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Variance is part of the game

When reading articles about sports betting, you often come across the term ‘variance’. Below we will explain what variance means and why it matters when we’re talking about sports betting.

Understanding variance

The variance measures how far a set of random numbers are spread out from their average. The following example will make this clear.

Suppose you have to choose between two investment options with the following profits, together with the probability of their outcomes:

Option I Option II
Probability Profits Probability Profits
25% 0 25% 99
50% 100 50% 100
25% 200 25% 101

First, you can easily calculate the expected value (EV) of each option. EV is a measure of what you can expect to win or lose per bet in the long run. In our example, both options have an expected value of 100, as the following calculations show:

EV of option I =  (0,25 * 0) + (0,50 * 100) + (0,25 * 200) = 100

EV of option II =  (0,25 * 99) + (0,50 * 100) + (0,25 * 101) = 100

So, up till now, it looks like both options are equally attractive, as they have the same EV.

However, when the variance of each option is taken into account, it becomes a different story. As said earlier, variance measures how far a set of random numbers (in our case: the profits) are spread out from their average. Both options have the same mean profit, as the following calculations show:

Mean profit of option I = (0 + 100 + 200) / 3 = 100.

Mean profit of option II = (99 + 100 + 101) / 3 = 100.

Even if you’re not that much into math, you will see that the profits of option I are much more spread from the mean than the profits of option II. Put in other words: option I’s profits 0 and 200 ‘lie far more away’ from 100 than option II’s profits 99 and 101.

Mathematicians say that the variance is much larger for option I, making it a far riskier option. The lesson is: variance = risk. As a sports bettor, you want to reduce your risk as much as possible. And a low risk means a low variance, as you now will understand.

In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean. Mathematicians use the following formula below; if we apply this formula to our example, option I’s variance is equal to 10000 and option II’s is equal to 1.

Variance formula

Why does variance matter?

Over a small number of bets, variance will have a dominating impact on your results. Over a large volume of bets (so, in the long run), variance will even out, giving way to your skills more and more as the determining factor for good results.

So, to become a profitable bettor in the long run, one has to deal with the variance in the short term. You should be aware of the fact that ‘outliers’ can have a huge impact on your results in the short term.

It is not always easy to deal with this. Moreover, it’s one of the most common reasons why beginning sports bettors tend to drop out. You could lose your confidence in the methods you are using, due to bad results. On the other hand, you can become too eager when you have achieved some good results.

So, pay attention to a well thought out bankroll management and a rational and statistical based betting strategy. Variance will even out in the long run; bettors who have a margin will be the ones being able to make profit.

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