Regression to the Mean

Worth looking into probability theory more

Regression to the mean is easy to confuse with the gambler's fallacy.

Example: Roulette

If I spin 10 times and they all land on red, then I have just witnessed a very unlikely event. The probability of that happening is 1/2^10, or 1/1024.

Now, under the delusion of the gambler's fallacy, I would guess that in the next 10 throws, fewer than 5 would be red. I would guess this as a delusional gambler because I believe that the number of black results must eventually even out with the number of red results.

This can be summarized as "the mistaken belief that random sequences have a systematic tendency towards reversal, i.e. that streaks of similar outcomes are more likely to end than continue"

The regression to the mean would guess that in the next 10 throws, fewer than 10 would be red.

"The confusion can be resolved by considering that the concept of 'regression to the mean' really has nothing to do with the past. It's merely the tautological observation that at each iteration of an experiment we expect the average outcome. So if we previously had an above average outcome then we expect a worse result, or if we had a below average outcome we expect a better one. The key point is that the expectation itself does not depend on any previous history as it does in the gambler's fallacy."

(tautological: true in every possible interpretation, i.e. "The ball is all green, or the ball is not all green")

Resources

http://onlinestatbook.com/2/sampling_distributions/samp_dist_mean.html