal distribution

moneyIt is common among punters to use a Poisson distribution model to predict the number of goals scored per team in a game of soccer. A problem with this is that the only input parameter used is the average.

Normal distribution (the bell or Gaussian distribution) differs from Poisson because it is a continuous distribution based on not one but two parameters: the average and the standard deviation.

Example

We want to bet on goal difference in soccer, which is the number of goals scored by the home team minus the number of goals scored by the away team. Draw = zero.

What we have in front of is as a base for our analysis is this data:

  • The largest home win was 7-0.
  • The largest away victory was 5-0.
  • The average goal difference for the matches of the season was 0.3789 (median & mode = 0).
  • The standard deviation was 1.9188.

We will now use two parameters – average and standard deviation – to create a standardized curve of normal distribution. We can see that approximately 68 percent of the distribution is found within one standard deviation away from the mean. We can also see that 95 percent of the distribution is found within two standard deviations away from the mean. What does this mean for you as a punter? Well, for starters, it shows that we can expect 68 percent of games to end up somewhere between approximately minus 1.5399 and plus 2.2977. (Of course, a minus 1.5399 goal difference isn’t possible in reality.)