Often misunderstood. It is better applied to stable means (toss of a coin, roll of a dice) rather than probability of winning football matches which is affected by which players play etc.
It simply states that if you have out/underperformed the mean in the short term, over time your short term mean will move back to the long term mean.
It does not say that the previous short terms sequence of events affects the next event
In City’s case: if we assume our (ahem) long-term mean wins is 6 out of 10 (or 0.6, ie close to this season), but short term mean is 6 out of 6, then although the chance of us winning the next game is unchanged (6/10), our average will move back to the mean:
Short term run: 6 games, 6 wins: Short team mean is 1
Next 10 games, 6 wins (ie no change to probability of winning any single game), total run is now 12 wins out of 16 games: Short term mean is now down to 0.73 ie it has reverted to mean despite no change in the probability of us winning any single game.
The belief that the short term run of events affects the probability of the next event is called Gambler’s Fallacy and has lost a lot of people a lot of money!!!
