Reversion to the Mean
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9-2-2021
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Reversion to the Mean
Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far. In other words, an extreme event is likely to be followed by a less extreme event.
Although this phenomenon appears to violate the definition of independent events, it simply reflects the fact that the probability density function 
of any random variable 
, by definition, is nonnegative over every interval and integrates to one over the interval 
. Thus, as you move away from the mean, the proportion of the distribution that lies closer to the mean than you do increases continuously. Formally,
for 
.
The Season 1 episode "Sniper Zero" (2005) of the television crime drama NUMB3RS mentions regression to the mean.
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