Variance and Standard Deviation

Understanding Variance in Sports Betting

Variance is a term that every sports bettor will experience, whether they know what it is or not. In simple terms, variance is the unpredictability of results in the short term. It is the statistical measure of the spread between numbers in a data set. In sports betting, it is the swings in your bankroll, both positive and negative. It is the reason why you can do everything right and still lose, and do everything wrong and still win.

Even if you have a positive expected value (+EV) betting strategy, you are not guaranteed to win every bet. In fact, you will likely lose a significant number of your bets. Variance is what causes these winning and losing streaks. A high variance means that your results will be more spread out from the average, with higher peaks and lower valleys. A low variance means that your results will be more consistent and closer to your expected outcome.

Standard Deviation: A Measure of Variance

Standard deviation is a statistical measure that quantifies the amount of variation or dispersion of a set of data values. A low standard deviation indicates that the data points tend to be close to the mean (also called the expected value), while a high standard deviation indicates that the data points are spread out over a wider range of values.

In sports betting, standard deviation can be used to measure the risk associated with a particular betting strategy. A strategy with a high standard deviation will have a wider range of possible outcomes, with the potential for both large wins and large losses. A strategy with a low standard deviation will have a more predictable range of outcomes.

How to Calculate Standard Deviation

While you can use online calculators to determine standard deviation, understanding how it is calculated can help you better understand the concept.

1. Calculate the mean (average) of your data set. For example, let's say you are tracking the number of goals a team scores per game. You would add up all the goals and divide by the number of games.
2. For each data point, subtract the mean and square the result. This is the variance for that data point.
3. Calculate the average of all the variances. This is the overall variance of the data set.
4. Take the square root of the variance. This is the standard deviation.

Example:

A team scores the following goals in 5 games: 2, 3, 1, 4, 0

1. Mean: (2 + 3 + 1 + 4 + 0) / 5 = 2 goals per game
2. Variances:
   • (2 - 2)^2 = 0
   • (3 - 2)^2 = 1
   • (1 - 2)^2 = 1
   • (4 - 2)^2 = 4
   • (0 - 2)^2 = 4
3. Overall Variance: (0 + 1 + 1 + 4 + 4) / 5 = 2
4. Standard Deviation: √2 ≈ 1.41

This means that the team's goal scoring is, on average, 1.41 goals away from their mean of 2 goals per game.

Practical Applications in Sports Betting

Understanding variance and standard deviation can help you in several ways:

• Bankroll Management: Knowing the variance of your betting strategy can help you determine the appropriate bankroll size. A high-variance strategy will require a larger bankroll to withstand the inevitable downswings.
• Assessing Risk: Standard deviation can be used to assess the risk of a particular bet. Bets on longshots will have a higher variance and standard deviation than bets on favorites.
• Evaluating Performance: By tracking your results and calculating the standard deviation, you can get a better understanding of your performance. If your results are consistently falling outside of the expected range, it may be an indication that your strategy is flawed.

The Normal Distribution and the Bell Curve

The normal distribution, also known as the bell curve, is a probability distribution that is symmetric about the mean. In a normal distribution, the majority of the data points are clustered around the mean, with fewer data points further away.

• Approximately 68% of the data falls within one standard deviation of the mean.
• Approximately 95% of the data falls within two standard deviations of the mean.
• Approximately 99.7% of the data falls within three standard deviations of the mean.

By creating a normal distribution curve for a particular statistic, such as goals scored or points per game, you can get a visual representation of the probability of different outcomes.

Conclusion

Variance and standard deviation are important concepts for any serious sports bettor to understand. While you can't eliminate variance, you can manage it by having a solid bankroll management plan and by understanding the risk associated with your bets. By using standard deviation to quantify this risk, you can make more informed betting decisions and give yourself the best possible chance of long-term success.