Variance and Risk

With a small sample of bets anything can happen in the result, but, over a large volume of bets the bettors’ bankroll will increase subject to bets being placed at +EV (positive edge) The difference between the peak and trough value of the investors account in investing is known as standard deviation and in betting it is known as variance



What Is Variance?

Variance, simply stated, is a measure of how far a set of values are spread out from one another. Low variance means the values are very tightly spread and high variance means that the values are very widely spread apart. Here are two examples of a set of values. The average for both Set A and Set B is 50. But, the variance of Set A is very low while the variance of Set B is very high.

SET A SET B
50 20
49 50
50 70
51 33
48 41
50 33
47 89
51 99
52 42
52 23


Variance and Risk (Continued)

What Kind of Variance Should We Expect in Sports Betting?

We would all prefer low variance, but, this isn't how it works. There will always be variance in sports betting. Variance can be high in the short term, but will reduce over the long term

It’s important to remember that the "law of large numbers" tells us, fewer bets will probably equal higher variance. It means that over the short run, sports betting has a higher probability of variance. It is not unusual for your bankroll to swing between -10% and -30% over a week. This is due to a low hit rate, but over the longer term the hit rate will even out and the bettors bankroll will increase in value

If we flip a coin 1,000 times we expect to experience a 7% variance in the results, which means 43% of the time the coin could land Heads and 57% of the time Tails, but if we flip a coin 5,000 times we expect to see heads 50% of the time and tails 50% of the time

Another way to think about this is to compare it to diversification in the stock market. If you buy every stock in the market, your yearly return should be relatively stable (excluding stack market crashes) But if you invest heavily in a few stocks in the stock market, your returns are likely to be much more variable

Risk

Sports betting with a +EV or edge is unlike other forms of wealth creation as it is mathematically certain to generate a profit. However, if the bettor cannot tolerate the inevitable levels of variance in their bankroll, they should only fund their bankroll with funds that are not required in the medium term (one year)