The Truth About Variance

In this article, we will attempt to determine where the edge lies while observing net results based on the number of bets.

If only it were that simple. How often have you heard a tipster attribute a bad streak of results to "bad variance"? Conversely, how often do you hear someone downplay a winning streak by calling it "good variance"?

Even if you find a viable edge in a betting market, profits are not necessarily guaranteed in the short term. Many bettors think they can handle losing streaks and understand variance, but do we really grasp its full extent? I put this to the test by analyzing my own betting data on a particular strategy I have worked on.

Here are the basics of the example:

A bankroll of €5,000

20% Kelly staking where possible

A turnover of €496,000

Expected Value (EV) of €14,600 (the profit I should have according to my edge)

Return on Investment (ROI) of 2.94% based on EV

Actual profit of €22,500

Actual ROI of 4.54%

Average odds placed: 2.38

Average true closing odds: 2.34

The first thing you may notice is that my actual profit and ROI are higher than expected. In fact, looking at a long-term view of my profits compared to the closing line, I have been above it for most of this period. Have I been lucky? I would say yes, according to the graph below:

If luck has been on my side, then the question is: how likely is it that my results could be replicated if someone were using the same strategy as me? Before giving the answer, try to answer the following questions:

Using the same parameters and over the same number of bets mentioned above, what is the probability...

That someone else would make €22,500 in profit?

That someone else would perform worse and only make €15,000 in profit?

That someone else would perform better and make €35,000 in profit?

Of losing the entire €5,000 bankroll?

This was tested over 10,000 simulations, and here are the results:

Do these results surprise you? They certainly surprised me. There was less than a 13% chance that I would achieve the results I did. I knew I was lucky before doing this simulation, but I didn’t realize HOW lucky.

Fortunately, the simulation showed that it was virtually impossible for me to lose my entire bankroll using my strategy and implied edge. However, there was still a small probability of making an overall loss. Over approximately 10,000 bets, this is what one should expect, but many bettors lack the patience, bankroll management, or psychological discipline to let this play out over the long term.

The graph below does not represent a flying comet made of colored threads but rather a visualization of the simulations conducted. What you may notice is that some simulations show a net loss over the first few thousand bets, but all gradually become more profitable as the number of bets increases.

So, we have concluded that I have been quite lucky so far, but what might I expect for the next 10,000 bets? There is actually a 20.5% chance that I will make no further profit and that my bankroll will remain flat, but a 54% chance that I will make at least another €7,500. The probability of hitting €50,000 in profit within this time frame is slim (2.5%).

The final graphs I will show you represent simulations after 20,000 and 30,000 bets. What do you notice? What stands out to me is that there are fewer extreme outliers. You can tell because the lines are more closely grouped together, with a higher volume of bets.

Conclusion

Of course, this is just one example, and the data is not entirely precise, but it provides insight into how variance can be more extreme than we realize, even with a strategy involving relatively low average odds. This gives even more reason not to lose hope during a bad losing streak and not to get ahead of yourself during a winning streak.

If you would like to try it yourself, you can use the website sportsbettingcalcs.com to run your own simulations. You might discover some interesting results!