Regression to the Mean

Often confused with the law of averages is the theory of regression to the mean. Regression to the mean suggests that if a player (gambler or team) performs significantly better or worse than normally expected, he will return to the average expectation of that player (regress back to the mean). Tthe definition above can be misinterpreted easily.

It does not suggest that if a team is doing really well that the opposition should be backed because it is bound to return to average. This is the most common misunderstanding of the theory of regression to the mean. Even in the stockmarket, shares could drop from $10.00 to $2.50, and stockbrokers may believe, that because of the theory of regression to the mean, they will purchase the stock with the expectation that it will return to $10.00. This is entirely wrong because we do not know and cannot know the normal expectation of a team or a player, or the price of a share. However, the theory of regression to the mean does have some principles in gambling, and I will show you how to use it to correct any bankroll management errors you might have, as well as learning to think somewhat differently from the general public (which is what it takes to win long-term).

Many people like to talk about streaks in gambling. A punter makes an error when deciding to increase the bet size, as he believes he is on a role. Likewise, other punters might 'jump on board' and follow the betting of these winning punters, because they are on a winning streak. However, we find that those winning punters inevitably will lose a few bets. Then, people will jump off the band wagon and onto another. The person betting will have lost more than he won, because he increased his bet size, despite the fact that he probably won more bets than he lost.

If you want to be really successful in gambling, you have to look at the long term. Anyone can get lucky in the short-term. It is winning in the long-term that counts. Stock market and property investors look at long term gains, so why shouldn't we when gambling? Any reasonable series of bets will have sequences of winning and losing runs.

Note that regression to the mean doesn't suggest that after a winning run you are due for a losing run. Rather, the regression to the mean theory looks at the long term regression to the mean.

Suppose a gambler has been betting for three years, and in each year, he has gained around 3% profit on his investment. In his fourth year, he is doing nothing different and betting the same way as previously, but instead, he made a 6% profit on his investment. This is a very large profit and no doubt he will be quite excited about such results. However, if we were to assume that his average yearly profit is 3%, then there is a good chance he just got lucky that year with a 6% profit, and perhaps in the future, we will see him returning 0% (no profit or loss), so as to average 3% overall. If, in his fifth year of gambling, he were to record a 2% loss, then there is a good chance that he will continue betting the way he is betting because he knows about the regression to the mean theory and he knows that in some years (or weeks/months) he will return better results than others but in the end, it will all turn out to be approximately his average.

However, we do not really know this average figure. We hypothesised above, that it was 3%, but it could be, in fact, 6%, and therefore, he was unlucky the first 3 years.

This theory can benefit the punter because there will always be times when it seems as though we can do no right and conversely, there will be times when it will seem that we can do no wrong! Just as long as the long-term average (whatever that might be) is positive, then this method will lead to being a successful professional punter. Never throw in the towel on bad running streaks and never increase the ante on winning streaks. If you know, that in the long term, your bets will be profitable, then be consistent in your betting and your bank balance will reflect your dependable methods of gambling.

Matt Elliott

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