Feb 22, 2021
Feb 22, 2021

The truth about variance

Where is the edge?

Net results vs. number of trades

The truth about variance

So you’ve done the hard work and found a strategy that works. You feel pretty confident you have an edge over the market. Now you just have to put your bets down and the profits will follow, right?

If only it was that simple. How often have you heard a tipster put a bad run of results down to “bad variance”? Conversely, how often do you hear anyone downplay their winning streak to “good variance”?

Even if you find a viable edge on a betting market, profits aren’t necessarily guaranteed in the short term. A lot of bettors think they can handle bad runs and understand variance, but do we really understand the true extent of it? I put this to the test with a sample of my own betting data on a particular strategy I have worked on.

  • - A $5,000 bankroll
  • - 20% Kelly staking where possible
  • - $496,000 turnover
  • - $14,600 in closing Expected Value (how much profit I should have according to my edge)
  • - 2.94% Closing EV return on investment (ROI)
  • - $22,500 actual profit
  • - 4.54% actual ROI
  • - Average odds placed - 2.38
  • - Average true closing odds - 2.34

The first thing you might notice is that my actual profit and ROI is bigger than I would expect. In fact, if you look at a long-term view of my profit compared to the closing line, it’s been above it for most of this run. So have I been lucky? I would definitely say so according to the graph below:


If luck has been on my side in this run, then the question for you is how likely is it that my results could be replicated if someone was using the same strategy as me? Before I give you the answers, have a go at answering the following questions:

  1. - Using the same parameters and over the same number of trades as I mentioned above, what’s the probability…
  2. - That someone else would make $22,500 in profit?
  3. - That someone else would perform worse and only make $15,000 in profit?
  4. - That someone else would perform better and make $35,000 in profit?
  5. - Of losing the entire $5000 bankroll?

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


Did the results surprise you? They certainly surprised me. There was less than a 13% chance of me hitting the results I did. I knew I was lucky before doing this simulation but I didn’t realise HOW lucky.

Thankfully, 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 slim chance of making an overall loss. Over 10,000 or so trades, this is what you should expect to see, but many bettors do not have the patience, bank roll management or psychological discipline to let this play out.

The graphic below isn’t a flying comet made of coloured yarn, but a visualization of the simulations that were run. What you might notice is that some of the simulations do show a net loss over the first few thousand trades but all gradually become more profitable as more bets are logged.


So we’ve concluded that I’ve got rather lucky so far, but what might I expect for the next 10,000 bets I place? There is actually a 20.5% chance that I make no more profit and my bankroll remains flat, but a 54% chance that I make at least another $7,500. For me to hit $50,000 profit in that time frame is slim (2.5%).

The final graphs I will show you are the simulations after 20,000 and 30,000 trades. What do you notice? What strikes me is there are less outliers with extreme values. You can tell because the lines are more closely bunched together with a larger volume of bets.


Final thoughts 

Of course, this is just one example and the data is certainly not 100% accurate, but this gives an insight into how variance can be more extreme than we realise, even with a reasonably low average odds strategy. It gives even more reason to not give up hope on a bad losing run and not to get too ahead of yourself when you’ve hit a hot streak. 

If you’d like to try yourself, you can use the sportsbettingcalcs site to run your own simulations. You might find something interesting in the results!

Special thanks to @sipox11 for his work generating the initial simulations and inspiring this article. 

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