A primer: regression to the mean

Imagine you take a fair coin (one with equal chance of getting heads or tails) and flip it ten times. The average (mean) result would be to flip five heads (as the coin is fair) but you find that you actually only flip two. You then repeat the experiment and get four heads. The mean result of the two experiments is three heads per ten flips, closer to expected average of five than the original experiment. The more times the experiment is repeated the closer the average result gets to the expected mean. This is an effect known as regression towards the mean where the average result after an experiment is repeated is closer to the mean than it was previously. As usual wikipedia has an excellent explanation.

‘Regression’ typically only has negative connotations but in ‘regression to the mean’ it isn’t used in that context. It demonstrates how much an action is based on luck and the tendency of random events to ‘average out’ if they are continually repeated.

The magnitude of regression to the mean can be determined and attribute a definable amount of how much a result (or set of results) are driven by skill and how much it is down to luck. It’s important to point out that regression to the mean has no predictive value in terms of future performance, you are equally likely of flipping a head next time regardless of whether the last flip yielded a head or a tail.

There are two extremes: actions that are completely luck based, such as the coin flipping example above, and those that are entirely due to skill.

For an experiment such as flipping a coin, where the outcome of each flip is entirely luck based, the results will always regress completely to the mean (the average result) provided the experiment is repeated enough times. For an action that is entirely based on skill there would be the same result every time the action is repeated regardless of how far from the mean the initial result is.

Actions in football (shooting, passing, tackling etc) sit somewhere between these two extremes. I’ll be looking at how much of these actions are due to skill and what proportion is driven by luck to see how large the spread of skill is across the teams in the premiership.


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