Understanding (and embracing) variance and regression to the mean

If a cricketer averages 50 with the bat over a long period but then has a season averaging 100, for the remainder of his career do you think is he more likely to average closer to 50 or 100?

The answer is 50 and you can call that cricketer Michael Clarke if you like. With a career average of around 50, he was Bradman-esque in 2012 when he averaged 106. But the year before he averaged 39 and this year it’s 46.

Mathematicians call this concept “regression to the mean” and it is absolutely relevant to all punters.

Short-term results can be deceiving either way, because there is such a thing as positive variance too. Following a month of winning every Saturday you might think that you have suddenly fine-tuned your form analysis skills to the point where you will continue to win very consistently.

However the most likely scenario is that you have merely enjoyed a lucky run and over a longer timeframe your winning (or loss) rate will revert back to its historical average. Regression to the mean results in short term under or over-performance being corrected over a longer period.

In layman’s terms you could say that variance is simply the ups and downs of gambling. Streaks are a natural and unavoidable occurrence which means you can be doing everything right as a punter, yet still be losing in the short-term. But as the sample size increases, variance decreases.

All professional punters have a very good grasp of variance because you can’t avoid it, which means it is absolutely essential that you understand it.

However the vast majority of punters either disregard variance or believe that somehow it doesn’t apply to them. That approach is (to put it bluntly) simply suicidal. The reason being is that whilst you can ignore variance, it certainly will not ignore you.

We all expect to win over a longer timeframe, but in the short term anything can happen. For example if we flip a coin 5 times and witnessed 4 heads we wouldn’t be completely surprised by an 80% win rate.

But if we flip the coin 5000 times it is highly likely that heads and tails will come up very close to 50% each. It would be very unusual to see anything more than 1% variance.

Back to horse racing and a real life example. For the last racing season, backing the Starting Price favourite in every race resulted in a loss on turnover of 4% based on best tote prices. But in the month of May punters actually won 3% backing all 1160 favourites. That is a substantial positive performance compared to the historical average.

It is very interesting to note that in June, immediately following the significant over-performance in May, favourites lost a massive 9% on turnover.

A similar thing occurred in two other months. January’s +1% was immediately followed by February’s -9%. And despite a 33% winning strike-rate overall for the year, there was one losing sequence of 21 straight.

Now let’s look at the 6th ranked horse in terms of SP.

Overall these horses lost 12% on turnover for the year, but for the month of October they won 5%. Hopefully you are not surprised to learn that in the following month (November ) they lost a massive 21% on turnover.

It’s important to know that the lower the win percentage, the greater the variance you will endure. In the SP6 above, the difference between the profitability of the best and worst month was 39%. Compare that to SP favourites where the difference was just 1/3 of that.

So if you are a longshot punter you need the mentality and betting bank that can cope with sustained losing runs.


Most punters bet too much and quit too early but you shouldn’t give up on a proven approach just because of a short-term losing run. Nor should you get overly excited by a short winning run.

Instead you have to be willing and able to accept variance by withstanding losing streaks and also not over-betting during a winning run. Stick with a solid money management plan (variance along with probability are the main reasons we have one in the first place) and always focus on the bigger picture.

Understanding the concept of regression to the mean and the inevitability of variance are crucial steps in progressing from a losing punter to a winning one.

Good punting
David Duffield